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DTSTART;TZID=America/New_York:20180924T175600
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DTSTAMP:20240213T102402Z
CREATED:20240213T102402Z
LAST-MODIFIED:20240213T102402Z
UID:10002417-1537811760-1537811760@live-hu-cmsa-222.pantheonsite.io
SUMMARY:9/24/2018 Topological Aspects of Condensed Matter Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/9-24-2018-topological-aspects-of-condensed-matter-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180910T103000
DTEND;TZID=America/New_York:20180910T120000
DTSTAMP:20240213T103024Z
CREATED:20240213T103024Z
LAST-MODIFIED:20240213T103024Z
UID:10002433-1536575400-1536580800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:9/10/18 Topology Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/9-10-18-topology-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180829T173600
DTEND;TZID=America/New_York:20180829T173600
DTSTAMP:20240213T102633Z
CREATED:20240213T102633Z
LAST-MODIFIED:20240213T102633Z
UID:10002424-1535564160-1535564160@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Topological Aspects of Condensed Matter Seminar
DESCRIPTION:As part of the Program on Topological Aspects of Condensed Matter\, a weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10. \n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n8/29/2018\nZeng-Cheng Gu\nTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory \nAbstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless\, the construction and classification of SPT phases in interacting fermion systems are much more complicated\, especially in 3D. In this talk\, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.\n\n\n9/10/2018\nDominic Else\, MIT \nVideo\nTitle: Phases and topology in periodically driven (Floquet) systems \nAbstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up\, I will review new topological invariants in free-fermion Floquet systems. Then\, I will discuss the richer physics that occurs in interacting Floquet phases\, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally\, time permitting\, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.\n\n\n9/17/2018\nAdrian Po\, MIT \nVideo\nTitle: A modern solution to the old problem of symmetries in band theory \nAbstract: There are 230 space groups and 1\,651 magnetic space groups in three dimensions. Thankfully\, these are finite numbers\, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory\, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk\, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product\, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues\, which offers great computational advantage compared to the traditional\, wave-function-based definitions of topological band invariants.\n\n\n9/24/2018\nMaxim Metlitski\nTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs \nAbstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless\, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases\, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore\, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.\n\n\n10/1/2018\nCancelled\n\n\n\n10/9/2018 \nTuesday \n3:00-4:30pm\nSagar Vijay\nTitle: Fracton Phases of Matter \nAbstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped\, point-like excitations (“fractons”) that are strictly immobile at zero temperature\, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions\, and these states of matter are a gateway for exploring mechanisms for quantum information storage\, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases\, constructions of these states using well-studied two-dimensional topological phases\, and a model in which the fracton excitations carry a protected internal degeneracy\, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.\n\n\n10/15/2018\nEthan Lake\nTitle: A primer on higher symmetries \nAbstract: The notion of a higher symmetry\, namely a symmetry whose charged objects have a dimension greater than zero\, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries\, higher symmetries can be gauged\, spontaneously broken\, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility\, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.\n\n\n10/22/2018 \nRoom G02\nYin-Chen He\, Perimeter\nTitle: Emergent QED3 and QCD3 in condensed matter system \nAbstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1)\, SU(N)\, U(N)\, etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome\, triangular lattice)\, quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.\n\n\n10/29/2018\nDominic Williamson\, Yale \nVideo\nTitle: Symmetry and topological order in tensor networks \nAbstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states\, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.\n\n\n11/13/2018 \nTuesday \n3:00-4:30pm\nJason Alicea\, Caltech\nTitle: Time-crystalline topological superconductors\n\n\n11/19/2018\nX. G. Wen\, MIT \nVideo\nTitle: A classification of 3+1D topological orders \nAbstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.\n\n\n12/3/2018 \n*Room G02*\nClaudio Chamon\, Boston University\nTitle: Many-body scar states with topological properties in 1D\, 2D\, and 3D. \nAbstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D\, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy\, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter\, including topological degeneracies.\n\n\n12/10/2018 \nRoom G02\nAnders Sandvik\, Boston University and Institute of Physics\, CAS\, Beijing\nTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets \nAbstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models\, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets\, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases\, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.\n\n\n1/8/2019\nLukasz Fidkowski\, Univ. of Washington \nVideo\nTitle: Non-trivial quantum cellular automata in 3 dimensions \nAbstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases\, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators\, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.\n\n\n3/18/2019\nAri Turner\, Technion \nVideo\nTitle:  Trapping Excitations at Phantasmagoric Wave Vectors \nAbstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization\, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this\, and also introduce “finite fields”\, which are the number systems one needs to define exponentials mod. 2.\n\n\n4/1/2019\nYi-Zhuang You (UCSD)\nTitle: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points \nAbstract: Noether’s theorem is one of the fundamental laws of physics\, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP)\, which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP\, which\, if true\, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum\, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current\, as signified by the vanishing anomalous dimension of the current operator\, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally\, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.\n\n\n4/8/2019\nAdam Nahum (Oxford)\nTitle: Emergent statistical mechanics of entanglement in random unitary circuits \nAbstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.\n\n\n4/16/2019 \nLyman 425 \n1:30pm\nXie Chen (Calthech)\nTitle: Foliated Fracton Order \nAbstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk\, I will present a new framework\, which we call the “foliated fracton order”\, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models\, but also points to the direction of search for interesting new features.\n\n\n4/24/2019 \n10:30am\nMichael Freedman (Microsoft Station Q) \nVideo\nTitle: Quantum cellular automata in higher dimensions \nAbstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.\n\n\n4/26/2019 \n10:30am\nMaissam Barkeshli (University of Maryland) \nVideo\nTitle: Relative anomalies in (2+1)D symmetry enriched topological states \nAbstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous\, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries\, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.\n\n\n5/3/2019\nYuan-Ming Lu (Ohio State)\nTitle: Spontaneous symmetry breaking from anyon condensation \nAbstract: In the context of quantum spin liquids\, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example\, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders\, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme\, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions\, and deconfined quantum criticality in one spatial dimension.\n\n\n5/9/2019 \n10:30am\nMichael Zaletel (UC Berkeley)\nTitle: Three-partite entanglement in CFTs and chiral topological orders \nAbstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement\, multi-partite entanglement is far richer\, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure\, the “entanglement of purification\,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly\, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders\, and solicit the audience’s help in proving or disproving it.\n\n\n5/28/2019 \n10:30am\nMasaki Oshikawa (U Tokyo)\nTitle: Gauge invariance\, polarization\, and conductivity \n  \nAbstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors\, and also to general constraints on the electric conductivity.\n\n\n7/18/2019\nEslam Khalaf (Harvard)\n\n\nTitle: Dynamical correlations in anomalous disordered wires \n\nAbstract: In a (multichannel) disordered wire\, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels\, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case\, the classical dynamics are described by diffusion + drift\, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.\n\nThe problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly\, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.\n\nThe mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former\, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter\, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end\, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/topological-aspects-of-condensed-matter-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180420T171800
DTEND;TZID=America/New_York:20180420T171800
DTSTAMP:20240213T101921Z
CREATED:20240213T101921Z
LAST-MODIFIED:20240213T101921Z
UID:10002412-1524244680-1524244680@live-hu-cmsa-222.pantheonsite.io
SUMMARY:4-20-2018 Social Science Applications Forum
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-20-2018-social-science-applications-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180417T120000
DTEND;TZID=America/New_York:20180417T133000
DTSTAMP:20240213T100938Z
CREATED:20240213T100552Z
LAST-MODIFIED:20240213T100938Z
UID:10002389-1523966400-1523971800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:4-17-2018 Special Algebraic Geometry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-17-2018-special-algebraic-geometry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180416T171600
DTEND;TZID=America/New_York:20180416T171600
DTSTAMP:20240213T101737Z
CREATED:20240213T101737Z
LAST-MODIFIED:20240213T101737Z
UID:10002409-1523898960-1523898960@live-hu-cmsa-222.pantheonsite.io
SUMMARY:4-16-2018 Social Science Applications Forum
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-16-2018-social-science-applications-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180413T163000
DTEND;TZID=America/New_York:20180413T173000
DTSTAMP:20240514T185400Z
CREATED:20240213T065558Z
LAST-MODIFIED:20240514T185400Z
UID:10002143-1523637000-1523640600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:On the fibration structure of known Calabi-Yau threefolds
DESCRIPTION:Speaker: Washington Tayor (MIT) \nTitle: On the fibration structure of known Calabi-Yau threefolds \nAbstract: In recent years\, there is increasing evidence from a variety of directions\, including the physics of F-theory and new generalized CICY constructions\, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results\, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered\, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-18-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/2018_04_13_11_01_32-e1523633302205.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180413T110000
DTEND;TZID=America/New_York:20180413T120000
DTSTAMP:20240213T101255Z
CREATED:20240213T101255Z
LAST-MODIFIED:20240213T101255Z
UID:10002403-1523617200-1523620800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:4-13-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-13-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180411T163000
DTEND;TZID=America/New_York:20180411T173000
DTSTAMP:20240515T144439Z
CREATED:20240213T065052Z
LAST-MODIFIED:20240515T144439Z
UID:10002134-1523464200-1523467800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Graph Structure in Polynomial Systems: Chordal Networks
DESCRIPTION:Speaker: Pablo Parillo (MIT) \nTitle: Graph Structure in Polynomial Systems: Chordal Networks \nAbstract: The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g.\, in solving the system). In this lecture we will provide a gentle introduction to this area\, focused on the key notions of chordality and treewidth\, which are of great importance in related areas such as numerical linear algebra\, database theory\, constraint satisfaction\, and graphical models. In particular\, we will discuss “chordal networks”\, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets\, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains\, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-11-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/2018_04_10_09_58_15-e1523369654177.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180404T163000
DTEND;TZID=America/New_York:20180404T163000
DTSTAMP:20240515T174223Z
CREATED:20240213T064751Z
LAST-MODIFIED:20240515T174223Z
UID:10002129-1522859400-1522859400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Black Holes and Naked Singularities
DESCRIPTION:Speaker: Ramesh Narayan\, Department of Astronomy\, Harvard University \nTitle: Black Holes and Naked Singularities \nAbstract: Black Hole solutions in General Relativity contain Event Horizons and Singularities. Astrophysicists have discovered two populations of black hole candidates in the Universe: stellar-mass objects with masses in the range 5 to 30 solar masses\, and supermassive objects with masses in the range million to several billion solar masses. There is considerable evidence that these objects have Event Horizons. It thus appears that astronomical black hole candidates are true Black Holes. Direct evidence for Singularities is much harder to obtain since\, at least in the case of Black Holes\, the Singularities are hidden inside the Event Horizon. However\, General Relativity also permits Naked Singularities which are visible to external observers. Toy Naked Singularity models have been constructed\, and some observational features of accretion flows in these spacetimes have been worked out.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-4-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-040418-e1522340269661.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180328T163000
DTEND;TZID=America/New_York:20180328T173000
DTSTAMP:20240515T174531Z
CREATED:20240213T064501Z
LAST-MODIFIED:20240515T174531Z
UID:10002125-1522254600-1522258200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:A Mean Field View of the Landscape of Two-Layers Neural Networks
DESCRIPTION:Speaker: Andrea Montanari (Stanford) \nTitle: A Mean Field View of the Landscape of Two-Layers Neural Networks \nAbstract: Multi-layer neural networks are among the most powerful models in machine learning and yet\, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function)\, a problem which is usually attacked using stochastic gradient descent (SGD). Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case\, does this happen because local minima are absent\, or because SGD somehow avoids them? In the second\, why do local minima reached by SGD have good generalization properties? We consider a simple case\, namely two-layers neural networks\, and prove that –in a suitable scaling limit– the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples\, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to ‘average-out’ some of the complexities of the landscape of neural networks\, and can be used to capture some important variants of SGD as well. [Based on joint work with Song Mei and Phan-Minh Nguyen]
URL:https://live-hu-cmsa-222.pantheonsite.io/event/3-28-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-032818-e1521831836462-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180315T150000
DTEND;TZID=America/New_York:20180315T160000
DTSTAMP:20240213T100209Z
CREATED:20240213T100139Z
LAST-MODIFIED:20240213T100209Z
UID:10002381-1521126000-1521129600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Dmytro Shklyrov HMS Focused Lecture Series
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/dmytro-shklyrov-hms-focused-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180307T163000
DTEND;TZID=America/New_York:20180307T173000
DTSTAMP:20240515T175119Z
CREATED:20240213T063843Z
LAST-MODIFIED:20240515T175119Z
UID:10002121-1520440200-1520443800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Harmonic functions and the chromatic polynomial
DESCRIPTION:Speaker: Richard Kenyon\, Brown \nTitle: Harmonic functions and the chromatic polynomial
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-7-2018-colloquium/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-030718-e1520356183643.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180302T110000
DTEND;TZID=America/New_York:20180302T120000
DTSTAMP:20240213T095700Z
CREATED:20240213T095700Z
LAST-MODIFIED:20240213T095700Z
UID:10002372-1519988400-1519992000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:3-2-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/3-2-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180227T150000
DTEND;TZID=America/New_York:20180227T160000
DTSTAMP:20240213T100343Z
CREATED:20240213T100343Z
LAST-MODIFIED:20240213T100343Z
UID:10002386-1519743600-1519747200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2-27-2018 HMS Lecture
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-27-2018-hms-lecture/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180226T163000
DTEND;TZID=America/New_York:20180226T173000
DTSTAMP:20240515T175404Z
CREATED:20240213T063608Z
LAST-MODIFIED:20240515T175404Z
UID:10002119-1519662600-1519666200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Computer-assisted analysis of singularity formation of a regularized 3D Euler equation
DESCRIPTION:Speaker: Tom Hou\, Caltech \nTitle: Computer-assisted analysis of singularity formation of a regularized 3D Euler equation \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-26-2018-colloquium/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-022618-e1519319166314.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180223T100000
DTEND;TZID=America/New_York:20180223T110000
DTSTAMP:20240213T100016Z
CREATED:20240213T100016Z
LAST-MODIFIED:20240213T100016Z
UID:10002377-1519380000-1519383600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2-23-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-23-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180221T163000
DTEND;TZID=America/New_York:20180221T173000
DTSTAMP:20240515T175648Z
CREATED:20240213T063335Z
LAST-MODIFIED:20240515T175648Z
UID:10002115-1519230600-1519234200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Essential concepts of Causal inference—a remarkable history
DESCRIPTION:Speaker: Don Rubin (Harvard Statistics) \nTitle: Essential concepts of Causal inference—a remarkable history \nAbstract: I believe that a deep understanding of cause and effect\, and how to estimate causal effects from data\, complete with the associated mathematical notation and expressions\, only evolved in the twentieth century.  The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing.  The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics.  The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s\, when such experiments began to be used in controlled medical trials\, and then in social science — in education and economics.  Humans are more complex than plants and animals\, however\, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of “hawthorne” and placebo effects.  The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people\, started in the 1970s and continue to this day\, and include the bridging of classical mathematical ideas of experimentation\, including fractional replication and geometrical formulations from the early twentieth century\, with modern ideas that rely on powerful computing to implement aspects of design and analysis. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-21-2018-colloquium/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-022118-e1518810758992.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180216T110000
DTEND;TZID=America/New_York:20180216T110000
DTSTAMP:20240213T101018Z
CREATED:20240213T101018Z
LAST-MODIFIED:20240213T101018Z
UID:10002397-1518778800-1518778800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2-16-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-16-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180214T163000
DTEND;TZID=America/New_York:20180214T173000
DTSTAMP:20240515T180124Z
CREATED:20240213T063118Z
LAST-MODIFIED:20240515T180124Z
UID:10002113-1518625800-1518629400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:A new program on quantum subgroups
DESCRIPTION:Speaker: Zhengwei Liu (Harvard Physics) \nTitle: A new program on quantum subgroups \nAbstract: Quantum subgroups have been studied since the 1980s. The A\, D\, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence\, we introduce a new program that our group at Harvard is developing. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/02-14-2018-colloqium/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-021418-e1518126484875.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180209T110000
DTEND;TZID=America/New_York:20180209T110000
DTSTAMP:20240213T102158Z
CREATED:20240213T102158Z
LAST-MODIFIED:20240213T102158Z
UID:10002416-1518174000-1518174000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:02-09-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/02-09-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180208T170000
DTEND;TZID=America/New_York:20180208T180000
DTSTAMP:20240515T181311Z
CREATED:20240213T062806Z
LAST-MODIFIED:20240515T181311Z
UID:10002110-1518109200-1518112800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Sequences: random\, structured or something in between
DESCRIPTION:Speaker: Fan Chung (University of California\, San Diego) \nTitle: Sequences: random\, structured or something in between \nAbstract: There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns; testing or validating various ‘random-like’ behavior; analyzing or comparing different statistics\, etc. In this talk\, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/02-08-2018-colloquium/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-020818-e1518025233926.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180202T144400
DTEND;TZID=America/New_York:20180202T144400
DTSTAMP:20240213T102555Z
CREATED:20240213T102555Z
LAST-MODIFIED:20240213T102555Z
UID:10002423-1517582640-1517582640@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2-2-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-2-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180126T143700
DTEND;TZID=America/New_York:20180126T143700
DTSTAMP:20240213T102934Z
CREATED:20240213T102934Z
LAST-MODIFIED:20240213T102934Z
UID:10002431-1516977420-1516977420@live-hu-cmsa-222.pantheonsite.io
SUMMARY:01-26-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/01-26-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180125T142100
DTEND;TZID=America/New_York:20180125T142100
DTSTAMP:20240213T103415Z
CREATED:20240213T103415Z
LAST-MODIFIED:20240213T103415Z
UID:10002441-1516890060-1516890060@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Quantum Cohomology\, Nakajima Varieties and Quantum groups
DESCRIPTION:During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology\, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th\, from 1:00 to 3:00pm in room G10\, CMSA Building. \nYou can watch Prof. Sheshmani describe the series here. \nThe Syllabus is as follows: \n\n\n\nDate………..\nTopic\nVideo/Audio\n\n\n1-25-2018\nGromov-Witten invariants  \nDefinition\, examples via algebraic geometry I\nVideo / Audio / Combined  \n\n*due to technical difficulties the audio and video are split for this lecture.\n\n\n 2-01-2018\nGromov-Witten invariants  \nVirtual Fundamental Class I (definition)\nVideo / Audio / Combined  \n\n*due to technical difficulties the audio and video are split for this lecture\n\n\n2-13-2018\nGromov-Witten invariants  \nVirtual Fundamental Class II (computation in some cases)\n\n\n\n 2-15-2018\nComputing GW invariants  \nThree level GW classes \nGenus zero invariants of the projective plane\n\n\n\n 2-20-2018\nQuantum Cohomology  \nSmall Quantum Cohomology (Definition and Properties) I\n\n\n\n2-22-2018\nQuantum Cohomology  \nSmall Quantum Cohomology (Definition and Properties) II\n\n\n\n2-27-2018\nQuantum Cohomology  \nBig Quantum Cohomology I\n\n\n\n 3-1-2018\nQuantum Cohomology  \nBig Quantum Cohomology II \nGW potential \nWDVV equation\n\n\n\n3-6-2018\nGW invariants via Quantum Cohomology  \nThe Quintic threefold case \nThe P^2 case\n\n\n\n\nGW invariants via Quantum Cohomology  \nDubrovin (quantum) connection\n\n\n\n\nNakajima varieties  \n-Algebraic and symplectic reduction\n\n\n\n\nNakajima varieties  \nQuasi maps to Nakajima varieties\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nSmall Quantum Cohomology of Hilb^n (C2) I\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nSmall Quantum Cohomology of Hilb^n (C2) II\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nSmall Quantum Cohomology of Hilb^n (C2) III\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) I\n \n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) II\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) III\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) IV\n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/quantum-cohomology-nakajima-varieties-and-quantum-groups/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180123T170000
DTEND;TZID=America/New_York:20180123T170000
DTSTAMP:20240213T103131Z
CREATED:20240213T103131Z
LAST-MODIFIED:20240213T103131Z
UID:10002436-1516726800-1516726800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2018 HMS Focused Lecture Series
DESCRIPTION:As part of their CMSA visitation\, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building\, 20 Garden Street\, Room G10. \nThe schedule will be updated below. \n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\nJanuary 23\, 25\, 30 and February 1  \n3-5pm \n*Room G10*\nIvan Losev  \n(Northeastern)\nTitle: BGG category O: towards symplectic duality  \nAbstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson\, Ginzburg and Soergel on the Koszul duality for such categories\, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting. \nApproximate (optimistic) plan of the lectures: \n1) Preliminaries and BGG category O. \n2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem. \n3) Localization theorem continued. Soergel modules. \n4) Koszul algebras and Koszul duality for categories O. \nTime permitting: other instances of Symplectic duality. \nPrerequisites: \nSemi-simple Lie algebras and their finite dimensional representation theory. \nSome  Algebraic geometry. No prior knowledge of category O/ Geometric \nRepresentation theory is assumed. \nScanned from a Xerox Multifunction Device\n\n\nFebruary 27\,  \nand March 1 \n3-5pm\nColin Diemer  \n(IHES)\nTitle: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS.  \nAbstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit\, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov\, Kontsevich\, Pantev)\, the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting\, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting\, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).\n\n\nMarch 6 and 8  \n4-5pm\nAdam Jacob  \n(UC Davis)\nTitle: The deformed Hermitian-Yang-Mills equation  \nAbstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation\, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry\, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions\, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible\, and cover joint work with T.C. Collins and S.-T. Yau.\n\n\nMarch 6\, 8\, 13\, 15  \n3-4pm\nDmytro Shklyarov  \n(TU Chemnitz)\nTitle: On categories of matrix factorizations and their homological invariants  \nAbstract: The talks will cover the following topics: \n1. Matrix factorizations as D-branes. According to physicists\, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements. \n2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds\, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models. \n3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data\, namely\, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type\, open varieties\, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which\, just as their non-equivariant cousins\, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.\n\n\nApril 10 & 12  \n3-4pm\nMauricio Romo  \n(IAS)\nTitle: Gauged Linear Sigma Models\, Supersymmetric Localization and Applications  \nAbstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs\, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds\, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk\, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms\, anomalous GLSMs). \nLecture notes\n\n\nApril 17\, 19\, 26  \n3-5pm\nAndrew  Harder  \n(University of Miami)\nTitle: Perverse sheaves of categories on surfaces  \nAbstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S\, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc. \nI’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry\, symplectic geometry\, and category theory. Finally\, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space. \n \n \n \n\n\nMay 15\, 17  \n1-3pm\nCharles Doran  \n(University of Alberta)\n\n\n\n\n\n\nLecture One:\nTitle: Picard-Fuchs uniformization and Calabi-Yau geometry\nAbstract:\n\n\n\n\n\n\nPart 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties\, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces\, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application\, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.\n\nPart 2:  We next consider families with one natural complex structure modulus\, (e.g.\, elliptic curves\, rank 19 K3 surfaces\, b_1=4 Calabi-Yau threefolds\, …)\, where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology\, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular\, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.\n\n\n  \n\nLecture Two:\nTitle: Calabi-Yau fibrations: construction and classification\nAbstract: \nPart 1:  Codimension one Calabi-Yau submanifolds induce fibrations\, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals. \nPart 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold\, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2018-hms-focused-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180113T152500
DTEND;TZID=America/New_York:20180113T152500
DTSTAMP:20240213T062547Z
CREATED:20240213T062547Z
LAST-MODIFIED:20240213T062547Z
UID:10002108-1515857100-1515857100@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2020-2021 Colloquium\, Wednesdays
DESCRIPTION:During the Spring 2021 semester\, and until further notice\, all seminars will take place virtually.\nThe 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually\, using zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed. \nTo learn how to attend\, please fill out this form. \nInformation on previous colloquia can be found here.\n \nSpring 2021:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n1/27/2021\nEvelyn Tang (Max Planck Institute for Dynamics and Self-Organization) \nSlides\n\nVideo\nTitle: Topology protects chiral edge currents in stochastic systems \nAbstract: Living systems can exhibit time-scales much longer than those of the underlying components\, as well as collective dynamical behavior. How such global behavior is subserved by stochastic constituents remains unclear. I will present two-dimensional stochastic networks that consist of out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. I will discuss the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity. As these emergent edge currents are associated to macroscopic timescales and length scales\, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock\, stochastic growth and shrinkage\, and synchronization.\n\n\n2/3/2021\nAndré Luiz de Gouvêa (Northwestern) \nVideo\nTitle: The Brave Nu World \nAbstract: Neutrinos are the least understood of the fundamental particles that make up the so-called Standard Model of Particle Physics. Measuring neutrino properties and identifying how they inform our understanding of nature at the smallest distant scales is among the highest priorities of particle physics research today. I will discuss our current understanding of neutrinos\, concentrating on the observation of neutrino oscillations and neutrino masses\, along with all the open questions that came of these discoveries from the end of the 20th century.\n\n\n2/10/2021\nMykhaylo Shkolnikov (Princeton) \nVideo\nTitle: Probabilistic approach to free boundary problems and applications \nAbstract: We will discuss a recently developed probabilistic approach to (singular) free boundary problems\, such as the supercooled Stefan problem. The approach is based on a new notion of solution\, referred to as probabilistic\, which arises naturally in the context of large system limits of interacting particle systems. In the talk\, I will give an example of how such interacting particle systems arise in applications (e.g.\, finance)\, then obtain a solution of a free boundary problem in the large system limit\, and discuss how this solution can be analyzed mathematically (thereby answering natural questions about the systemic risk in financial systems and neural synchronization in the brain). The talk is based on recent and ongoing joint works with Sergey Nadtochiy\, Francois Delarue\, Jiacheng Zhang and Xiling Zhang\n\n\n2/17/2021\n9:00 – 10:00PM ET\nC. Seshadhri (UC Santa Cruz) \nVideo\nTitle: Studying the (in)effectiveness of low dimensional graph embeddings \nAbstract: Low dimensional graph embeddings are a fundamental and popular tool used for machine learning on graphs. Given a graph\, the basic idea is to produce a low-dimensional vector for each vertex\, such that “similarity” in geometric space corresponds to “proximity” in the graph. These vectors can then be used as features in a plethora of machine learning tasks\, such as link prediction\, community labeling\, recommendations\, etc. Despite many results emerging in this area over the past few years\, there is less study on the core premise of these embeddings. Can such low-dimensional embeddings effectively capture the structure of real-world (such as social) networks? Contrary to common wisdom\, we mathematically prove and empirically demonstrate that popular low-dimensional graph embeddings do not capture salient properties of real-world networks. We mathematically prove that common low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients\, which have been widely established to be empirically true for real-world networks. Empirically\, we observe that the embeddings generated by popular methods fail to recreate the triangle structure of real-world networks\, and do not perform well on certain community labeling tasks. (Joint work with Ashish Goel\, Caleb Levy\, Aneesh Sharma\, and Andrew Stolman.)\n\n\n2/24/2021\nDavid Ben-Zvi (U Texas) \nVideo\nTitle: Electric-Magnetic Duality for Periods and L-functions \nAbstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh\, in which ideas originating in quantum field theory are applied to a problem in number theory.\nA fundamental aspect of the Langlands correspondence — the relative Langlands program — studies the representation of L-functions of Galois representations as integrals of automorphic forms. However\, the data that naturally index the period integrals (spherical varieties for G) and the L-functions (representations of the dual group G^) don’t seem to line up.\nWe present an approach to this problem via the Kapustin-Witten interpretation of the [geometric] Langlands correspondence as electric-magnetic duality for 4-dimensional supersymmetric Yang-Mills theory. Namely\, we rewrite the relative Langlands program as duality in the presence of supersymmetric boundary conditions. As a result the partial correspondence between periods and L-functions is embedded in a natural duality between Hamiltonian actions of the dual groups.\n\n\n3/3/2021 \n9:00pm ET\nOmer Tamuz (Caltech)\nTitle: Monotone Additive Statistics \nAbstract: How should a random quantity be summarized by a single number? We study mappings from random variables to real numbers\, focussing on those with the following two properties: (1) monotonicity with respect to first-order stochastic dominance\, and (2) additivity for sums of independent random variables. This problem turns out to be connected to the following question: Under what conditions on the random variables X and Y does there exist an independent Z so that X + Z first-order stochastically dominates Y + Z? \n(Joint work with Tobias Fritz\, Xiaosheng Mu\, Luciano Pomatto and Philipp Strack.)\n\n\n3/10/2021 \n9:00pm ET\nPiotr Indyk (MIT)\nTitle: Learning-Based Sampling and Streaming \nAbstract: Classical algorithms typically provide “one size fits all” performance\, and do not leverage properties or patterns in their inputs. A recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. In this talk I will present two examples of this type\, in the context of streaming and sampling algorithms. In particular\, I will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (ICLR’19)\, and (b) sampling algorithms for estimating the support size of a distribution (ICLR’21). Both algorithms use an ML-based predictor that\, given a data item\, estimates the number of times the item occurs in the input data set. (The talk will cover material from papers co-authored with T Eden\, CY Hsu\, D Katabi\, S Narayanan\, R Rubinfeld\, S Silwal\, T Wagner and A Vakilian.\n\n\n3/17/2021\n9:00pm ET\nChiu-Chu Melissa Liu (Columbia)\nTitle: Topological Recursion and Crepant Transformation Conjecture \nAbstract: The Crepant Transformation Conjecture (CTC)\, first proposed by Yongbin Ruan and later refined/generalized by others\, relates Gromov-Witten (GW) invariants of K-equivalent smooth varieties or smooth Deligne-Mumford stacks. We will outline a proof of all-genus open and closed CTC for symplectic toric Calabi-Yau 3-orbifolds based on joint work with Bohan Fang\, Song Yu\, and Zhengyu Zong. Our proof relies on the Remodeling Conjecture (proposed by Bouchard-Klemm-Marino-Pasquetti and proved in full generality by Fang\, Zong and the speaker) relating open and closed GW invariants of a symplectic toric Calabi-Yau 3-orbifold to invariants of its mirror curve defined by Chekhov-Eynard-Orantin Topological Recursion.\n\n\n3/24/2021\nWeinan E (Princeton) \nVideo\nTitle: Machine Learning and PDEs \nAbstract: I will discuss two topics:\n(1) Machine learning-based algorithms and “regularity” theory for very high dimensional PDEs;\n(2) Formulating machine learning as PDE (more precisely\, integral-differental equation) problems.\n\n\n3/31/2021\nThore Graepel (DeepMind/UCL) \nVideo\nTitle: From AlphaGo to MuZero – Mastering Atari\, Go\, Chess and Shogi by Planning with a Learned Model \nAbstract: Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains\, such as chess and Go\, where a perfect simulator is available. However\, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which\, by combining a tree-based search with a learned model\, achieves superhuman performance in a range of challenging and visually complex domains\, without any knowledge of their underlying dynamics. MuZero learns a model that\, when applied iteratively\, predicts the quantities most directly relevant to planning: the reward\, the action-selection policy\, and the value function. When evaluated on 57 different Atari games – the canonical video game environment for testing AI techniques\, in which model-based planning approaches have historically struggled – our new algorithm achieved a new state of the art. When evaluated on Go\, chess and shogi\, without any knowledge of the game rules\, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.\n\n\n4/7/2021\nKui Ren (Columbia)\nTitle: Inversion via Optimization: Revisiting the Classical Least-Squares Formulation of Inverse Problems \nAbstract: The classical least-squares formulation of inverse problems has provided a successful framework for the computational solutions of those problems. In recent years\, modifications and alternatives have been proposed to overcome some of the disadvantages of this classical formulation in dealing with new applications. This talk intends to provide an (likely biased) overview of the recent development in constructing new least-squares formulations for model and data-driven solutions of inverse problems.\n\n\n4/14/2021\nSiu-Cheong Lau (Boston U)\nTitle: An algebro-geometric formulation of computing machines \nAbstract: Neural network in machine learning has obvious similarity with quiver representation theory.  The main gap between the two subjects is that network functions produced from two isomorphic quiver representations are not equal\, due to the presence of non-linear activation functions which are not equivariant under the automorphism group.  This violates the important math/physics principle that isomorphic objects should produce the same results.  In this talk\, I will introduce a general formulation using moduli spaces of framed modules of (noncommutative) algebra and fix this gap.  Metrics over the moduli space are crucial.  I will also explain uniformization between spherical\, Euclidean and hyperbolic moduli.\n\n\n4/21/2021\nVasco Carvalho (Cambridge)\nTitle: The Economy as a Complex Production Network\nAbstract: A modern economy is an intricately linked web of specialized production units\, each relying on the flow of inputs from their suppliers to produce their own output\, which in turn is routed towards other downstream units. From this production network vantage point we: (i) present the theoretical foundations for the role of such input linkages as a shock propagation channel and as a mechanism for transforming micro-level shocks into macroeconomic\, economy-wide fluctuations (ii) selectively survey both empirical and simulation-based studies that attempt to ascertain the relevance and quantitative bite of this argument and (time permitting) (iii) discuss a range of domains where this networked production view is currently being extended to.\n\n\n4/28/2021 \n9:00 – 10:00pm ET\nShamit Kachru (Stanford) \nSlides\nTitle: K3 Metrics from String Theory \nAbstract: Calabi-Yau manifolds have played a central role in important developments in string theory and mathematical physics.  Famously\, they admit Ricci flat metrics — but the proof of that fact is not constructive\, and the metrics remain mysterious.  K3 is perhaps the simplest non-trivial compact Calabi-Yau space.  In this talk\, I describe two different methods of constructing (smooth\, Ricci flat) K3 metrics\, and a string theory duality which relates them.  The duality re-sums infinite towers of disc instanton corrections via a purely classical infinite-dimensional hyperkahler quotient construction\, which can be practically implemented.\n\n\n\n\n\nFall 2020:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n9/23/2020\nDavid Kazhdan (Hebrew University)\nTitle: On Applications of Algebraic Combinatorics to Algebraic Geometry \nAbstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.\n\n\n10/7/2020 \n10:00am\nMariangela Lisanti (Princeton University) \nVideo\nTitle: Mapping the Milky Way’s Dark Matter Halo with Gaia \nAbstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release\, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem\, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium\, as typically assumed\, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments\, which search for the interactions of these particles in terrestrial targets.\n\n\n10/14/2020\nGil Kalai (Hebrew University and IDC Herzliya) \nVideo\nTitle: Statistical\, mathematical\, and computational aspects of noisy intermediate-scale quantum computers \nAbstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics\, statistics and computational complexity which arose in my study of NISQ systems and are related to\na) My general argument “against” quantum computers\,\nb) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.\nRelevant papers:\nYosef Rinott\, Tomer Shoham and Gil Kalai\, Statistical aspects of the quantum supremacy demonstration\, https://gilkalai.files.\nwordpress.com/2019/11/stat-quantum2.pdf\nGil Kalai\, The Argument against Quantum Computers\, the Quantum Laws of Nature\, and Google’s Supremacy Claims\, https://gilkalai.files.\nwordpress.com/2020/08/laws-blog2.pdf\nGil Kalai\, Three puzzles on mathematics\, computations\, and games\, https://gilkalai.files.\nwordpress.com/2019/09/main-pr.pdf\n\n\n10/21/2020\nMarta Lewicka (University of Pittsburgh) \nVideo\nTitle: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models \nAbstract: We propose results that relate the following two contexts:\n(i) Given a Riemann metric G on a thin plate\, we study the question of what is its closest isometric immersion\, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.\n(ii) We perform the full scaling analysis of E^h\, in the context of dimension reduction as the plate’s thickness h goes to 0\, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization\, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).\nFor each n\, we identify conditions for the validity of the corresponding scaling\, in terms of the vanishing of Riemann curvatures of G up to appropriate orders\, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth\, swelling\, shrinkage\, plasticity\, etc. Our results display the interaction of calculus of variations\,\ngeometry and mechanics of materials in the prediction of patterns and shape formation.\n\n\n10/28/2020\nJonathan Heckman (University of Pennsylvania) \nVideo\nTitle: Top Down Approach to Quantum Fields \nAbstract: Quantum Field theory (QFT) is the common language of particle physicists\, cosmologists\, and condensed matter physicists. Even so\, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made in understanding QFT using the geometry of extra dimensions predicted by string theory\, highlighting in particular the special role of seemingly “exotic”  higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs\, and are now using this to extra observables from strongly correlated systems in theories with more than four spacetime dimensions\, as well as in spacetimes with four or fewer spacetime dimensions. Along the way\, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems\n\n\n11/4/2020\n9:00pm ET\nSurya Ganguli (Stanford) \nVideo\nTitle: Weaving together machine learning\, theoretical physics\, and neuroscience through mathematics \nAbstract: An exciting area of intellectual activity in this century may well revolve around a synthesis of machine learning\, theoretical physics\, and neuroscience.  The unification of these fields will likely enable us to exploit the power of complex systems analysis\, developed in theoretical physics and applied mathematics\, to elucidate the design principles governing neural systems\, both biological and artificial\, and deploy these principles to develop better algorithms in machine learning.  We will give several vignettes in this direction\, including:  (1) determining the best optimization problem to solve in order to perform regression in high dimensions;  (2) finding exact solutions to the dynamics of generalization error in deep linear networks; (3) developing interpretable machine learning to derive and understand state of the art models of the retina; (4) analyzing and explaining the origins of hexagonal firing patterns in recurrent neural networks trained to path-integrate; (5) delineating fundamental theoretical limits on the energy\, speed and accuracy with which non-equilibrium sensors can detect signals\nSelected References:\nM. Advani and S. Ganguli\, Statistical mechanics of optimal convex inference in high dimensions\, Physical Review X\, 6\, 031034\, 2016.\nM. Advani and S. Ganguli\, An equivalence between high dimensional Bayes optimal inference and M-estimation\, NeurIPS\, 2016.\nA.K. Lampinen and S. Ganguli\, An analytic theory of generalization dynamics and transfer learning in deep linear networks\, International Conference on Learning Representations (ICLR)\, 2019.\nH. Tanaka\, A. Nayebi\, N. Maheswaranathan\, L.M. McIntosh\, S. Baccus\, S. Ganguli\, From deep learning to mechanistic understanding in neuroscience: the structure of retinal prediction\, NeurIPS 2019.\nS. Deny\, J. Lindsey\, S. Ganguli\, S. Ocko\, The emergence of multiple retinal cell types through efficient coding of natural movies\, Neural Information Processing Systems (NeurIPS) 2018.\nB. Sorscher\, G. Mel\, S. Ganguli\, S. Ocko\, A unified theory for the origin of grid cells through the lens of pattern formation\, NeurIPS 2019.\nY. Bahri\, J. Kadmon\, J. Pennington\, S. Schoenholz\, J. Sohl-Dickstein\, and S. Ganguli\, Statistical mechanics of deep learning\, Annual Reviews of Condensed Matter Physics\, 2020.\nS.E. Harvey\, S. Lahiri\, and S. Ganguli\, A universal energy accuracy tradeoff in nonequilibrium cellular sensing\, https://arxiv.org/abs/2002.10567\n\n\n11/11/2020\nKevin Buzzard (Imperial College London) \nVideo\nTitle: Teaching proofs to computers \nAbstract: A mathematical proof is a sequence of logical statements in a precise language\, obeying some well-defined rules. In that sense it is very much like a computer program. Various computer tools have appeared over the last 50 years which take advantage of this analogy by turning the mathematical puzzle of constructing a proof of a theorem into a computer game. The newest tools are now capable of understanding some parts of modern research mathematics. In spite of this\, these tools are not used in mathematics departments\, perhaps because they are not yet capable of telling mathematicians *something new*.\nI will give an overview of the Lean theorem prover\, showing what it can currently do. I will also talk about one of our goals: using Lean to make practical tools which will be helpful for future researchers in pure mathematics.\n\n\n11/18/2020\nJose A. Scheinkman (Columbia) \nVideo\nTitle: Re-pricing avalanches \nAbstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive.  Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper\, we show that a state-dependent  pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment.  These fluctuations\, in turn\, cause fluctuations  in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)\n\n\n11/25/2020 \n10:45am\nEric J. Heller (Harvard) \nVideo\nTitle: Branched Flow \nAbstract: In classical and quantum  phase space flow\, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In  evolution under smooth\, random\, weakly deflecting  but persistent perturbations\, a remarkable regime develops\, called branched flow. Lying between the first cusp catastrophes at the outset\, leading to fully chaotic  statistical flow much later\, lies the visually beautiful regime of branched flow.  It applies to tsunami wave propagation\, freak wave formation\, light propagation\, cosmic microwaves arriving from pulsars\, electron flow in metals and devices\, sound propagation in the atmosphere and oceans\, the large scale structure of the universe\, and much more. The mathematical structure of this flow is only partially understood\, involving exponential instability coexisting with “accidental” stability. The flow is qualitatively universal\, but this has not been quantified.  Many questions arise\, including the scale(s) of the random medium\,  and the time evolution of manifolds and “fuzzy” manifolds in phase space.  The classical-quantum (ray-wave)  correspondence in this flow is only partially understood.  This talk will be an introduction to the phenomenon\, both visual and mathematical\, emphasizing unanswered questions\n\n\n12/2/2020\nDouglas Arnold (U of Minnesota) \nVideo\nTitle: Preserving geometry in numerical discretization \nAbstract: An important design principle for numerical methods for differential equations is that the discretizations preserve key geometric\, topological\, and algebraic structures of the original differential system.  For ordinary differential equations\, such geometric integrators were developed at the end of the last century\, enabling stunning computations in celestial mechanics and other applications that would have been impossible without them.  Since then\, structure-preserving discretizations have been developed for partial differential equations.  One of the prime examples has been the finite element exterior calculus or FEEC\, in which the structures to preserve are related to Hilbert complexes underlying the PDEs\, the de Rham complex being a canonical example.  FEEC has led to highly successful new numerical methods for problems in fluid mechanics\, electromagnetism\, and other applications which relate to the de Rham complex.  More recently\, new tools have been developed which extend the applications of FEEC far beyond the de Rham complex\, leading to progress in discretizations of problems from solid mechanics\, materials science\, and general relativity.\n\n\n12/9/2020\nManuel Blum and Lenore Blum (Carnegie Mellon) \nVideo\nTitle: What can Theoretical Computer Science Contribute to the Discussion of Consciousness? \nAbstract: The quest to understand consciousness\, once the purview of philosophers and theologians\, is now actively pursued by scientists of many stripes. We study consciousness from the perspective of theoretical computer science. This is done by formalizing the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him\, Stanislas Dehaene\, and others. We give a precise formal definition of a Conscious Turing Machine (CTM)\, also called Conscious AI\, in the spirit of Alan Turing’s simple yet powerful definition of a computer. We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness.\nAfter formally defining CTM\, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness\, the range of related concepts that the model explains easily and naturally\, and the extent of the theory’s agreement with scientific evidence
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2020-2021-colloquium-wednesdays/
CATEGORIES:Colloquium
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DTSTART;TZID=America/New_York:20170914T150000
DTEND;TZID=America/New_York:20170914T160000
DTSTAMP:20240212T072955Z
CREATED:20240212T072955Z
LAST-MODIFIED:20240212T072955Z
UID:10001875-1505401200-1505404800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Algebraic Geometry Seminar\, Thursdays
DESCRIPTION:This seminar will not be held in the Spring 2018 Semester. \nThe Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building\, 20 Garden Street\, Room G10. \nThe schedule will be updated as details are confirmed. \n  \n  \n\n\n\nDate\nName\nTitle/Abstract\n\n\n09-14-17\n Yu-Wei Fan (Harvard Math)\n\nEntropy of an autoequivalence on Calami-Yau manifolds \nAbstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories\, and provide counterexamples of a conjecture by Kikuta-Takahashi. \n\n\n\n11-1-17 \n*5:00pm\, G10*\n Shamil Shakirov\, Harvard Math\n\nUndulation invariants of plane curves \nAbstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object\, defined by explicit polynomial equations (e.g. a curve or a surface)\, satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem\, described by Cayley and Salmon in 1852\, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries\, and we conjecture a generalization for r = 5 \n\n\n\n11-2-17 \n \nAlexander Moll\, IHES\n\nHilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves \nABSTRACT: By Grojnowski and Nakajima\, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand\, by Pressley-Segal\, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First\, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second\, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem\, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes\, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits\, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence. \n\n\n\n11-9-17\n  TBD\n  TBD\n\n\n11-16-17\n TBD\n TBD\n\n\n11-23-17\n  TBD\n  TBD\n\n\n11-30-17\n  TBD\n  TBD\n\n\n12-7-17\n  TBD\n  TBD\n\n\n12-15-17\n  TBD\n  TBD
URL:https://live-hu-cmsa-222.pantheonsite.io/event/algebraic-geometry-seminar-thursdays/
CATEGORIES:Seminars
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170908T130000
DTEND;TZID=America/New_York:20170908T160000
DTSTAMP:20240209T112503Z
CREATED:20240209T112503Z
LAST-MODIFIED:20240209T112503Z
UID:10001855-1504875600-1504886400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Combinatorics & Complexity Seminar\, Fridays
DESCRIPTION:The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building\, 20 Garden Street\, Room G10. \nThe list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received. \nAdditional information on CMSA’s Combinatorics and Complexity program can be found here. \n  \n\n\n\nDate\nName\nTitle/Abstract\n\n\n09-08-17\n\nTBA\n\n\n09-15-2017\n\nTBA\n\n\n09-22-17\n\nTBA\n\n\n09-29-17\n\nTBA\n\n\n10-06-17\n\n TBA\n\n\n10-13-2017\n\nTBA\n\n\n10-20-2017\n\nTBA\n\n\n10-27-2017\n\nTBA\n\n\n11-03-2017\n\nTBA\n\n\n11-10-2017\n\nTBA\n\n\n11-17-2017\n\nTBA\n\n\n11-24-2017\n\nTBA\n\n\n12-01-2017\n\nTBA\n\n\n12-08-2017\n\n TBA
URL:https://live-hu-cmsa-222.pantheonsite.io/event/combinatorics-complexity-seminar-fridays/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170502T133000
DTEND;TZID=America/New_York:20170502T133000
DTSTAMP:20240213T102711Z
CREATED:20240213T102711Z
LAST-MODIFIED:20240213T102711Z
UID:10002427-1493731800-1493731800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:5-2-2017 Social Sciences Application Forum
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/5-2-2017-social-sciences-application-forum/
CATEGORIES:Seminars
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