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DTSTART;TZID=America/New_York:20220429T093000
DTEND;TZID=America/New_York:20220429T110000
DTSTAMP:20240229T090935Z
CREATED:20240215T100221Z
LAST-MODIFIED:20240229T090935Z
UID:10002735-1651224600-1651230000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Machine Learning the Gravity Equation for International Trade
DESCRIPTION:Member Seminar \nSpeaker: Sergiy Verstyuk \nTitle: Machine Learning the Gravity Equation for International Trade \nAbstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next\, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally\, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-29-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220408T084500
DTEND;TZID=America/New_York:20220408T101500
DTSTAMP:20240301T105121Z
CREATED:20240214T084325Z
LAST-MODIFIED:20240301T105121Z
UID:10002595-1649407500-1649412900@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning
DESCRIPTION:Speaker: Jörn Boehnke \nTitle: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning \nAbstract:  In the standard regression discontinuity setting\, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage\, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage\, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score\, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations\, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally\, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-8-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220401T090000
DTEND;TZID=America/New_York:20220401T103000
DTSTAMP:20240301T110938Z
CREATED:20240214T084536Z
LAST-MODIFIED:20240301T110938Z
UID:10002596-1648803600-1648809000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Diffusive growth sourced by topological defects
DESCRIPTION:Member Seminar \nSpeaker: Farzan Vafa \nTitle: Diffusive growth sourced by topological defects \nAbstract: In this talk\, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time\, and predict that in the presence of a positive defect\, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature\, we exploit the fact that for axisymmetric surfaces\, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry\, for polar order and small bending modulus\, is a deformed football.\nWe apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells\, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting\, we show that the defect configuration consisting of a bound +1 defect state\, which is stabilized by activity\, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles\, consistent with observations of a basal marine invertebrate Hydra
URL:https://live-hu-cmsa-222.pantheonsite.io/event/4-1-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220325T093000
DTEND;TZID=America/New_York:20220325T103000
DTSTAMP:20240301T110538Z
CREATED:20240214T084728Z
LAST-MODIFIED:20240301T110538Z
UID:10002597-1648200600-1648204200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Periods for singular CY families and Riemann–Hilbert correspondence
DESCRIPTION:Member Seminar \nSpeaker: Tsung-Ju Lee \nTitle: Periods for singular CY families and Riemann–Hilbert correspondence \nAbstract: A GKZ system\, introduced by Gelfand\, Kapranov\, and Zelevinsky\, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory\, algebraic geometry and mirror symmetry. In this talk\, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/3-25-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220318T093000
DTEND;TZID=America/New_York:20220318T103000
DTSTAMP:20240301T111106Z
CREATED:20240214T084936Z
LAST-MODIFIED:20240301T111106Z
UID:10002599-1647595800-1647599400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Moduli Space of Metric SUSY Graphs
DESCRIPTION:Member Seminar \nSpeaker: Yingying Wu \nTitle: Moduli Space of Metric SUSY Graphs \nAbstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk\, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then\, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties\, followed by a discussion on the connection with the classical case.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/3-18-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220304T093000
DTEND;TZID=America/New_York:20220304T103000
DTSTAMP:20240301T111217Z
CREATED:20240214T085309Z
LAST-MODIFIED:20240301T111217Z
UID:10002600-1646386200-1646389800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds
DESCRIPTION:Member Seminar \nSpeaker: Martin Lesourd \nTitle: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds \nAbstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger\, Prof. S-T. Yau\, and two others are with R. Unger\, and Prof. D. A. Lee.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/3-4-2022-member-seminar/
LOCATION:Hybrid – G10
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220218T093000
DTEND;TZID=America/New_York:20220218T103000
DTSTAMP:20240301T111555Z
CREATED:20240301T111555Z
LAST-MODIFIED:20240301T111555Z
UID:10002895-1645176600-1645180200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Quadratic reciprocity from a family of adelic conformal field theories
DESCRIPTION:Member Seminar \nSpeaker:An Huang \nTitle: Quadratic reciprocity from a family of adelic conformal field theories \nAbstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically\, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra\, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore\, there is an adelic version of this family of conformal field theories\, parameterized by the choice of a number field\, together with a Hecke character. Tate’s thesis gives the Green’s functions of these theories\, and ensures that these Green’s functions satisfy an adelic product formula. In particular\, the local L-factors contribute to the prefactors of these Green’s functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of Q. At the Archimedean place\, the desired holomorphic factorization follows from the global conformal symmetry.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-18-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220211T093000
DTEND;TZID=America/New_York:20220211T103000
DTSTAMP:20240301T111928Z
CREATED:20240214T085713Z
LAST-MODIFIED:20240301T111928Z
UID:10002602-1644571800-1644575400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Amplituhedra\, Scattering Amplitudes and Triangulations
DESCRIPTION:Member Seminar \nSpeaker: Matteo Parisi \nTitle: Amplituhedra\, Scattering Amplitudes and Triangulations \nAbstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular\, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes\, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known\, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory\, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts\, such as matroid theory\, torus orbits in the Grassmannian\, and tropical geometry. Based on joint works with Lauren Williams\, Melissa Sherman-Bennett\, Tomasz Lukowski [arXiv:2104.08254\, arXiv:2002.06164].
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-11-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220204T093000
DTEND;TZID=America/New_York:20220204T103000
DTSTAMP:20240301T112029Z
CREATED:20240214T090103Z
LAST-MODIFIED:20240301T112029Z
UID:10002603-1643967000-1643970600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Survey on stability of the positive mass theorem
DESCRIPTION:Member Seminar \nSpeaker: Dan Lee \nTitle: Survey on stability of the positive mass theorem \nAbstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero\, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk\, I will discuss various results related to this question.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-4-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220128T093000
DTEND;TZID=America/New_York:20220128T103000
DTSTAMP:20240301T112154Z
CREATED:20240214T090436Z
LAST-MODIFIED:20240301T112154Z
UID:10002605-1643362200-1643365800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Singular Calabi-Yau mirror symmetry
DESCRIPTION:Speaker: Bong Lian \nTitle: Singular Calabi-Yau mirror symmetry \nAbstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler\, Gauss and Legendre\, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over 6 lines have been studied more recently by many authors\, including Matsumoto\, Sasaki\, Yoshida and others\, mainly from the viewpoint of their moduli spaces and their comparisons.  I will outline a higher dimensional generalization from the viewpoint of mirror symmetry. We will introduce a new compactification of the moduli space cyclic covers\, using the idea of ‘abelian gauge fixing’ and ‘fractional complete intersections’. This produces a moduli problem that is amenable to tools in toric geometry\, particularly those that we have developed jointly in the mid-90’s with S. Hosono and S.-T. Yau in our study of toric Calabi-Yau complete intersections. In dimension 2\, this construction gives rise to new and interesting identities of modular forms and mirror maps associated to certain K3 surfaces. We also present an essentially complete mirror theory in dimension 3\, and discuss generalization to higher dimensions. The lecture is based on joint work with Shinobu Hosono\, Tsung-Ju Lee\, Hiromichi Takagi\, Shing-Tung Yau.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/1-28-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220121T093000
DTEND;TZID=America/New_York:20220121T103000
DTSTAMP:20240301T112306Z
CREATED:20240214T090725Z
LAST-MODIFIED:20240301T112306Z
UID:10002607-1642757400-1642761000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:AdS with Scale Separation
DESCRIPTION:Member Seminar \nSpeaker: Daniel Junghans\n\nTitle: AdS with Scale Separation \nAbstract: I will talk about Anti-de Sitter solutions in string theory with a parametric separation between the AdS curvature scale and the Kaluza-Klein scale. In particular\, I will discuss recent progress on computing backreaction corrections in such solutions\, and I will explain how to construct solutions without Romans mass that can be lifted to M-theory.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/1-21-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220114T093000
DTEND;TZID=America/New_York:20220114T103000
DTSTAMP:20240301T112406Z
CREATED:20240214T090947Z
LAST-MODIFIED:20240301T112406Z
UID:10002609-1642152600-1642156200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Light strings\, strong coupling\, and the Swampland
DESCRIPTION:Member Seminar \nSpeaker: Max Wiesner\n\nTitle: Light strings\, strong coupling\, and the Swampland \nAbstract: In this talk\, I will start by reviewing central ideas of the so-called Swampland Program. The Swampland Program aims to identify criteria that distinguish low-energy effective field theories\, that can be consistently coupled to quantum gravity\, from those theories that become inconsistent in the presence of quantum gravity. \nIn my talk I will specialize to four-dimensional effective field theories with N=2 and N=1 supersymmetry. In weakly-coupled regions of the scalar field space of such theories\, it has been shown that light strings are crucial to realize certain Swampland criteria. Complementary to that\, the focus of this talk will be on the role of such light strings away from these weak-coupling regimes. In this context\, I will first discuss a relation between light perturbative strings and strong coupling singularities in the Kähler moduli space of 4d N=1 compactifications of F-theory. More precisely\, in regions of moduli space\, in which a critical string classically becomes light\, I will show that non-perturbative corrections yield to strong coupling singularities for D7-brane gauge theories which obstruct weak-coupling limits. Moreover\, I will demonstrate that in the vicinity of this strong coupling singularity\, the critical\, light string in fact leaves the spectrum of BPS strings thereby providing an explanation for the obstruction of the weak coupling limit. \nI will then move on and discuss the backreaction of perturbative strings in 4d EFTs. Away from the string core\, the backreaction of such strings necessarily leads to strong coupling regions where naively the energy stored in the backreaction diverges. I will show how the introduction of additional non-critical strings can regulate this backreaction and how this can be used to study the spectrum of BPS strings and their tensions even beyond weak coupling regions. In this context\, I will demonstrate how the requirement\, that the total string tension should not exceed the Planck scale\, constrains the possible BPS string charges.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/1-14-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211210T093000
DTEND;TZID=America/New_York:20211210T103000
DTSTAMP:20240301T110742Z
CREATED:20240214T072023Z
LAST-MODIFIED:20240301T110742Z
UID:10002556-1639128600-1639132200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:On the solution space of the Ising perceptron model
DESCRIPTION:Member Seminar  \nSpeaker: Changji Xu \nTitle: On the solution space of the Ising perceptron model \nAbstract:  Consider the discrete cube $\{-1\,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1\,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1\,1\}^N$ independently with probability $p$. The solution space is the intersection of these half spaces. In this talk\, we will talk about its sharp threshold phenomenon\, the frozen structure of the solution space\, and the Gardner formula.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-10-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211203T093000
DTEND;TZID=America/New_York:20211203T103000
DTSTAMP:20240301T110847Z
CREATED:20240214T072504Z
LAST-MODIFIED:20240301T110847Z
UID:10002558-1638523800-1638527400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Black Holes\, 2D Gravity\, and Random Matrices
DESCRIPTION:Member Seminar \nSpeaker: Dan Kapec \nTitle: Black Holes\, 2D Gravity\, and Random Matrices \nAbstract: I will discuss old and new connections between black hole physics\, 2D quantum gravity\, and random matrix theory. Black holes are believed to be very complicated\, strongly interacting quantum mechanical systems\, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional\, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model\, but this result raises more questions than it answers. If time permits\, I will discuss some extensions of these results and possible future directions.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-3-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211119T093000
DTEND;TZID=America/New_York:20211119T103000
DTSTAMP:20240301T110941Z
CREATED:20240214T072706Z
LAST-MODIFIED:20240301T110941Z
UID:10002560-1637314200-1637317800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:China’s financial regulatory reform\, financial opening-up\, and Central Bank Digital Currency (CBDC)
DESCRIPTION:Member Seminar \nSpeaker: Kan Lin \nTitle: China’s financial regulatory reform\, financial opening-up\, and Central Bank Digital Currency (CBDC) \nAbstract: In this talk\, I will explain the overall situation of China’s financial industry and review the development of China’s financial regulatory system reform from 1949 to 2021. Then\, I will explain the policies of the 3 stages of financial opening-up\, 2001–08\, 2008–18\, 2018≠present. In particular\, the latest round of opening-up from 2018 has brought great opportunities for foreign institutions. China has the world’s largest banking industry with assets totaling $53 trillion\, and accounts for 1/3 of the growth in global insurance premiums over the next 10 years. I will also introduce the progress of research & development of China’s Central Bank Digital Currency (CBDC\, or E-CNY). By October 2021\, 140 million people had opened E-CNY wallets\, and 1.6 million merchants could accept payments using eCNY wallets\, including utilities\, catering services\, transportation\, retail\, and government services.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-19-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211112T093000
DTEND;TZID=America/New_York:20211112T103000
DTSTAMP:20240301T111040Z
CREATED:20240214T072852Z
LAST-MODIFIED:20240301T111040Z
UID:10002561-1636709400-1636713000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Universal relations between entanglement\, symmetries\, and entropy
DESCRIPTION:Member Seminar \nSpeaker: Gabriel Wong  \nTitle: Universal relations between entanglement\, symmetries\, and entropy \nAbstract: Entanglement is an essential property of quantum systems that distinguishes them from classical ones.   It is responsible for the nonlocal character of quantum information and provides a resource for quantum teleportation and quantum computation. In this talk I will provide an introduction to quantum entanglement and explain the essential role it plays in two seemingly unrelated subjects: implementation of measurement-based quantum computation and microstate counting of black holes in quantum gravity.   Time permitting\, I will also discuss attempts to characterize entanglement in string theory. A unifying theme that illuminates the entanglement structure of these diverse systems is the role of surface symmetries and (entanglement) edge modes. We will explain how these universal aspects of entanglement are captured in the framework of extended topological quantum field theory.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-12-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211105T093000
DTEND;TZID=America/New_York:20211105T113000
DTSTAMP:20240301T111130Z
CREATED:20240214T073106Z
LAST-MODIFIED:20240301T111130Z
UID:10002562-1636104600-1636111800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The Greene-Plesser Construction Revisited
DESCRIPTION:Member Seminar  \nSpeaker: Chuck Doran \nTitle: The Greene-Plesser Construction Revisited \nAbstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach\, uncover the hints it gives for some more general mirror constructions\, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-5-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T093000
DTEND;TZID=America/New_York:20211029T103000
DTSTAMP:20240301T111455Z
CREATED:20240214T073521Z
LAST-MODIFIED:20240301T111455Z
UID:10002563-1635499800-1635503400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The complex Monge-Ampere equation in K\”ahler geometry
DESCRIPTION:Speaker: Freid Tong \nTitle: The complex Monge-Ampere equation in Kahler geometry \nAbstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry\, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk\, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry\, with a particular focus on the a priori C^0 estimates and their various applications. In the end\, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations\, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-29-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211022T093000
DTEND;TZID=America/New_York:20211022T103000
DTSTAMP:20240301T111559Z
CREATED:20240214T073722Z
LAST-MODIFIED:20240301T111559Z
UID:10002564-1634895000-1634898600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Wall-crossing from Higgs bundles to vortices
DESCRIPTION:Speaker: Du Pei \nTitle: Wall-crossing from Higgs bundles to vortices \nAbstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk\, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-22-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211015T093000
DTEND;TZID=America/New_York:20211015T103000
DTSTAMP:20240301T111732Z
CREATED:20240214T073928Z
LAST-MODIFIED:20240301T111732Z
UID:10002566-1634290200-1634293800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:C-P-T Fractionalization\, and Quantum Criticality Beyond the Standard Model
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: C-P-T Fractionalization\, and Quantum Criticality Beyond the Standard Model \nAbstract: Discrete spacetime symmetries of parity P or reflection R\, and time-reversal T\, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F\, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures\, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT)\, or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320. \nIn the second part of my talk\, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition\, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-15-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211008T093000
DTEND;TZID=America/New_York:20211008T103000
DTSTAMP:20240301T111834Z
CREATED:20240214T074201Z
LAST-MODIFIED:20240301T111834Z
UID:10002568-1633685400-1633689000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Knowledge Graph Embeddings and Inference
DESCRIPTION:Member Seminar \nSpeaker: Michael Douglas \nTitle: Knowledge Graph Embeddings and Inference \nAbstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.\nA popular KG representation method is graph embedding\, which facilitates question answering\, inferring missing edges\, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning\, network learning\, and unstructured statistical inference\, and describe experiments to measure the contributions of each mechanism. \nJoint work with M. Simkin\, O. Ben-Eliezer\, T. Wu\, S. P. Chin\, T. V. Dang and A. Wood.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-8-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211001T093000
DTEND;TZID=America/New_York:20211001T103000
DTSTAMP:20240301T111944Z
CREATED:20240214T074545Z
LAST-MODIFIED:20240301T111944Z
UID:10002569-1633080600-1633084200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Instability of naked singularities in general relativity
DESCRIPTION:Member Seminar \nSpeaker: Jue Liu \nTitle: Instability of naked singularities in general relativity \nAbstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture\, proposed by Penrose\, which roughly states that for generic physical spacetime\, the singularities (if existed) must be hidden behind the black holes. Unfortunately\, the singularities visible to faraway observers\, which are called by naked singularities\, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime\, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases\, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method\, and it is this wild method that helps us to extend some results to the asymmetric cases.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-1-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210924T093000
DTEND;TZID=America/New_York:20210924T103000
DTSTAMP:20240301T112341Z
CREATED:20240214T075925Z
LAST-MODIFIED:20240301T112341Z
UID:10002575-1632475800-1632479400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Stability and convergence issues in mathematical cosmology
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal \nTitle: Stability and convergence issues in mathematical cosmology \nAbstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk\, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized\, one needs to study its stability properties. Therefore\, I will briefly discuss the stability issue and its consequences (e.g.\, structure formation\, etc).
URL:https://live-hu-cmsa-222.pantheonsite.io/event/9-24-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210917T093000
DTEND;TZID=America/New_York:20210917T103000
DTSTAMP:20240301T112535Z
CREATED:20240214T080149Z
LAST-MODIFIED:20240301T112535Z
UID:10002577-1631871000-1631874600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Geometry\, Entanglement and Quasi Local Data
DESCRIPTION:Member Seminar \nSpeaker: Itamar Shamir \nTitle: Geometry\, Entanglement and Quasi Local Data \nAbstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/9-17-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210910T093000
DTEND;TZID=America/New_York:20210910T103000
DTSTAMP:20240304T100309Z
CREATED:20240213T114336Z
LAST-MODIFIED:20240304T100309Z
UID:10002512-1631266200-1631269800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Threshold phenomena in random graphs and hypergraphs
DESCRIPTION:Member Seminar \nSpeaker: Michael Simkin \nTitle: Threshold phenomena in random graphs and hypergraphs \nAbstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics\, computer science\, and other fields. \nThe model is defined as follows: Given a natural number $n$ and a parameter $p \in [0\,1]$\, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$\, independent of all others. Despite their apparent simplicity\, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena. \nA central feature is the appearance of threshold phenomena: For all monotone properties (e.g.\, connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e.\, with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/9-10-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201120T150200
DTEND;TZID=America/New_York:20210101T150200
DTSTAMP:20240307T111352Z
CREATED:20240209T015737Z
LAST-MODIFIED:20240307T111352Z
UID:10001789-1605884520-1609513320@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Members’ Seminar
DESCRIPTION:The CMSA Members’ Seminar will occur every Friday at 9:30am ET on 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 seminar is organized by Tianqi Wu. The Schedule will be updated below. \nPrevious seminars can be found here. \nSpring 2021:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n1/29/2021\nCancelled\n\n\n\n2/5/2021\nItamar Shamir\nTitle: Boundary CFT and conformal anomalies \nAbstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories\, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.\n\n\n2/12/2021\nLouis Fan\nTitle:  Joint distribution of Busemann functions in corner growth models \nAbstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape\, understanding of the optimal paths\, or geodesics\, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions\, simultaneously in all directions of growth\, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.\n\n\n2/19/2021\nDaniel Junghans\nTitle: Control issues of the KKLT scenario in string theory \nAbstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding\, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular\, we show that\, generically\, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.\n\n\n2/26/2021\nTsung-Ju Lee\nTitle: SYZ fibrations and complex affine structures \nAbstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover\, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin\, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk\, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.\n\n\n3/5/2021\nCancelled\n\n\n\n3/11/2021 \n9:00pm ET\nRyan Thorngren\nTitle:  Symmetry protected topological phases\, anomalies\, and their classification \nAbstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs)\, especially as their theory relates to index theorems in geometry\, cobordism of manifolds\, and group cohomology.\n\n\n3/18/2021 \n9:00pm ET\nRyan Thorngren\nTitle:  Symmetry protected topological phases\, anomalies\, and their classification\nAbstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs)\, especially as their theory relates to index theorems in geometry\, cobordism of manifolds\, and group cohomology.\n\n\n3/26/2021 \n8:30am ET\nAghil Alaee\nTitle:  Rich extra dimensions are hidden inside black holes \nAbstract: In this talk\, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.\n\n\n4/2/2021\n8:30am ET\nEnno Keßler\nTitle: Super Stable Maps of Genus Zero \nAbstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might\, in the future\, lead to a supergeometric generalization of Gromov-Witten invariants.\n\n\n4/9/2021\nJuven Wang \nVideo\nTitle: Ultra Unification \nAbstract: Strong\, electromagnetic\, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work\, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension\, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase)\, or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase)\, or right-handed neutrinos\, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects\, etc.\, whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math\, QFT\, and condensed matter terminology\, and elaborate more on the nonperturbative global anomalies of Z2\, Z4\, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860\, arXiv:2008.06499\, arXiv:2006.16996\, arXiv:1910.14668.\n\n\n4/16/2021\nSergiy Verstyuk\nTitle: Deep learning methods for economics \nAbstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way\, interpretability of neural networks features prominently.\n\n\n4/23/2021\nYifan Wang\nTitle: Virtues of Defects in Quantum Field Theories \nAbstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems\, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra\, precision studies of defect observables\, and the implications thereof for strongly coupled dynamics. In this talk\, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics\, and that open new windows to nonperturbative effects in quantum gravity.\n\n\n4/30/2021\nYun Shi\nTitle: D-critical locus structure for local toric Calabi-Yau 3-fold \nAbstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory\, originally introduced by Kontsevich-Soibelman\, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk\, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt\, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.\n\n\n5/7/2021\nThérèse Yingying Wu\nTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2 \nAbstract: In this talk\, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere\, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.\n\n\n5/14/2021\nDu Pei\nTitle: Three applications of TQFTs \nAbstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk\, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds\, and 3) smooth structures on 4-manifolds.\n\n\n5/21/2021\nFarzan Vafa\nTitle: Active nematic defects and epithelial morphogenesis \nAbstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis\, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics\, cellular division rates\, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects\, and cells accumulate at positive defects and are depleted at negative defects.  We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle\, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles\, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].\n\n\n\n\n\nFall 2020:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n9/11/2020\nMoran Koren\nTitle:  Observational Learning and Inefficiencies in Waitlists \nAbstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model\, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents\, upon receiving an offer\, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives\, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.\n\n\n9/18/2020\nMichael Douglas\nTitle: A talk in two parts\, on strings and on computers and math \nAbstract: I am dividing my time between two broad topics. The first is string theory\, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics\, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert\,GPT) which have led to breakthroughs on natural language processing\, describe their potential for helping us do math\, and sketch some related theoretical problems.\n\n\n9/25/2020\nCancelled – Math Science Lecture\n\n\n\n10/2/2020\nCancelled – Math Science Lecture\n\n\n\n10/9/2020\nWai Tong (Louis) Fan\nTitle: Stochastic PDE as scaling limits of interacting particle systems \nAbstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details\, including randomness and discreteness of individuals\, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.\nIn this talk\, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE\, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE\, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.\n\n\n10/16/2020\nTianqi Wu\nTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space \nAbstract: In 1908\, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem\, in the hyperbolic setting\, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture\, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.\n\n\n10/23/2020\nChangji Xu\nTitle: Random Walk Among Bernoulli Obstacles \nAbstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk\, we will discuss some recent results about the behaviors of the conditional random walk\, in quenched\, annealed\, and biased settings.\n\n\n10/30/2020\nMichael Simkin\nTitle: The differential equation method in Banach spaces and the $n$-queens problem \nAbstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE\, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.\nWe apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose\, uniformly at random\, a space with no queens in its row\, column\, or either diagonal\, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore\, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$\, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.\n\n\n11/6/2020\nKenji Kawaguchi\nTitle: Deep learning: theoretical results on optimization and mixup \nAbstract: Deep neural networks have achieved significant empirical success in many fields\, including the fields of computer vision\, machine learning\, and artificial intelligence. Along with its empirical success\, deep learning has been theoretically shown to be attractive in terms of its expressive power. However\, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization\, robustness\, and generalization\, during the optimization process of a neural network. In this talk\, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.\n\n\n11/13/2020\nOmri Ben-Eliezer\nTitle: Sampling in an adversarial environment \nAbstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance\, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations\, the existing statistical literature does not apply. \nWe propose a new sequential adversarial model capturing these situations\, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results\, techniques\, and applications reveal close connections to various areas in mathematics and computer science\, including VC theory\, discrepancy theory\, online learning\, streaming algorithms\, and computational geometry. \nBased on joint works with Noga Alon\, Yuval Dagan\, Shay Moran\, Moni Naor\, and Eylon Yogev.\n\n\n11/20/2020\nCharles Doran\nTitle: The Calabi-Yau Geometry of Feynman Integrals \nAbstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk\, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry\, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.\n\n\n\nColloquia & Seminars\,Seminars
URL:https://live-hu-cmsa-222.pantheonsite.io/event/members-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170203T113700
DTEND;TZID=America/New_York:20170203T113700
DTSTAMP:20240213T094454Z
CREATED:20240213T094454Z
LAST-MODIFIED:20240213T094454Z
UID:10002361-1486121820-1486121820@live-hu-cmsa-222.pantheonsite.io
SUMMARY:02-03-2017 CMSA Members’ Seminar
DESCRIPTION:Hansol Hong\, Harvard \nTitle: Homological Mirror Functors \nAbstract: I will first give a brief introduction to mirror symmetry\, which intertwines symplectic geometry and complex geometry of a pair of Kahler manifolds\, and explain mirror construction using formal deformation of a Lagrangian submanifold.  We will see that counting of holomorphic discs bounding Lagrangian naturally gives rise to a mirror space (Landau-Ginzburg model) and  a functor from Fukaya category to its mirror matrix factorization category. I will mainly focus on one specific example to give a concrete description of the construction.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/02-03-2017-cmsa-members-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20161117T182900
DTEND;TZID=America/New_York:20161117T182900
DTSTAMP:20240213T091100Z
CREATED:20240213T091100Z
LAST-MODIFIED:20240213T091100Z
UID:10002297-1479407340-1479407340@live-hu-cmsa-222.pantheonsite.io
SUMMARY:11-17-16 CMSA Members’ Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-17-16-cmsa-members-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20161117T110100
DTEND;TZID=America/New_York:20161117T110100
DTSTAMP:20240307T093627Z
CREATED:20240213T092229Z
LAST-MODIFIED:20240307T093627Z
UID:10002322-1479380460-1479380460@live-hu-cmsa-222.pantheonsite.io
SUMMARY:11-17-2016 CMSA Member’s Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-17-2016-cmsa-members-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20161017T182600
DTEND;TZID=America/New_York:20161017T182600
DTSTAMP:20240213T090458Z
CREATED:20240213T090458Z
LAST-MODIFIED:20240213T090458Z
UID:10002285-1476728760-1476728760@live-hu-cmsa-222.pantheonsite.io
SUMMARY:10-17-16 Mathematical Physics Seminar
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-17-16-mathematical-physics-seminar/
CATEGORIES:Member Seminar
END:VEVENT
END:VCALENDAR