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DTSTART;TZID=America/New_York:20250127T150000
DTEND;TZID=America/New_York:20250127T160000
DTSTAMP:20250124T171827Z
CREATED:20240907T194212Z
LAST-MODIFIED:20250124T171827Z
UID:10003471-1737990000-1737993600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:A homotopy of 2d SCFTs and an implication for Topological Modular Forms
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Vivek Saxena (YITP Stony Brook and NHETC Rutgers) \nTitle: A homotopy of 2d SCFTs and an implication for Topological Modular Forms \nAbstract: The Segal-Stolz-Teichner conjecture states that there exists an isomorphism between deformation classes of two-dimensional N=(0\,1) superconformal field theories (SCFTs) and generalized cohomology classes known as Topological Modular Forms (TMFs). Such 2d N=(0\,1) SCFTs arise naturally in physics as worldsheet theories of (possibly compactified) heterotic strings. Recently\, this connection was used to prove the absence of global anomalies in heterotic string theories and make predictions about topological terms in their low-energy effective actions\, among other things. \nIn this talk\, after giving a brief overview of these ideas\, I will describe a physics ”proof” (using methods from 2d CFT) of a mathematical conjecture of Tachikawa and Yamashita about TMF classes in degree 31. Specifically\, by examining the two worldsheet theories corresponding to two T-dual nine-dimensional spacetime non-supersymmetric heterotic string theories (namely the $(E_8)_1 \times (E_8)_1$ theory and the $(E_8)_2$ theory)\, I will argue that the $(E_8)_2$ theory corresponds to the unique nontrivial torsion element $[(E_8)_2]$ of TMF$^{31}$ with zero mod-2 elliptic genus.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qft_12725/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QFT-and-Physical-Mathematics-1.27.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241213T100000
DTEND;TZID=America/New_York:20241213T113000
DTSTAMP:20241210T165540Z
CREATED:20240907T194348Z
LAST-MODIFIED:20241210T165540Z
UID:10003474-1734084000-1734089400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Nonlinear Bosonization of (Non-)Fermi Liquids
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Yi-Hsien Du (MIT) \nTitle: Nonlinear Bosonization of (Non-)Fermi Liquids \nAbstract: Fermi liquid theory is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid theory as an effective field theory. In this approach\, the space of low-energy states of a Fermi liquid is identified with a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonized description of the Fermi liquid with nonlinear corrections fixed by the geometry of the Fermi surface. I will present that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. The approach can be extended to encompass non-Fermi liquids\, which correspond to strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. I will also discuss how Berry curvature can be captured in the effective field theory approach.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_121324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QFT-and-Physical-Mathematics-12.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241212T100000
DTEND;TZID=America/New_York:20241212T110000
DTSTAMP:20241219T193206Z
CREATED:20241209T191304Z
LAST-MODIFIED:20241219T193206Z
UID:10003601-1733997600-1734001200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The Quantum GIT conjecture
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Daniel Pomerleano (UMass Boston) \nTitle: The Quantum GIT conjecture \nAbstract: Let X be a Fano variety with G action. The quantum GIT conjecture predicts a formula for the quantum cohomology of “anti-canonical” GIT quotients X//G in terms of the equivariant quantum cohomology of X. The formula is motivated by ideas from 3- dimensional gauge theory (“Coulomb branches”) and provides a vast generalization of Batyrev’s formula for the quantum cohomology of a toric Fano variety. I will describe our ongoing work with C. Teleman proving this conjecture. Along the way\, I will also discuss integral versions of certain classical facts in the theory of Hamiltonian G-manifolds which are of independent interest. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathphys_121224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-12.12.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241210T110000
DTEND;TZID=America/New_York:20241210T120000
DTSTAMP:20241210T202435Z
CREATED:20240903T181118Z
LAST-MODIFIED:20241210T202435Z
UID:10003419-1733828400-1733832000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The Einstein-Vlasov system in a large data regime
DESCRIPTION:General Relativity Seminar \nSpeaker: Nikolaos Athanasiou\, University of Crete\, Greece \nTitle: The Einstein-Vlasov system in a large data regime \nAbstract: In this talk\, our object of study is the Einstein-Vlasov system with a massless Vlasov matter field. Complementing various important works obtaining the stability of Minkowski spacetime as a solution to this system\, we look at the large data regime\, motivated in turn by the signature for decay rates of various Ricci\, curvature and matter components\, first introduced by X. An. Our work provides a semi-global existence result and a trapped surface formation result for the Einstein-Vlasov system in the absence of spherical symmetry. Our proof is based on a double null gauge. Interestingly\, we give a new way of obtaining estimates for the Vlasov matter\, purely by commuting with various vector fields and without the need to use Jacobi fields.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/general-relativity-seminar-121024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-GR-Seminar-12.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241206T120000
DTEND;TZID=America/New_York:20241206T130000
DTSTAMP:20241203T164917Z
CREATED:20240919T144747Z
LAST-MODIFIED:20241203T164917Z
UID:10003527-1733486400-1733490000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:On the Coulomb branch scaling dimensions of 4d N=2 SCFTs
DESCRIPTION:Member Seminar \nSpeaker: Robert Moscrop \nTitle: On the Coulomb branch scaling dimensions of 4d N=2 SCFTs \nAbstract: To each four dimensional N=2 superconformal field theory of rank-r\, one can associate an r-tuple of numbers given by the scaling dimensions of a special set of protected operators whose VEVs parameterise the Coulomb branch. In this talk\, I will demonstrate how the special geometry of the Coulomb branch heavily constrains not only the values of the scaling dimensions\, but also the possible r-tuples of such numbers that can occur.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar-120624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-12.6.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241205T103000
DTEND;TZID=America/New_York:20241205T120000
DTSTAMP:20241119T150954Z
CREATED:20241119T141605Z
LAST-MODIFIED:20241119T150954Z
UID:10003621-1733394600-1733400000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Quantum Cellular Automata
DESCRIPTION:Special Seminar \nSpeaker: Jeongwan Haah\, Stanford University \nTitle: Quantum Cellular Automata \nAbstract: A discrete time evolution on lattice systems that has a notion of lightcone is called a quantum cellular automaton. Lattice translation in 1D is a well-known example of QCA that is nontrivial in the sense that it is not a local Hamiltonian evolution. In higher dimensions\, more subtle QCA are found in relation to certain topological phases of matter\, but the scope of all QCA is far from being fully determined. I will report the status of our understanding on this subject\, emphasizing the role of locally generated simple subalgebras.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/seminar_12524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Special Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Special-Seminar-12.5.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241204T140000
DTEND;TZID=America/New_York:20241204T150000
DTSTAMP:20241212T205959Z
CREATED:20240907T180227Z
LAST-MODIFIED:20241212T205959Z
UID:10003410-1733320800-1733324400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Can Transformers Reason Logically? A Study in SAT-Solving
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Leyan Pan\, Georgia Tech \nTitle: Can Transformers Reason Logically? A Study in SAT-Solving \nAbstract: Transformer-based LLMs have apparently demonstrated capabilities that resembles human reasoning. In our recent work\, we investigated the Boolean reasoning abilities of decoder-only Transformers equipped with Chain-of-Thought\, establishing that a Transformer model can decide all 3-SAT instances up to a bounded size (i.e.\, number of variables and clauses). In this talk\, I will first review recent studies that formally examine the expressiveness of Transformer models. Next\, I will explain how we establish an equivalence between Chain-of-Thought reasoning and algorithm\, in our case\, the DPLL SAT-solving algorithm. I will then discuss how to encode 3-SAT formulas and partial assignments as vectors so that the high-level operations in DPLL can be represented as vector operations and implemented using attention mechanisms within Transformers. Finally\, I will present experimental results that support our theoretical predictions. I will also address why standard Transformers can only solve reasoning problems of bounded length\, leading to failures in length-generalization\, and discuss potential solutions to overcome this limitation.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/newtech_12424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-NTM-Seminar-12.4.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241203T110000
DTEND;TZID=America/New_York:20241203T120000
DTSTAMP:20241125T194606Z
CREATED:20240903T192215Z
LAST-MODIFIED:20241125T194606Z
UID:10003429-1733223600-1733227200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mass for the large and for the small
DESCRIPTION:General Relativity Seminar \nSpeaker: Tin Yau Tsang\, Courant Institute\, New York University \nTitle: Mass for the large and for the small\n\nAbstract: Seeking a meaningful geometric (physical) invariant to describe a spacetime has sparked research in both mathematics and physics. In this talk\, we will first see the fundamental progress made by Schoen-Yau and Witten on ADM (Arnowitt-Deser-Misner) mass. Then\, we will see the progress on quasilocal masses in recent years. In particular\, we would discuss the Hamiltonian formulation and the behaviour of quasilocal masses with the presence of apparent horizons.\n  \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/general-relativity-seminar-12324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-GR-Seminar-12.3.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241202T163000
DTEND;TZID=America/New_York:20241202T173000
DTSTAMP:20241126T142827Z
CREATED:20240903T195308Z
LAST-MODIFIED:20241126T142827Z
UID:10003440-1733157000-1733160600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Computability on $\mathbb R$ and other continuum-size structures
DESCRIPTION:Colloquium \nSpeaker: Russell Miller\, CUNY \nTitle: Computability on $\mathbb R$ and other continuum-size structures \nAbstract: We begin by recalling the notion of a computable function on the real numbers $\mathbb R$\, developed independently by Gregorczyk and Lacombe over sixty years ago. Using this notion\, we note that the real numbers that are themselves computable form a countable subfield of $\mathbb R$ with exactly the same first-order properties as $\mathbb R$ itself. (Logicians would therefore call it an \emph{elementary subfield}.) So\, in a first-order sense\, everything that happens in $\mathbb R$ is already exemplified in this much nicer subfield. However\, even when one knows that an existential statement holds for all parameters\, it may be impossible (both in $\mathbb R$ and in the subfield) to give a computable procedure for producing witnesses. Similar results hold in $\mathbb C$. \nWe will then turn to a different continuum-sized structure: the absolute Galois group $\operatorname{Gal}(\mathbb Q)$ of the rational numbers. Once again the computable elements of this group form a subgroup\, but now it is an open problem whether the group and the subgroup have the same first-order theory\, let alone whether this is an elementary subgroup. (If they do have the same theory\, this would put nice upper bounds on the complexity of the theory of $\operatorname{Gal}(\mathbb Q)$.) However\, using joint work with Kundu\, we can show that once again there is no computable procedure for producing witnesses to the truth of (true) existential statements\, either in the full group or in the subgroup.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/colloquium-12224/
LOCATION:CMSA Room G10\, 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-12.2.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241125T163000
DTEND;TZID=America/New_York:20241125T173000
DTSTAMP:20241119T192853Z
CREATED:20240903T195237Z
LAST-MODIFIED:20241119T192853Z
UID:10003439-1732552200-1732555800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematical Structures of Scattering Amplitudes
DESCRIPTION:Colloquium \nSpeaker: Anastasia Volovich\, Brown University \nTitle: Mathematical Structures of Scattering Amplitudes \nAbstract: Planar N=4 Yang-Mills scattering amplitudes have been computed to very high loop order. They have many remarkable properties that have sparked interest from mathematicians working on combinatorics\, algebraic geometry\, and number theory. At the same time\, several methods that have been developed for N=4 Yang-Mills can often be applied to more general quantum field theories\, including QCD. I will overview some of these exciting developments.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/colloquium-112524/
LOCATION:CMSA Room G10\, 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-11.25.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241122T120000
DTEND;TZID=America/New_York:20241122T130000
DTSTAMP:20241118T172611Z
CREATED:20240919T144708Z
LAST-MODIFIED:20241118T172611Z
UID:10003525-1732276800-1732280400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Identity crises phenomena in the large cardinal hierarchy
DESCRIPTION:Member Seminar \nSpeaker: Alejandro Poveda \nTitle: Identity crises phenomena in the large cardinal hierarchy\n\nAbstract: It is well-known that certain mathematical questions cannot be answered on the grounds of the standard foundation of mathematics. Large cardinal axioms constitute a series of postulates about the higher infinite which permit to classify these undecidable problems in a coherent hierarchy way. Specifically\, large cardinals together with ZFC (the standard axiomatic of Mathematics) provide a complete classification of all mathematical theories according to the so-called consistency strength. One of the main tenets of modern set theory has been to investigate how the large-cardinal hierarchy is organized across the mathematical universe. To a large extent this hierarchy is nicely disposed and such a disposition is unambiguous (i.e.\, immune to the independence phenomenon).\n\nIn an unexpected turn of events\, in the late 70’s Magidor discovered the identity crisis phenomena of the large cardinal hierarchy. Magidor proved that certain strata of the hierarchy are susceptible to be modified via Cohen’s method of forcing. Specifically\, he showed that the first strongly compact cardinal can be either the first measurable cardinal or the first supercompact cardinal. It turns out that the first measurable is always much smaller than the first supercompact. These discrepancies on the identity of the first strongly compact cardinal were termed by Magidor the Identity Crisis Phenomenon.\n\nIn this talk I plan to provide an introduction to the world of large cardinals keeping an eye on the identity crises phenomena. Time permitting\, I’ll present a few recent results answering questions by Magidor and discuss their connection with Woodin’s Ultimate-L Conjecture.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar-112224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-11.22.24_Page_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241121T103000
DTEND;TZID=America/New_York:20241121T113000
DTSTAMP:20241115T175402Z
CREATED:20240924T174856Z
LAST-MODIFIED:20241115T175402Z
UID:10003599-1732185000-1732188600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Skein valued curve counts for the topological vertex and knot conormals
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Tobias Ekholm\, Uppsala University \nTitle: Skein valued curve counts for the topological vertex and knot conormals \nAbstract: Combining the invariance of holomorphic curve counts in the skein module with a study of holomorphic curves at infinity of the vertex we find three simple skein operator polynomials that annihilates the (skein valued) topological vertex. We show that these operator polynomials together with natural initial conditions determine the partition function uniquely and then demonstrate that the original Aganagic-Klemm-Marino-Vafa formula for the topological vertex interpreted as a skein valued curve count satisfies the operator polynomials. This is joint work with Longhi and Shende. We end with a general discussion of similar ‘skein D-modules’ for knot conormals. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathphys_112124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.21.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241121T090000
DTEND;TZID=America/New_York:20241121T103000
DTSTAMP:20241203T144846Z
CREATED:20240923T152934Z
LAST-MODIFIED:20241203T144846Z
UID:10003528-1732179600-1732185000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Bjorn Poonen\, MIT
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: November 21\, 2024 \nTime: 9:00 – 10:30 am ET \nLocation: CMSA G10\, 20 Garden Street\, Cambridge MA & via Zoom \nSpeaker: Bjorn Poonen\, MIT \nTitle: Ranks of elliptic curves \nAbstract: Elliptic curves are simplest varieties whose rational points are not fully understood\, and they are the simplest projective varieties with a nontrivial group structure.  In 1922 Mordell proved that the group of rational points on an elliptic curve is finitely generated.  We will survey what is known and what is believed about this group. \n  \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathscilit2024_bp/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Math Science Literature Lecture Series
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/Mathlit_Poonen_11x17.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241120T150000
DTEND;TZID=America/New_York:20241120T160000
DTSTAMP:20241115T183220Z
CREATED:20241010T135347Z
LAST-MODIFIED:20241115T183220Z
UID:10003593-1732114800-1732118400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:A new construction of c = 1 conformal blocks
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Qianyu Hao\, University of Geneva \nTitle: A new construction of c = 1 conformal blocks\n\nAbstract: The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example\, when c = 1\, they are related to tau functions of Painlevé equations. I will first explain what Virasoro conformal blocks are. Then I will describe a new way to construct Virasoro blocks at c = 1 on C by using the “abelian” Heisenberg conformal blocks on a branched double cover of C. The main new idea in our work is to use a spectral network. It is closely related to the idea of nonabelianization of the flat connections in the work of Gaiotto-Moore-Neitzke and Neitzke-Hollands. This nonabelianization construction enables us to compute the harder-to-get Virasoro blocks using the simpler abelian objects. This is based on a joint work with Andrew Neitzke.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathphys_112024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.20.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241119T110000
DTEND;TZID=America/New_York:20241119T120000
DTSTAMP:20241115T150935Z
CREATED:20240903T181051Z
LAST-MODIFIED:20241115T150935Z
UID:10003418-1732014000-1732017600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The Einstein-Euler system with a physical vacuum boundary in spherical symmetry
DESCRIPTION:General Relativity Seminar \nSpeaker: Marcelo Disconzi\, Vanderbilt University \nTitle: The Einstein-Euler system with a physical vacuum boundary in spherical symmetry \nAbstract: We establish local well-posedness for the Einstein-Euler system with a physical vacuum boundary in spherical symmetry. Our proof relies on a new way of thinking about Einstein’s equations in spherical symmetry that is well-adapted to the fluid’s characteristics on the free boundary. We also exploit the Einstein constraint equations in spherical symmetry in a new way\, as a tool to understand the evolution problem. This is joint work with Jared Speck.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/general-relativity-seminar-111924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-GR-Seminar-11.19.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241118T140000
DTEND;TZID=America/New_York:20241118T150000
DTSTAMP:20241108T184917Z
CREATED:20241108T183204Z
LAST-MODIFIED:20241108T184917Z
UID:10003620-1731938400-1731942000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Emergent Non-Invertible Symmetries —The Adjoint QCD Example
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Shani Nadir Meynet (Uppsala) \nTitle: Emergent Non-Invertible Symmetries — The Adjoint QCD Example \nAbstract: After reviewing some general properties of generalized symmetries and the renormalization group (RG) flow for quantum field theories (QFT)\, I’ll describe how the recently discovered non-invertible symmetries can be used to study theories at strong coupling. I’ll illustrate these facts using (3+1)-dimensional adjoint QCD with two flavors as an example. This theory can be obtained by mass deforming a pure N=2 super Yang-Mills theory. Relying on supersymmetric results\, dynamical abelianization and monopole condensation\, we are able to get to the description of an infrared (IR) phase as an abelian theory flowing to a CP1 sigma model. In this scenario\, the IR phase has an emergent non-invertible symmetry\, which is matched with the non-invertible symmetry of the IR CP1 phase. This result illustrates how an emergent non-invertible symmetry can be used to provide a bridge connecting gauge theories at strong coupling and their IR via dynamical abelianization. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_111824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241115T120000
DTEND;TZID=America/New_York:20241115T130000
DTSTAMP:20241115T144349Z
CREATED:20240919T144643Z
LAST-MODIFIED:20241115T144349Z
UID:10003524-1731672000-1731675600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Quantum Criticality in Black Hole Scattering
DESCRIPTION:Member Seminar \nSpeaker: Uri Kol \nTitle: Quantum Criticality in Black Hole Scattering \nAbstract: Perturbation theory around rotating black holes captures a few important effects in the physics of gravitational waves emitted from binary mergers. Despite a long and rich history\, developing a qualitative understanding of the system remains a challenging problem. In this talk I will describe an emergent critical phenomena arising in black hole perturbation theory\, which is reminiscent of the structure found in quantum many-body systems. A critical point is identified at zero temperature\, giving rise to a wide “quantum” critical region at finite temperatures that is dominated by critical fluctuations. In the critical region\, the physics is exclusively described by a set of critical exponents\, therefore leading to robust predictions. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar-111524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-11.15.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241114T100000
DTEND;TZID=America/New_York:20241114T110000
DTSTAMP:20241112T151542Z
CREATED:20241107T191256Z
LAST-MODIFIED:20241112T151542Z
UID:10003598-1731578400-1731582000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:(Un)likely intersections
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Tom Scanlon\, UC Berkeley \nTitle: (Un)likely intersections\n\nAbstract: The Zilber-Pink conjectures predicts that for an ambient special variety  (such as an abelian variety or a Shimura variety)\, if   is an irreducible algebraic subvariety which is not contained a proper special subvariety of  (e.g. a proper algebraic subgroup in the abelian variety case or a variety of Hodge type in the case of Shimura varieties)\, then the union of the unlikely intersections  as  ranges over the special subvarieties of  with  is not Zariski dense in .  While various instances of this conjecture have been proven\, it remains open in most cases of interest.  In this lecture\, I will describe some of my work with Jonathan Pila in which we prove an effective function field version of this conjecture along with a counterpart to the Zilber-Pink conjecture proven with Sebastian Eterović:  after accounting for some geometric obstructions\, the likely intersections\, i.e. the union of the intersections  with  special and \,  are dense in the Euclidean topology in .   Our techniques for both results come from o-minimal complex analysis and differential algebra.\n\n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathphys_111424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.14.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241112T110000
DTEND;TZID=America/New_York:20241112T120000
DTSTAMP:20241107T211753Z
CREATED:20240903T192017Z
LAST-MODIFIED:20241107T211753Z
UID:10003427-1731409200-1731412800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:pp Waves: Quasinormal Modes & Hidden Symmetries of Black Holes
DESCRIPTION:General Relativity Seminar \nSpeaker: Ahmed Seta\, Harvard University \nTitle: pp Waves: Quasinormal Modes & Hidden Symmetries of Black Holes \nAbstract: The spectrum of quasinormal modes of 4D flat space black holes is not analytically tractable\, but there are two asymptotic limits where the QNM spectrum is under control: weak damping and strong damping. In this talk\, I will explain how these asymptotic QNMs are controlled by dynamical symmetries of the wave equation in certain kinematic limits.  These two asymptotic limits are\, in turn\, captured by the two classes of bound null geodesics in the black hole geometry: the photon ring and the horizon. I will also discuss the Penrose limit: a scaling limit into the geometry experienced by these geodesics\, which results in a plane-wave spacetime where the dynamical symmetries get enhanced into isometries.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/general-relativity-seminar-111224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-GR-Seminar-11.12.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241108T120000
DTEND;TZID=America/New_York:20241108T130000
DTSTAMP:20241105T154430Z
CREATED:20240919T144552Z
LAST-MODIFIED:20241105T154430Z
UID:10003523-1731067200-1731070800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:ADHM spaces and their quantizations
DESCRIPTION:Member Seminar \nSpeaker: Vasily Krylov\, CMSA \nTitle: ADHM spaces and their quantizations \nAbstract: In their paper “Construction of Instantons\,” Atiyah\, Drinfeld\, Hitchin\, and Manin introduced an algebraic construction of the moduli space of instantons on R^4\, now also known as the “ADHM space.” This is a Poisson complex variety; it has been actively studied by both mathematicians and physicists. In this talk\, I will review the ADHM construction\, present examples\, and discuss various geometric and algebraic properties of ADHM spaces. I will also describe natural quantizations of these Poisson varieties. I will explain a joint result with Etingof\, Losev\, and Simental\, providing explicit formulas for the dimensions and characters of all finite-dimensional representations of these quantizations. Time permitting\, I will illustrate some predictions of the 3D mirror symmetry in the example of ADHM spaces\, following our joint paper with Shlykov.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar-11824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-11.8.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241107T100000
DTEND;TZID=America/New_York:20241107T110000
DTSTAMP:20241104T171029Z
CREATED:20241104T150020Z
LAST-MODIFIED:20241104T171029Z
UID:10003597-1730973600-1730977200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Bounds and Dualities of Type II Little String Theories
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Fabian Ruehle (Northeastern University) \nTitle: Bounds and Dualities of Type II Little String Theories \nAbstract: The goal of this seminar is to introduce Type II Little String Theories (LSTs)\, which are six-dimensional supersymmetric QFTs. We explore how to geometrically engineer these theories within the context of M-/F-theory (top-down) as well as consistent QFT realizations (bottom-up). After that\, we turn to the worldsheet theory of LSTs\, which are two-dimensional N=(0\,4) SCFTs. Using anomaly inflow and unitarity\, we derive strong constraints on the rank of their global symmetry algebras.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathphys_11724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-11.7.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241106T140000
DTEND;TZID=America/New_York:20241106T150000
DTSTAMP:20241108T192620Z
CREATED:20241021T164918Z
LAST-MODIFIED:20241108T192620Z
UID:10003617-1730901600-1730905200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Dylan Foster\, Microsoft Research \nTitle: Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning \nAbstract: Imitation learning (IL) aims to mimic the behavior of an expert in a sequential decision making task by learning from demonstrations\, and has been widely applied to robotics\, autonomous driving\, and autoregressive language generation. The simplest approach to IL\, behavior cloning (BC)\, is thought to incur sample complexity with unfavorable quadratic dependence on the problem horizon\, motivating a variety of different online algorithms that attain improved linear horizon dependence under stronger assumptions on the data and the learner’s access to the expert.In this talk\, we revisit the apparent gap between offline and online IL from a learning-theoretic perspective\, with a focus on general policy classes up to and including deep neural networks. Through a new analysis of behavior cloning with the logarithmic loss\, we will show that it is possible to achieve horizon-independent sample complexity in offline IL whenever (i) the range of the cumulative payoffs is controlled\, and (ii) an appropriate notion of supervised learning complexity for the policy class is controlled. When specialized to stationary policies\, this implies that the gap between offline and online IL is smaller than previously thought. We will then discuss implications of this result and investigate the extent to which it bears out empirically. \nBio: Dylan Foster is a principal researcher at Microsoft Research\, New York. Previously\, he was a postdoctoral fellow at MIT\, and received his PhD in computer science from Cornell University\, advised by Karthik Sridharan. His research focuses on problems at the intersection of machine learning\, AI\, interactive decision making. He has received several awards for his work\, including the best paper award at COLT (2019) and best student paper award at COLT (2018\, 2019). \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/newtech_11624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-NTM-Seminar-11.6.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241104T163000
DTEND;TZID=America/New_York:20241104T173000
DTSTAMP:20241016T202352Z
CREATED:20240903T195045Z
LAST-MODIFIED:20241016T202352Z
UID:10003436-1730737800-1730741400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The mathematics of evolution
DESCRIPTION:Colloquium \nSpeaker: Martin Nowak (Harvard) \nTitle: The mathematics of evolution \nAbstract: All living systems are guided by evolutionary dynamics. Evolution is a search process which occurs in populations of reproducing individuals. The three fundamental forces of evolution are mutation\, selection and cooperation. I will present basic ideas in the mathematical description of evolutionary dynamics\, including quasi-species theory\, evolutionary game theory\, and evolutionary graph theory. I will discuss specific problems such as origin of life\, emergence of complexity\, mechanisms of cooperation\, evolution of cancer and how to overcome resistance to targeted therapy. \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/colloquium-11424/
LOCATION:CMSA Room G10\, 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-11.4.2024.docx.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241031T100000
DTEND;TZID=America/New_York:20241031T110000
DTSTAMP:20241022T180010Z
CREATED:20241022T175333Z
LAST-MODIFIED:20241022T180010Z
UID:10003596-1730368800-1730372400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mirror Construction for Nakajima Quiver Varieties
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Ju Tan (Boston University) \nTitle: Mirror Construction for Nakajima Quiver Varieties \nAbstract: Quiver possesses a rich representation theory. On the one hand\, it exhibits a deep connection with instantons and coherent sheaves as illuminated by the ADHM construction and the works of many others. On the other hand\, quivers also capture the formal deformation space of a Lagrangian submanifold. In this talk\, we will discuss these relations more explicitly from the perspective of SYZ mirror symmetry. In particular\, we will introduce the notion of framed Lagrangian immersions\, the Maurer-Cartan deformation spaces of which are Nakajima quiver varieties/ stacks. Besides\, we will realize the ADHM construction as a mirror symmetry phenomenon. This is based on the joint work with Jiawei Hu and Siu-Cheong Lau. \n  \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mathphys_103124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=application/pdf:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-10.31.2024.docx.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241028T090000
DTEND;TZID=America/New_York:20241030T170000
DTSTAMP:20241106T191859Z
CREATED:20240105T032648Z
LAST-MODIFIED:20241106T191859Z
UID:10001111-1730106000-1730307600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Mathematics and Machine Learning Closing Workshop
DESCRIPTION:Mathematics and Machine Learning Closing Workshop \nDates: October 28 – Oct. 30\, 2024 \nLocation: Room G10\, CMSA\, 20 Garden Street\, Cambridge MA \nThe closing workshop will provide a forum for discussing the most current research in these areas\, including work in progress and recent results from program participants. We will devote one day to frontier topics in interactive theorem proving\, such as mathematical library development and AI for mathematical search and theorem proving. \n  \nYoutube Playlist \n \nOrganizers \n\nFrancois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nMichael Freedman (Harvard CMSA)\nFabian Ruehle (Northeastern)\nGeordie Williamson (Univ. of Sydney)\n\nSpeakers \n\nAnkit Anand\, Google Deepmind Montreal\nJeremy Avigad\, Carnegie Mellon University\nAngelica Babei\nMatej Balog\, Deepmind\nGergely Bérczi\, Aarhus University\nTristan Buckmaster\, New York University\nGiorgi Butbaia\, University of New Hampshire\nEdgar Costa\, MIT\nAlex Davies\, DeepMind\nBin Dong\, Beijing International Center for Mathematical Research\nKit Fraser-Taliente\, University of Oxford\nJavier Gomez-Serrano\, Brown University\nJim Halverson\, Northeastern University\nThomas Harvey\, MIT\nAmaury Hayat\, Ecole des Ponts Paristech\nYang-Hui He\, City University of London\nJürgen Jost\, Max Planck Institute for Mathematics in the Sciences\nPetros Koumoutsakos\, Harvard University\nKyu-Hwan Lee\, University of Connecticut\nDavid Lowry-Duda\, ICERM\nStephane Mallat\, Flatiron/College de France\nAbbas Mehrabian\, Google Deepmind Montreal\nCengiz Pehlevan\, Harvard University\nFabian Ruehle\, Northeastern University\nEric Vanden-Eijnden\, Courant/NYU\nAdam Wagner\, Worcester Polytechnic Institute\nMelanie Matchett Wood\, Harvard University\n\n  \nSchedule (download PDF) \nMonday Oct. 28\, 2024 \n9:00–9:30 amMorning refreshments \n9:30–9:45 amIntroductions \n9:45–10:45 amJürgen Jost\, Max Planck Institute for Mathematics in the Sciences \nTitle: Data visualization with category theory and geometry \nAbstract: While data often come in a high-dimensional feature space\, they typically exhibit intrinsic constraints and regularities\, and they can therefore often be represented on a lower-dimensional\, but possibly highly curved Riemannian manifold. Still\, for visualization purposes\, that dimension still needs to be lowered to 2 or 3. We present the mathematical foundations for such schemes\, in particular UMAP\, and describe an improved such method. \n10:45–11:00 amBreak \n11:00 am–12:00 pmAnkit Anand\, Google Deepmind Montreal\, Abbas Mehrabian\, Google Deepmind Montreal \nTitle: From Theorem Proving to Disproving: Modern machine learning versus classical heuristic search in automated theorem proving and extremal graph theory \nAbstract: Machine learning is widely believed to outperform classical methods\, but this is not always the case. Firstly\, we describe how we adapted the idea of hindsight experience replay from reinforcement learning to the automated theorem proving domain\, so as to use the intermediate data generated during unsuccessful proofs. We show that provers trained in this way can outperform previous machine learning approaches and compete with the state-of-the-art heuristic-based theorem prover E in its best configuration\, on the popular benchmarks MPTP2078\, M2k and Mizar40. The proofs generated by our algorithm are also almost always significantly shorter than E’s proofs. Based on this paper\, which was presented at ICML 2022: https://proceedings.mlr.press/v162/aygun22a.html. Secondly\, we study a central extremal graph theory problem inspired by a 1975 conjecture of Erdős\, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero\, a neural network-guided tree search\, with tabu search\, a heuristic local search method. Using either method\, by introducing a curriculum—jump-starting the search for larger graphs using good graphs found at smaller sizes—we improve the state-of-the-art lower bounds for several sizes. Joint work with Tudor Berariu\, Joonkyung Lee\, Anurag Murty Naredla\, Adam Zsolt Wagner\, and other colleagues at Google DeepMind. Based on this paper\, which was presented at IJCAI 2024: https://arxiv.org/abs/2311.03583. \n12:00–1:30 pmLunch Break \n1:30–2:30 pmFabian Ruehle\, Northeastern University\, Giorgi Butbaia\, University of New Hampshire \nTitle: Rigorous results 
from ML using RL \nAbstract: We explain how to use Reinforcement Learning in Mathematics to obtain provably correct results. After a brief introduction to Reinforcement Learning\, I will illustrate the idea using an example from Number Theory\, where we solve a Diophantine Equation related to String Theory\, and two from Knot Theory. The first knot theory problem is to identify unknots\, while the second is concerned with identifying so-called ribbon knots. The latter play an important role in the search for counter-examples to the smooth Poincare conjecture. \n2:30–2:45 pmBreak \n2:45–3:45 pmCengiz Pehlevan\, Harvard University \nTitle: Solvable Models of Scaling and Emergence in Deep Learning \n3:45–4:00 pmBreak \n4:00–4:30 pmMatej Balog\, Deepmindvia Zoom \nTitle: FunSearch: Mathematical discoveries from program search with large language models \nAbstract: Large language models (LLMs) have demonstrated tremendous capabilities in solving complex tasks\, from quantitative reasoning to understanding natural language. However\, LLMs sometimes suffer from confabulations (or hallucinations)\, which can result in them making plausible but incorrect statements. This hinders the use of current large models in scientific discovery. We introduce FunSearch (short for searching in the function space)\, an evolutionary procedure based on pairing a pretrained LLM with a systematic evaluator. We demonstrate the effectiveness of this approach to surpass the best-known results in important problems\, pushing the boundary of existing LLM-based approaches. Applying FunSearch to a central problem in extremal combinatorics—the cap set problem—we discover new constructions of large cap sets going beyond the best-known ones\, both in finite dimensional and asymptotic cases. This shows that it is possible to make discoveries for established open problems using LLMs. We showcase the generality of FunSearch by applying it to an algorithmic problem\, online bin packing\, finding new heuristics that improve on widely used baselines. In contrast to most computer search approaches\, FunSearch searches for programs that describe how to solve a problem\, rather than what the solution is. Beyond being an effective and scalable strategy\, discovered programs tend to be more interpretable than raw solutions\, enabling feedback loops between domain experts and FunSearch\, and the deployment of such programs in real-world applications. \n4:30–5:00 pmEdgar Costa\, MIT \nTitle: Machine learning L-functions \nAbstract: We report on multiple experiments related to L-functions data. L-functions are complex functions that encode significant information about number theory and algebraic geometry\, playing a crucial part in the Langlands program\, a foundational set of conjectures connecting number theory with other mathematical domains. We focused on two L-function datasets. The first includes about 250k rational L-functions of small arithmetic complexity with diverse origins. Multiple dimensionality reduction techniques were used to analyze invariants and behavioral trends\, focusing on how differing origins impact the results. The second dataset is composed of L-functions associated with Maass forms. Although these L-functions are non-rational\, they also share the low arithmetic complexity of the first dataset. The crux of our investigation here is determining whether this set manifests similar characteristics to the first one. Based on this exploration\, we propose a simple heuristic method to deduce their Fricke sign\, an unknown invariant for 40% of the data. This is joint work with: Joanna Biere\, Giorgi Butbaia\, Alyson Deines\, Kyu-Hwan Lee\, David Lowry-Duda\, Tom Oliver\, Tamara Veenstra\, and Yidi Qi. \n  \n  \nTuesday Oct. 29\, 2024  \n9:15–9:45 amMorning refreshments \n9:45–10:45 amYang-Hui He\, London Institute for Mathematical Sciences Via Zoom \nTitle: AI assisted mathematics \nAbstract: We argue how AI can assist mathematics in three ways: theorem-proving\, conjecture formulation\, and language processing. Inspired by initial experiments in geometry and string theory in 2017\, we summarize how this emerging field has grown over the past years\, and show how various machine-learning algorithms can help with pattern detection across disciplines ranging from algebraic geometry to representation theory\, to combinatorics\, and to number theory.  At the heart of the program is the question how does AI help with theoretical discovery\, and the implications for the future of mathematics. \n10:45–11:00 amBreak \n11:00 –11:30Angelica Babei \nTitle: Learning Euler factors of elliptic curves with transformers \nAbstract: The L-function of an elliptic curve is at the core of the BSD conjecture\, and its Euler factors encode important arithmetic information about the curve. For example\, understanding these Euler factors using machine learning techniques has recently led to discovering the phenomenon of murmurations. In this talk\, we present some results on learning Euler factors based on 1. other nearby factors\, and 2. the Weierstrass equation of the curve.  \n11:30–12:00 pmDavid Lowry-Duda\, ICERM \nTitle: Exploring patterns in number theory with deep learning: a case study with the Möbius and squarefree indicator functionsAbstract: We report on experiments using neural networks and Int2Int\, the integer sequence to integer sequence transformer made by François Charton for this CMSA program. We initially study the Möbius function. This function appears as the coefficients of the reciprocal of the Riemann zeta function and is famously hard to understand. Predicting the Möbius function is closely related to predicting the squarefree indicator function\, leading us to perform similar experiments there. Finally\, we’ll discuss how varying the input representation and model affects the strength of the predictions and allows us to explain most (but not all) of the predictive strength and behavior. \n12:00–1:30 pmLunch \n1:30–2:30 pmAmaury Hayat\, Ecole des Ponts Paristech\, Melanie Matchett Wood\, Harvard University\, Alex Davies\, DeepMind\, Jeremy Avigad\, Carnegie Mellon University \nTitle: Machine learning and theorem proving \nAbstract: Recent successes in machine learning have raised hopes that neural networks could one day assist mathematicians in proving theorems. This raises the question of an appropriate setting to apply machine learning methods to theorem proving. Formal languages\, such as Lean\, provide automatic verification of mathematical proofs and thus offer a natural environment. Nevertheless\, some challenges emerge\, particularly because these languages are often designed to verify correctness rather than find a solution\, while mathematicians often perform reasoning steps to do both at the same time. This talk will present recent applications of machine learning methods to theorem proving in Lean\, highlight current challenges\, and explore what these developments might mean for the future of mathematics. \n  \n2:30–2:45 pmBreak \n2:45–3:45 pmAdam Wagner\, Worcester Polytechnic Institute\, Kit Fraser-Taliente\, University of Oxford\, Gergely Bérczi\, Aarhus University\, Thomas Harvey\, MIT \nTitle: Sparse subgraphs of the d-cube with diameter d \nAbstract: Erdos et al studied spanning subgraphs of the $d$-cube which have the same diameter $d$ as the cube itself. They asked the following natural question: what is the maximum number of edges one can delete from the $d$-dimensional hypercube\, without increasing its diameter? We will discuss how we can use PatternBoost\, a simple machine learning algorithm that alternates local and global optimization steps\, to find good constructions for this problem \n3:45–4:00 pmBreak \n4:00–4:30 pmPetros Koumoutsakos\, Harvard University \n4:30–5:00 pm \nStéphane Mallat\,  Flatiron/College de France \nTitle: Image Generation by Score Diffusion and the Renormalisation Group \nAbstract: Score based diffusions generate impressive models of images\, sounds and complex physical systems. Are they generalising or memorising? How can deep network estimate high-dimensional scores without curse of dimensionality? This talk shows that generalisation does occur for deep network estimation of scores\, with enough training data.  The ability to avoid the curse of dimensionality seems to rely on multiscale properties revealed by a renormalisation group decomposition coming from statistical physics. Applications to models of turbulences will be introduced and discussed. \n  \nWednesday Oct. 30\, 2024 \n9:15–9:45 amMorning refreshments \n9:45–10:45 amBin Dong\, Beijing International Center for Mathematical Research(via Zoom)  \nTitle: AI for Mathematics: From Digitization to Intelligentization \nAbstract: This presentation explores the synergistic relationship between AI and mathematics\, beginning with a brief historical overview of their mutually beneficial interactions. It then examines notable existing work in AI for mathematics\, highlighting their achievements and limitations.  Next\, I will share preliminary findings from the ongoing AI4M research project at Peking University\, including our work on creating high-quality mathematical datasets through formalization (digitization)\, and our future plans for developing intelligent applications using these datasets. The presentation concludes with a forward-looking perspective on the opportunities and challenges within this exciting interdisciplinary field. \n10:45–11:00 am Break \n11:00 am–12:00 pm Eric Vanden-Eijnden\, Courant/NYUvia Zoom \nTitle: Generative modeling with flows and diffusions\, with applications to scientific computing. \nAbstract: Generative models based on dynamical transport have recently led to significant advances in unsupervised learning. At mathematical level\, these models are primarily designed around the construction of a map between two probability distributions that transform samples from the first into samples from the second.  While these methods were first introduced in the context of image generation\, they have found a wide range of applications\, including in scientific computing where they offer interesting ways to reconsider complex problems once thought intractable because of the curse of dimensionality. In this talk\, I will discuss the mathematical underpinning of generative models based on flows and diffusions\, and show how a better understanding of their inner workings can help improve their design. These results indicate how to structure the transport to best reach complex target distributions while maintaining computational efficiency\, both at learning and sampling stages.  I will also discuss applications of generative AI in scientific computing\, in particular in the context of application with models and no data (as opposed to the more standard data andno model)\, such as Monte Carlo sampling\, with applications to the statistical mechanics and Bayesian inference\, as well as the numerical integration and interpretation of random dynamical systems driven out of equilibrium. \n12:00–1:30 pm Lunch \n1:30–2:30 pm Kyu-Hwan Lee\, University of Connecticut \nTitle: Discovering New Mathematical Structures with Machine Learning \nAbstract: Can machine learning help discover new mathematical structures? In this talk\, I will present two case studies: murmurations in number theory and loadings of partitions related to Kronecker coefficients in representation theory and combinatorics. The focus will be on the paradigm of examining mathematical objects collectively\, rather than individually\, to create datasets suitable for machine learning experiments and interpretations. \n2:30–2:45 pm Break \n2:45–3:45 pm James Halverson\, Northeastern University \nTitle: Learning the Topological Invariance of Knots \nAbstract: This talk focuses on using machine learning for the defining problem in knot theory\, the classification of knots up to ambient space isotopy. We will train transformers and convolutional neural networks to distinguish topologically inequivalent knots\, given only representatives of the classes and no a priori knowledge of topological invariants. In this scheme\, we find that equivalent knots are well-clustered in the embedding space of the neural network\, and a trained decoder maps effectively from the embedding space back to knot space. Preliminary results will be presented on a new approach to resolving the Jones unknot conjecture. \n3:45–4:00 pmBreak \n4:00–5:00 pm Tristan Buckmaster\, New York University\, Javier Gomez-Serrano\, Brown Universityvia Zoom \n  \n  \nImage by Sue Side. https://www.sueside.com/\n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mmlworkshop_1024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/ML_Closing-workshop_v3-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241025T120000
DTEND;TZID=America/New_York:20241025T130000
DTSTAMP:20241022T155009Z
CREATED:20240919T144515Z
LAST-MODIFIED:20241022T155009Z
UID:10003522-1729857600-1729861200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Formality Theorem and Webs
DESCRIPTION:Member Seminar \nSpeaker: Ahsan Khan \nTitle: Formality Theorem and Webs \nAbstract: The “formality theorem” of Kontsevich was a key result that implies that every Poisson manifold admits a deformation quantization. I will review the ideas behind the formality theorem and discuss a potentially novel viewpoint on it involving webs and twisted masses.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/member-seminar-102524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=application/pdf:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Member-Seminar-10.25.24.docx.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241025T103000
DTEND;TZID=America/New_York:20241025T120000
DTSTAMP:20240912T145420Z
CREATED:20240912T144420Z
LAST-MODIFIED:20240912T145420Z
UID:10003501-1729852200-1729857600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/mml_meeting_102524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241025T090000
DTEND;TZID=America/New_York:20241025T103000
DTSTAMP:20241018T221702Z
CREATED:20240907T194046Z
LAST-MODIFIED:20241018T221702Z
UID:10003469-1729846800-1729852200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The spin-statistics theorem for TFTs
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Luuk Stehouwer\, Dalhousie University \nTitle: The spin-statistics theorem for TFTs \nAbstract: In quantum field theory (QFT) the spin-statistics theorem says that in a unitary QFT\, a particle has half-integer spin if and only if it is a fermion. I show how to phrase this statement in the language of functorial field theories. More precisely\, I explain when a functorial field theory “has fermions” and “has spinors” and when they are “related”. I will then restrict to topological field theories (TFTs) and define unitary TFTs. There are counterexamples of the spin-statistics theorem for non-unitary TFTs. I will prove that every unitary TFT satisfies the spin-statistics theorem. \n  \n  \n 
URL:https://live-hu-cmsa-222.pantheonsite.io/event/qm_102524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QFT-and-Physical-Mathematics-10.25.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241024T143000
DTEND;TZID=America/New_York:20241024T154500
DTSTAMP:20240930T200138Z
CREATED:20240930T200138Z
LAST-MODIFIED:20240930T200138Z
UID:10003609-1729780200-1729784700@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://live-hu-cmsa-222.pantheonsite.io/event/deeplearning_102424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241023T140000
DTEND;TZID=America/New_York:20241023T150000
DTSTAMP:20241108T192710Z
CREATED:20241021T140701Z
LAST-MODIFIED:20241108T192710Z
UID:10003616-1729692000-1729695600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Aryo Lotfi (EPFL) \nTitle: How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad \nAbstract: Can Transformers predict new syllogisms by composing established ones? More generally\, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity\, but this does not address the learnability objective. This paper puts forward the notion of ‘globality degree’ of a target distribution to capture when weak learning is efficiently achievable by regular Transformers\, where the latter measures the least number of tokens required in addition to the tokens histogram to correlate nontrivially with the target. As shown experimentally and theoretically under additional assumptions\, distributions with high globality cannot be learned efficiently. In particular\, syllogisms cannot be composed on long chains. Furthermore\, we show that (i) an agnostic scratchpad cannot help to break the globality barrier\, (ii) an educated scratchpad can help if it breaks the globality at each step\, however not all such scratchpads can generalize to out-of-distribution (OOD) samples\, (iii) a notion of ‘inductive scratchpad’\, that composes the prior information more efficiently\, can both break the globality barrier and improve the OOD generalization. In particular\, some inductive scratchpads can achieve length generalizations of up to 6x for some arithmetic tasks depending on the input formatting.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/newtech_102324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=application/pdf:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-NTM-Seminar-10.23.24.docx-1-1.pdf
END:VEVENT
END:VCALENDAR