Program on Classical, quantum, and probabilistic integrable systems - novel interactions and applications Dates: March 24–May 24, 2025 Location: CMSA, 20 Garden Street, Cambridge MA 02138 Register Online Exactly solvable models have played pivotal roles in mathematics and physics throughout their history. The program is dedicated to exploring and developing a more recent wave of […]
Quantum Field Theory and Physical Mathematics Seminar Speaker: Cameron Krulewski, MIT Title: Homotopical Methods for Free and Interacting Fermionic SPTs Abstract: We develop and compute homotopical "free-to-interacting maps" to compare classifications of fermionic symmetry-protected topological phases (SPTs), determining when such phases are stable under interactions or, alternatively, interaction-enabled. Generalizing work of Freed-Hopkins, we construct maps […]
General Relativity Seminar Speaker: Sifan Yu, National University of Singapore Title: Low-regularity Local Well-posedness of the Elastic Wave System Abstract: In this talk, I will present a recent work on the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials, we prove a low-regularity local well-posedness result for the corresponding elastic wave equations. For such materials, we can split the […]
Geometry and Quantum Theory Seminar Speaker: Bowen Yang, CMSA Title: Introduction to the probabilistic approach to Louville theory III Abstract: I will continue with the construction of Liouville CFT from probabilistic methods, following a review by Guillarmou, Kupiainen, and Rhodes (arXiv:2403.12780). The talk will emphasize technical aspects of Gaussian free fields (GFF) and contrast them with Brownian […]
https://youtu.be/mwpbMSNZOh0 New Technologies in Mathematics Seminar Speaker: Michael Albergo (Harvard) Title: Learning Dynamical Transport without Data Abstract: Algorithms based on dynamical transport of measure, such as score-based diffusion models, have resulted in great progress in the field of generative modeling. However, these algorithms rely on access to an abundance of data from the target distribution. […]
Mathematical Physics and Algebraic Geometry Seminar Speaker: Rafael Álvarez García (Harvard University) Title: (Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture Abstract: We analyze infinite-distance limits in the complex structure moduli space of six-dimensional F-theory, providing an algebro-geometric classification and a physical interpretation. From the point of view of the Swampland Program, the motivation is to understand the […]
When: April 4, 2025 - April 5, 2025 Where: Science Center Hall C Address: 1 Oxford Street, Cambridge, MA 02138, United States Speaker: Michael Chapman - NYU | Pazit Haim-Kislev - Institute for Advanced Study | Jianfeng Lin - Tsinghua University | Laura Monk - University of Bristol | Ramon van Handel - Princeton University IN-PERSON REGISTRATION Limited […]
Member Seminar Speaker: Hugo Cui Title: Learning diffusion models in high-dimensions Abstract: We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of […]
Full Name Role Office # Affiliation Dates Email Address Amol Aggarwal Classical, Quantum, and Probabilistic Integrable Systems Program Organizer 203 Columbia University & Clay Mathematics Institute amolagga@gmail.com Guillaume Barraquand Classical, Quantum, and Probabilistic Integrable Systems Program Organizer 207 École normale supérieure, Paris guillaume.barraquand@ens.fr Denis Bernard Classical, Quantum, and Probabilistic Integrable Systems Program Organizer 207 École […]
Quantum Field Theory and Physical Mathematics Seminar Speaker: Matthew Yu (Oxford) Title: A new tangential structure for type IIA string theory Abstract: The Green-Schwarz anomaly cancellation condition says that the target space of heterotic string theory must come with a string structure for the theory to be consistent. In this talk we discuss a new tangential […]
Colloquium Speaker: Ben Webster, University of Waterloo & Perimeter Institute Title: 3-d Mirror Symmetry Abstract: I'll give an introduction (or update, for those who've been introduced) to 3d mirror symmetry from the perspective of a mathematician.
https://youtu.be/JJ88e4H4b8Q CMSA/Tsinghua Math-Science Literature Lecture Date: April 8, 2025 Time: 9:00 - 10:30 am ET Location: CMSA G10, 20 Garden Street, Cambridge MA & via Zoom Speaker: Scott Sheffield (MIT) Title: Yang-Mills theory and random surfaces Abstract: The Clay Institute famously offered one million dollars to anyone who could mathematically construct and understand a certain continuum […]
CMSA Q&A Seminar Speaker: Eric Maskin, Harvard University Topic: The Mathematics of Voting
https://youtu.be/zvvUFPOwseo New Technologies in Mathematics Seminar Speaker: Baran Hashemi, Technical University of Munich Title: Can Transformers Do Enumerative Geometry? Abstract: How can Transformers model and learn enumerative geometry? What is a systematic procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Neural Enumerative Reasoning model for computation of ψ-class intersection numbers on the moduli space […]
Mathematical Physics and Algebraic Geometry Seminar Speaker: Ki Fung Chan (Chinese University of Hong Kong) Title: 3d Mirror Symmetry is 2d Mirror Symmetry Abstract: We introduce an approach to studying 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex […]
Member Seminar Speaker: Bowen Yang Title: Homological Invariants in Translation-Invariant Pauli Stabilizer Codes Abstract: Pauli stabilizer codes serve as foundational models in quantum error correction and the study of exotic quantum phases. In this talk, we explore the application of homological methods to translationally invariant Pauli stabilizer codes with qudits of varying dimensions. We introduce a series of invariants, […]
Quantum Field Theory and Physical Mathematics Seminar Speaker: Mitch Weaver, KAIST Title: The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub-algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified […]
Colloquium Speaker: Andrey Smirnov, University of North Carolina at Chapel Hill Title: Quantum K-theory at roots of unity Abstract: In this talk, I will discuss a version of quantum K-theory introduced by A.Okounkov, which can be defined through quasimap counts. In this framework, the quantum K-theory ring is obtained as a specialization of the equivariant […]
General Relativity Seminar Speaker: Aghil Alaee, Clark University Title: Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds Abstract: One of the fundamental conjectures in mathematical relativity is the positivity of total mass (if it is defined!) for complete non-compact Riemannian manifolds assuming appropriate lower bounds on scalar curvature. This conjecture has been proved for […]
CMSA Q&A Seminar Speaker: Noah Golowich (MIT) Topic: What is length generalization in large language models?
Speaker: Scott Aaronson, Department of Computer Science, University of Texas, Austin Scott Aaronson is the founding director at the Quantum Information Center at the University of Texas at Austin. Date: April 17, 2025 Time: 4:00-5:00 pm ET (Reception following in the Math Common Room) Location: Harvard Science Center Hall A In-person Registration Zoom Webinar Registration […]
Mathematical Physics and Algebraic Geometry Seminar
CMSA Q&A Seminar Speaker: Alexei Borodin (MIT) Topic: Connections between physics and probability
New Technologies in Mathematics Seminar Speaker: Matthias Wilhelm (University of Southern Denmark) Title: Machine learning for analytic calculations in theoretical physics Abstract: In this talk, we will present recent progress on applying machine-learning techniques to improve calculations in theoretical physics, in which we desire exact and analytic results. One example are so-called integration-by-parts reductions of […]
Mathematical Physics and Algebraic Geometry Seminar
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