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 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 their influence […]
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 […]
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 […]
Geometry and Quantum Theory Seminar Speaker: Anadil Saeed Rao, Northeastern University Title: Instantons on Taub-NUT space and Bow Construction Abstract: In this talk I will discuss Yang-Mills Instantons in a very special geometric setting: the Taub-NUT space, which itself is a Gravitational Instanton. In the first part of the talk I will review the essentials of gravitational […]
CMSA Q&A Seminar Speaker: Noah Golowich (MIT) Topic: What is length generalization in large language models?
https://youtu.be/VplMHWSZf5c 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 Title: How Much […]
Colloquium Speaker: Ila Fiete, MIT Title: Modeling the emergence of complex cortical structure from simple precursors in the brain: maps, hierarchies, and modules Abstract: Modular and hierarchical structures are ubiquitous in the brain. Two distinct hypotheses for such morphogenesis involve genetic specification (the positional information hypothesis) or spontaneous structure emergence from symmetry breaking (the pattern […]
General Relativity Seminar Speaker: Christopher Stith, University of Michigan Title: Hyperbolic equations in a double null gauge Abstract: The hyperbolic nature of the Einstein equations is well-known and has been used in many different contexts. More recently, the double null gauge has proven to be a powerful tool for quantitative analysis of the Einstein equations. It has […]
Geometry and Quantum Theory Seminar Speakers: Bryan Wang Peng Jun (Harvard) and Bowen Yang (CMSA) Title: Classifying Space for Phases of Matrix Product States Abstract: In this talk we will introduce recent work of Beaudry-Hermele-Pflaum-Qi-Spiegel-Stephen (arXiv:2501.14241), on constructing a classifying space for phases of matrix product states (MPS).
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 Speaker: Ziming Ji, Northeastern University Title: Mass gap in AdS space Abstract: AdS space can be used as an IR regulator of QFT. The asymptotic conformal boundary in AdS space provides rich, unique observables. We study asymptotic free theories in two-dimensional AdS space. By changing the AdS curvature scale \Lambda […]
Freedman CMSA Seminar Speaker: Slava Dzhenzher, MIPT Title: Adversarial KA Abstract: Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or «expressing» functions, we test its robustness by analyzing its ability to withstand adversarial attacks. We find KA to be robust to countable collections of continuous adversaries, but unearth a […]
Colloquium Speaker: Peter Sarnak, IAS & Princeton University Title: Bass-Note Spectra of locally uniform geometries Abstract: We formulate and report on the problem of the Bass-Note Spectrum of an invariant operator as one varies over locally uniform geometries. In the Euclidean setting this recasts classical problems of Mahler from the geometry of numbers in a new […]
Geometry and Quantum Theory Seminar Speakers: Anadil Saeed Rao (Northeastern) and Vasily Krylov (CMSA/Harvard) Title: Algebraic approach to the bow construction Abstract: Anadil will finish his part of the talk. Vasily will then explain how to understand moduli spaces of instantons on R^4, monopoles on R^3, and instantons on Taub-NUT spaces algebraically as so-called bow varieties. We […]
Mathematical Physics and Algebraic Geometry Seminar Speaker: Fabian Hahner, University of Washington Title: From superspace to twisted supergravity Abstract: In this talk, I will present a geometric perspective on the pure spinor superfield formalism, which proves fruitful for studying twisted supergravity. For eleven-dimensional supergravity, we use this technique to construct the full interacting theory together with […]
Member Seminar Speaker: Han Shao, Harvard CMSA Title: Incentives for data sharing in federated learning Abstract: Federated learning has recently emerged as a powerful approach for enabling collaboration across large populations of learning agents. However, agents may have incentives to defect from the collaboration—that is, to withdraw or contribute less data than expected—due to the […]