Member Seminar Speaker: Sunghyuk Park Title: Quantum UV-IR map and curve counts in skeins Abstract: Quantum UV-IR map (a.k.a. q-nonabelianization map), introduced by Neitzke and Yan, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically, it can be described as a map between skein […]
Speakers: Dan Freed (Harvard Math and CMSA), Denis Auroux (Harvard Math)
https://youtu.be/wTQH6mRDXhw New Technologies in Mathematics Seminar Speaker: Ronen Eldan, Microsoft Research Title: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent Abstract: While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent […]
Member Seminar Speaker: Chuck Doran Title: Modularity of Landau-Ginzburg Models Abstract: Fano varieties are the basic building blocks of algebraic varieties. Smooth Fano varieties have been classified in dimensions one (the projective line), two (del Pezzo surfaces), and three (Mori-Mukai classification). What does Mirror Symmetry have to say about such classifications? By studying the Landau-Ginzburg models mirror to […]
CMSA Q and A Seminar Speakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University) Topics: Michael Douglas: "What is non-commutative field theory?" Mayuko Yamashita: "What is differential cohomology?"
https://youtu.be/Sc6k06wVX3s New Technologies in Mathematics Seminar Speaker: François Charton, Meta AI Title: Transformers for maths, and maths for transformers Abstract: Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics. Problems of […]
Member Seminar Speaker: Kai Xu (CMSA) Title: Moduli of vector bundles on curve and semiorthogonal decomposition Abstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, derived Schur-Weyl duality for current groups and derived […]
Speaker: Yu-Shen Lin (Boston University) Title: Gravitational Instantons Abstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and […]
CMSA Q and A Seminar Speakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign) Topics: Dan Freed: What is framing anomaly? How is it different from other anomalies? Dan Berwick-Evans: What is Atiyah-Singer index theorem?
Member Seminar Speaker: Benjamin McKenna Title: Random matrices and large deviations Abstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years, classical results have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with special integrals over matrix groups. Some of these […]
CMSA Q and A Seminar Speakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA) Topics: Dan Freed: What is Dijkgraaf-Witten theory? Sunghyuk Park: What happened at the Clay Math Institute Workshop?
https://youtu.be/u-pkmdkQoMU New Technologies in Mathematics Seminar Speaker: Alex Gu, MIT Dept. of EE&CS Title: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models Abstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute […]