Colloquia & Seminars

Title: Complete Calabi-Yau Metrics and Optimal Transport

Differential Geometry and Physics Seminar Speaker: Tristan Collins, University of Toronto Title: Complete Calabi-Yau Metrics and Optimal Transport Abstract: I will discuss the connection between optimal transport and the existence of complete Calabi-Yau metrics on log Calabi-Yau varieties.  I will explain how the geometric problem of constructing complete Calabi-Yau metrics gives rise to problems in the boundary regularity theory for optimal transport, and how ideas from geometry can be used to make progress on some of these problems.  This talk will survey joint works with Li, Tong, Tong-Yau, Firester, and Tong-Firester.

Title: Algebra Seminar

Algebra Seminar  

Title: Some results about saturation

Member Seminar Speaker: Stephen Landsittel Title: Some results about saturation Abstract: Given a local ring R we can ask when saturation of ideals in R commutes with other operations on ideals (such as extension to a ring containing R). We show that the condition that extension of ideals along a ring map R \to S commutes with saturation controls inherent properties of the rings R & S, such as Cohen-Macaulayness and unramifiedness.

Title: Freedman Seminar: Michael Freedman, CMSA & Slava Krushkal, University of Virginia

Freedman Seminar Speakers: Michael Freedman, CMSA and Slava Krushkal, University of Virginia (2-3 pm and 3:15-4:15 pm) Title: Formulating 4D surgery for AI agents Abstract: The topological category surgery exact sequence is still open for free groups (and most groups of exponential growth). The lack of knowledge is about both surgery and s-cobordism; and the source of the mystery is the same in both cases. Thinking about how to present this problem to AIs has had its own value. In a pair of talks we will explain how we have thought about the problem in the past and how we are thinking about it now.

Title: Reflexive Polytopes and the Convergence of Feynman Integrals

Quantum Field Theory and Physical Mathematics Seminar Speaker: Pierre Vanhove (Institute of Theoretical Physics - Saclay) Title: Reflexive Polytopes and the Convergence of Feynman Integrals Abstract: In the parametric representation, Feynman integrals can be viewed as Euler integrals defined by the Symanzik polynomials of a graph. The convergence properties of these integrals are intimately tied to the combinatorial geometry of their associated Newton polytopes; specifically, finiteness is guaranteed when the polytope contains interior points. We present a classification of Feynman integrals associated with polytopes containing a unique interior point, identifying a subset that are reflexive. Our results show that such reflexive polytopes are surprisingly scarce within the space of Feynman graphs. We conclude by computing several infinite families...

Title: Bijections for hyperplane arrangements of Coxeter type

Colloquium Speaker: Olivier Bernardi, Brandeis University Title: Bijections for hyperplane arrangements of Coxeter type Abstract: This talk is about real hyperplane arrangements whose hyperplanes are of the form {xi −xj = s} or {xi +xj = s}. We describe a bijective framework for a large family of such arrangements which we call transitive. For each transitive arrangement A, we give a bijection between the regions of A and a set of decorated trees. Particular cases include the families of Catalan, Shi, semiorder and Linial arrangements in type A, B, C, D and BC. We also derive some general enumerative formulas for such families of transitive arrangements.

Title: Geometry and Quantum Theory Seminar

Geometry and Quantum Theory Seminar Speakers: Dan Freed and Bowen Yang

Title: Automated Theory Formation and Interestingness in Mathematics

New Technologies in Mathematics Seminar Speaker: George Tsoukalas, UT Austin Dept. of Computer Science and Google DeepMind. Title: Automated Theory Formation and Interestingness in Mathematics Abstract: Advances in modern learning systems are beginning to demonstrate utility for select problems in research mathematics. A broader challenge is that of developing new theories automatically. This area has a rich history, and is tied to some of the earliest work in AI. In particular, a central question in this study was measuring the "interestingness" of mathematical concepts. In this talk, I will review this historical context and present our recent work on using large language models to synthesize interestingness measures that guide theory exploration in elementary number theory from scratch. I will conclude...

Title: Differential Geometry and Physics Seminar

Differential Geometry and Physics Seminar Speaker: Monica Jinwoo Kang, Texas A&M University

Title: Differential Geometry and Physics Seminar

Differential Geometry and Physics Seminar Speaker: Yinan Wang, Peking University

Title: Algebra Seminar

Algebra Seminar  

Title: Member Seminar

Member Seminar  

Title: Quantum Field Theory and Physical Mathematics Seminar

Quantum Field Theory and Physical Mathematics Seminar Speaker: tba

Title: Colloquium

Colloquium Speaker: Pankaj Metha, Boston University

Title: Geometry and Quantum Theory Seminar

Geometry and Quantum Theory Seminar Speaker: Sanjay Raman