Colloquia & Seminars

Title: (Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture

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 fate of open-moduli infinite-distance limits in relation with the Distance Conjecture. From an F-theory perspective, the infinite-distance limits correspond to degenerations of elliptic threefolds leading to non-minimal singularities in codimension one and higher. We show how such non-crepant singularities can be removed by a systematic sequence of blow-ups of the bases of the infinite-distance degenerations, making their central fibers a union of log...

Title: Learning diffusion models in high-dimensions

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 the resulting generated density, and evidence how mode(l) collapse can arise.  On the other hand, we discuss how in a case where the architectural bias is suited to the target density, these simple models can efficiently learn to sample from a binary Gaussian mixture target distribution.  

Title: Quantum Field Theory and Physical Mathematics

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 structure called string^h, first introduced by Devalapurkar, as a spin^c analogue of string. Approximating the correct tangential structure of string theory has many implications, primarily is the Swampland program via the cobordism conjecture of Mcnamara and Vafa. We will show that the spectrum of string^h has the notable property that it orients tmf_1(n), just like how the spectrum of string orients tmf, by...

Title: 3-d Mirror Symmetry

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.  

Title: CMSA Q&A Seminar: Eric Maskin

CMSA Q&A Seminar Speaker: Eric Maskin, Harvard University Topic: The Mathematics of Voting

Title: New Technologies in Mathematics Seminar

New Technologies in Mathematics Seminar  

Title: Mathematical Physics and Algebraic Geometry Seminar

Mathematical Physics and Algebraic Geometry Seminar      

Title: Member Seminar

Member Seminar Speaker: Puskar Mondal

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar Speaker: Mitch Weaver, KAIST

Title: Colloquium

Colloquium  

Title: General Relativity Seminar

General Relativity Seminar

Title: CMSA Q&A Seminar: Noah Golowich

CMSA Q&A Seminar Speaker: Noah Golowich (MIT) Topic: What is length generalization in large language models?

Title: New Technologies in Mathematics Seminar

New Technologies in Mathematics Seminar  

Title: Mathematical Physics and Algebraic Geometry Seminar

Mathematical Physics and Algebraic Geometry Seminar      

Title: Member Seminar

Member Seminar Speaker: Han Shao