Colloquia
Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in ACLC, Room 010 (unless otherwise advertised) with refreshments preceding at 3:15pm in Parker Hall, Room 244.
Nov 07, 2024 03:30 PM
NOTE: TIME (3:30) AND DATE (Thursday, Nov. 7) CHANGE
Refreshments will be served in Parker 244, 3:00-3:25 p.m.
Speaker: Liding Yao (Zassenhaus Assistant Professor (postdoc) at The Ohio State University)
Title: On nonsmooth Frobenius-type theorems and their H\”older estimates
Abstract: In this talk I will discuss several results from my thesis concerning the integrable structures on manifolds. The Frobenius-type theorems describe the necessary and sufficient conditions on a locally integrable structure for when it is equal to the span of (some real and complex) coordinate vector fields. The typical examples are - The Frobenius theorem, that an involutive real subbundle is spanned by some real coordinate vector fields - The Newlander-Nirenberg theorem, that an involutive almost complex structure is spanned by some complex coordinate vector fields - Nirenberg’s complex Frobenius theorem, which is the combination of the above two cases. In the talk we will introduce the involutive condition with weakest regularity assumption. We obtain the Frobenius theorem when the subbundle is only log-Lipschitz continuous. For a \(C^{k,s}\) complex Frobenius structure, we show that there is a \(C^{k,s}\) coordinate chart such that the structure is spanned by coordinate vector fields that are \(C^{k,s−\epsilon}\) for all \(\epsilon >0\), where the \(\epsilon>0\) loss in the result is optimal.
Oct 18, 2024 04:00 PM
DMS Colloquium: Chris Kapulkin
Aug 30, 2024 04:00 PM
Abstract: For many years, mathematicians have used computers to perform computations that inform their research and lead to new conjectures. More recently, computers have been used to formally verify correctness of proofs via software known as proof assistants. This talk will be an introduction to proof assistants - what they are, why they are used, and what the mathematical community has accomplished with them.
A short introduction to the most commonly used proof assistant, Lean, will also be given. Together, we will use Lean to formally verify that every natural number is either even or odd, a fact that shouldn't surprise many but is a good illustration of what working with a proof assistant is like. Those interested in following the proof on their own computers are encouraged to install Lean ahead of the talk by going to:
DMS Colloquium: Jordan Awan
Apr 26, 2024 04:00 PM
(please note special location--228 Parker Hall)
Speaker: Jordan Awan (Purdue)
Abstract: Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often produces complex and intractable sampling distributions. In this paper, we propose a simulation-based "repro sample" approach to produce statistically valid confidence intervals and hypothesis tests, which builds on the work of Xie and Wang, 2022. We show that this methodology is applicable to a wide variety of private inference problems, appropriately accounts for biases introduced by privacy mechanisms (such as by clamping), and improves over other state-of-the-art inference methods such as the parametric bootstrap in terms of the coverage and type I error of the private inference. We also develop significant improvements and extensions for the repro sample methodology for general models (not necessarily related to privacy), including (1) modifying the procedure to ensure guaranteed coverage and type I errors, even accounting for Monte Carlo error, and (2) proposing efficient numerical algorithms to implement the confidence intervals and \(p\)-values.
DMS Colloquium: Haomin Zhou
Apr 19, 2024 04:00 PM
Please note special location for colloquium--Parker 228
Speaker: Haomin Zhou (Georgia Tech)
Title: Analysis and Computation of Parameterized Wasserstein Geometric Flow
Abstract: We introduce a new parameterization strategy that can be used to design algorithms simulating geometric flows on Wasserstein manifold, the probability density space equipped with optimal transport metric. The framework leverages the theory of optimal transport and the techniques like the push-forward operators and neural networks, leading to a system of ODEs for the parameters of neural networks. The resulting methods are mesh-less, basis-less, sample-based schemes that scale well to higher dimensional problems. The strategy works for Wasserstein gradient flows such as Fokker-Planck equation, and Wasserstein Hamiltonian flow like Schrodinger equation. Theoretical error bounds measured in Wasserstein metric is established.
This presentation is based on joint work with Yijie Jin (Math, GT), Shu Liu (UCLA), Has Wu (Wells Fargo), Xiaojing Ye (Georgia State), and Hongyuan Zha (CUHK-SZ).
DMS Colloquium: Dr. Grady Wright
Apr 12, 2024 04:00 PM
DMS Colloquium: Dr. Lateefah Id-Deen
Apr 05, 2024 04:00 PM
