Date: 01/31/2024
Speaker: Jonathan Bloom (Lafayette)
Title: Flag positroids and Bruhat Order
Abstract: Positroids are a rich combinatorial object. We will see how they can help us to simplify a topological problem about the Grassmannian. Positroids are in bijection with a number of sets of objects and we will discuss how a few of these connect to other areas of math. A natural way to build on the theory of positroids is by studying flag positroids. We will see that many results about positroids also hold for flag positroids. However, we will also highlight a result that is specific to flag positroids by explaining a surprising connection between flag positroids and the Bruhat order on the symmetric group. This talk will feature results from joint work with Chris Eur and Lauren Williams.
Date: 02/07/2024
Speaker: Sigurd Angenent (University of Wisconsin Madison)
Title: Dynamics of convex ancient mean curvature flow
Abstract: By applying the methods of topological dynamics we (in joint work with Daskalopoulos and Sesum) have tried to organize the many different ancient solutions to MCF (mean curvature flow) that have been found to date. I will present properties and conjectures concerning the set of all ancient convex mean curvature flows.
Date: 02/14/2024
Speaker: Daniel Soskin (Lehigh University)
Title: TBD
Abstract: TBD
Date: 02/21/2024
Speaker: Gábor Székelyhidi (Northwestern University)
Title: The Lagrangian mean curvature flow
Abstract: An interesting problem in differential geometry is to find special Lagrangian submanifolds, but so far we have limited tools for this. The Lagrangian mean curvature flow gives a possible approach, aiming to deform Lagrangian submanifolds to special Lagrangian ones. I will give an introduction to this topic, and explain what we know so far about singularities that can form along the flow, in connection with conjectures by Thomas-Yau and Joyce. The talk is partly based on joint work with Jason Lotay and Felix Schulze.
Date: 02/28/2024
Speaker: Roy Goodman (New Jersey Institute of Technology)
Title: TBD
Abstract: TBD
Date: 03/06/2024
Speaker: Chenlu Ke (Virginia Commonwealth)
Title: TBD
Abstract: TBD
Date: 03/20/2024
Speaker: Kaitlyn Hood (Purdue University)
Title: TBD
Abstract: TBD
Date: 03/27/2024
Speaker: Hao Shen (University of Wisconsin Madison)
Title: Stochastic quantization of Yang-Mills
Abstract: We will discuss the stochastic Yang-Mills flow, which is the deterministic Yang-Mills flow driven by a (very singular) space-time white noise. It turns out that due to singularity, even construction of local solutions is challenging. We will discuss our construction for a trivial bundle over 2 and 3 dimensional tori, but starting with a gentle introduction to Stochastic PDE. In the end, I will also discuss the meaning of "gauge equivalence” and “orbit space" in the singular setting, and show that the flow has the gauge covariance property (in the sense of probability law), yielding a Markov process on the orbit space. Based on joint work with Ajay Chandra, Ilya Chevyrev and Martin Hairer.
Date: 04/03/2024
Speaker: Jiayuan Wang (Lehigh University)
Title: TBD
Abstract: TBD
Date: 04/10/2024
Speaker: Ruixiang Zhang (University of California Berkeley)
Title: Fourier restriction type problems: New developments in the last 15 years
Abstract: Fourier restriction type problems form a class of important problems in harmonic analysis. They are also related to PDE, analytic number theory, geometric measure theory and mathematical physics. In the past 15 years, much progress has been made on these problems. In this talk, we will introduce Fourier restriction type problems and survey some recent results, and then conclude by mentioning some personal favorite future directions.
Date: 04/24/2024
Speaker: Jean-Luc Guermond (Texas A&M University)
Title: Spectral correctness of the approximation of the first-order form of Maxwell's equations.
Abstract: I will discuss the role of involutions in the approximation of Maxwell's equations written in first-order form and with non-homogeneous magnetic permeability and electric permittivity. Although the Sobolev smoothness index of the solution may be smaller than $\frac12$, it is shown that the approximation is spectrally correct. The convergence proof is based on a duality argument. One essential idea is that the smoothness index of the dual solution is always larger than $\frac12$ irrespective of the regularity of the material properties, whereas the smoothness of the solution may be smaller than $\frac12$. Discrete involutions also play a key role in the analysis.