Past Events
I will sketch a proof of the version of Rokhlin's theorem which states that the signature of every smooth closed spin 4 manifold is divisible by 16, assuming some other big theorems like Hirzebruch signature theorem. In particular, I want to discuss where the mysterious number 16 comes from.…
The Fourier transform has become an indispensable tool in analysis for studying a wide range of phenomena. This talk will review the basic properties of the Fourier transform and its use in studying the solutions of linear constant-coefficient PDEs. Once the basic results have been established,…
Persistence modules and their associated barcodes have originated in data sciences, but have recently had new applications in pure mathematics: in symplectic topology and in the study of Laplace eigenfunctions in particular. I will present a couple of my favorite such applications, one of which…
Quick review of fibre bundles, connections; Clifford algebra/modules; spinors; Dirac operators
A hyperkähler triple on a compact 4-manifold with boundary is a triple of symplectic 2-forms that are pointwise orthonormal with respect to the wedge product. It defines a Riemannian metric of holonomy contained in SU(2) and its restriction to the boundary defines a framing. In this talk, I will…
I will discuss some of my recent work on polynomial-factorial equations and the irrationality of numbers given by divisor series. The former work is joint with Hung Bui and Alexandru Zaharescu. I will go into some background and some ideas in the proofs.
Abstract: We discuss a recent result in which we investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by spatio-temporal regions in which u>0 and u<0. The…
A knot is called slice if it bounds a smoothly embedded disk in the four-ball. Much of low-dimensional topology revolves around obstructing this property of a knot. In this talk, we will introduce a method of obstructing sliceness which takes into account the actions of different symmetries on…