Past Events
I will introduce a few motivating questions in projection theory (Marstrand projection thm, Falconer’s…
A graph is said to be a (1-dimensional) expander if the second eigenvalue of its adjacency matrix is bounded away from 1, or almost-equivalently, if it has no sparse vertex cuts. There are several natural ways to generalize the notion of expansion to hypergraphs/simplicial complexes…
I will discuss joint work with Gunther Uhlmann regarding the anisotropic fractional Calderon problem for Dirac operators on closed manifolds; these give fractional analogues of Maxwell systems. Namely we show that knowledge of the source-to-solution map of the fractional Dirac…
Abstract
Abstract: We consider the long time dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schrödinger equation (NLS), (CSS) is L2-critical and has pseudoconformal invariance and solitons. However, there are two…
Abstract
An unavoidable pathology of non-normal matrices is that of spectral instability: their spectra and invariant subspaces can be highly sensitive to small perturbations. This instability can be captured by quantities such as the eigenvalue gaps, the condition number of the basis of eigenvectors,…
It is well known that local Tate duality extends to p-adic etale cohomology of schemes over local fields. In a joint work with Pierre Colmez and Sally Gilles we conjecture that it also extends to p-adic pro-etale cohomology of analytic spaces and prove it for analytic curves. I will discuss this…
Given a smooth function on the round sphere, is it possible to reconstruct it from knowing its integral along all great circles? We will embark on a a remarkably elementary journey, using only basic algebra and functional analysis, to answer this and other questions.
The question of whether a smooth complex variety with a positive first Chern class, called a Fano variety, has a Kahler-Einstein metric has been a major topic in complex geometry since the 1980s. In the last decade, algebraic geometry, or more…