# Upcoming Events

I will describe why the trivial knot S^2-->S^4 has non-unique spanning discs up to isotopy. This comes from a chain of deductions that include a description of the low-dimensional homotopy-groups of embeddings of S^1 in S^1xS^n …

Abstract: We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We systematically investigate all the possible…

Abstract: It is known in the physics literature that "high-frequency weak limits" of solutions to the Einstein vacuum equations are not necessarily vacuum solutions, but may have a non-trivial stress-energy-momentum tensor, which can be viewed physically as "effective matter fields" arising from…

Modular tensor categories encode the topological symmetries of 2-dimensional bosonic topological phases of matter, as the algebraic underpinnings of 2+1 dimensional topological…

Zoom link: https://stanford.zoom.us/j/848843604

A ``pure pair'' in a graph G is a pair (X,Y) of disjoint subsets of V(G) such that either every vertex in X is adjacent to every vertex in Y, or there are…

Ribbon categories are 3-dimensional algebraic structures that control quantum link polynomials and that give rise to 3-manifold invariants known as skein modules. I will describe how to use Khovanov-Rozansky link homology, a categorification of the gl(N) quantum link polynomial, to obtain a 4-…

Abstract: We develop a sharp boundary trace theory in arbitrary bounded

Lipschitz domains which, in contrast to classical results, allows forbidden endpoints in the Sobolev scale and permits the consideration of functions exhibiting very limited regularity. This is done at the (necessary…