Past Events

There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will describe a weak notion of equivalence for knots called concordance, and highlight some historical and recent connections between knot concordance and the study of 4-manifolds, with a…

An r-sunflower is a collection of r sets so that the intersection of any two are the same. Given a fixed constant r, how many sets of size w can we have so that no r of them form an r-sunflower? Erdos and Rado introduced this problem in 1960 and proved a bound of w^(w(1+o(1)), and…

Abstract: The long-time behavior of a passive scalar in a fluid has long been of interest in physics. In this talk I will discuss several recent rigorous results in this area for a passive scalar that is advected by a number of stochastic fluid models, including the stochastic Navier-Stokes…

Abstract: Experts have long realized the parallels between elliptic and parabolic theory of partial differential equations. It is well-known that elliptic theory may be considered a static, or steady-state, version of parabolic theory. And in particular, if a parabolic estimate holds, then by…

 In 2017, Gabai proved the light bulb theorem, showing that if $R$ and $R'$ are 2-spheres homotopically embedded in a 4-manifold with a common dual, then with some condition on 2-torsion in $\pi_1(X)$ one can conclude that $R$ and $R'$ are smoothly isotopic. Schwartz later showed that this…