Past Events

Around the motivic monodromy conjecture for non-degenerate hypersurfaces

I will discuss my ongoing effort to comprehend, from a geometric viewpoint, the motivic monodromy conjecture for a "generic" complex multivariate polynomial $f$, namely any polynomial $f$ that is non-degenerate with…

Doodling is a creative and fundamentally human activity, resulting in doodles with intricate and often hidden implicit structure. We will treat doodles as an example for how mathematics is done --- by starting with some doodles, we will ask ourselves some natural questions and see where they…

Let T be a subset of R^d, such as a ball, a cube or a cylinder, and consider all possibilities for packing translates of T, perhaps with its rotations, in some bounded domain in R^d. What does a typical packing of this sort look like? One mathematical formalization of this question is to fix the…

Abstract

In 1993, Erdős, Sárközy and Sós posed the question of whether there exists a set S of positive integers that is both a Sidon set and an asymptotic basis of order 3. This means that the sums of two elements of S are all distinct, while the sums of three elements of S cover all sufficiently large…

Learning and representing low-dimensional structures from noisy and possibly high-dimensional data is an indispensable component of modern data science. Recently, a special class of nonlinear embedding methods has become particularly influential, most notably, the t-distributed stochastic…

We discuss new methods for using the Heegaard Floer homology
of hypersurfaces to distinguish between smooth closed 4-manifolds that
are homeomorphic but non-diffeomorphic. Specifically, for a 4-manifold X
with b_1(X)=1, the minimum rank of the reduced Heegaard Floer homology
of…

Abstract: In this talk, I will first review existing results on singularity formation in incompressible and inviscid fluids. I will then describe a new mechanism for singularity formation in the 2D Boussinesq system. The initial data we choose is smooth except at one point, where it has Hölder…

Strong inversions are a class of order-2 symmetries of knots in S^3. Building on work of Lidman-Manolescu, Stoffregen-Zhang, and others, we will describe a relationship between the Khovanov homology of a knot with a strong inversion and its quotients by the inversion. We will also give a modest…

The disordered Ising ferromagnet is a disordered version of the ferromagnetic Ising model in which the coupling constants are quenched random, chosen independently from a distribution on the non-negative reals. A ground configuration is a configuration of the model in infinite volume whose…