Past Events
We give an asymptotic lower bound on the number of field extensions generated by algebraic points on superelliptic curves over $\mathbb{Q}$ with fixed degree $n$, discriminant bounded by $X$, and Galois closure $S_n$. For $C$ a fixed curve given by an affine equation $y^m = f(x)$ where $m \geq 2…
A brief introduction to the construction of Lagrangian Floer homology and its application to a case of Arnold’s conjecture concerning intersections between Hamiltonian isotopic Lagrangian submanifolds.
Abstract: Given a polynomial $P$ of constant degree in $d$ variables and consider the oscillatory integral $$I_P = \int_{[0,1]^d} e(P(\xi)) \mathrm{d}\xi.$$ Assuming $d$ is also fixed, what is a good upper bound of $|I_P|$? In this talk, I will introduce a ``stationary set'' method that gives an…
In this talk, I will discuss some recent progress on toroidalization principles for klt singularities. These toroidalizations allow us to prove theorems about the topology of klt singularities and…
Abstract: Pick two Erdős-Rényi G(n,1/2) graphs at random. What's the chance that they are isomorphic? Small right? How small? It's at most n!/2^(n choose 2) so less than 10^(-1300)…
Certain parametric versions of the classical isoperimetric and coarea inequalities turn out to be closely related to problems in Almgren-Pitts Min-Max theory. I will describe some results from an ongoing work with Larry Guth on parametric inequalities and the Weyl for volume spectrum in…
Whether the 3D incompressible Euler and Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In an effort to provide a rigorous proof of the potential Euler singularity revealed by Luo-Hou's computation…
We review several uses of color in the literature of solvable lattice models and track their connections to quantum group modules and to various applications to representation theory and symmetric function theory. My…