Past Events

After introducing and topologizing Teichmüller space, we will use Fenchel-Nielsen coordinates to sketch a proof that the Teichmüller space of a closed surface S_g, g≥2, is homeomorphic to a (6g-6)-dimensional ball. Next we’ll discuss the 9g-9 theorem, which says that elements of Teich(S_g) are…

Last quarter I gave a kiddie talk about classifying polyhedra, and cutting up polygons into equal area pieces. Today we'll instead be cutting up polyhedra and guarding polygons.

1. Given any two polygons of equal area, one can cut the first shape into finitely many pieces and rearrange…

Abstract: The stability of black hole spacetimes is a critical question in mathematical relativity. The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the…

Our speaker this week is Ravi Vakil.

Title: The space of vector bundles on spheres: algebra, geometry, topology

Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X \times S^2: the “moduli space” BU…

Abstract: Open positroid varieties are certain subvarieties of the Grassmannian that arise in the study of total positivity and have surprising applications in many areas of mathematics and physics. After reviewing some history and background, I will discuss our recent joint work with…

We prove that the size of the product set of any finite arithmetic progression A in integers with size N is at least N^{2}/(log N)^{c+o(1)}, where 2c=1-(1+loglog 2)/(log 2).  This matches the bound in the celebrated Erdős…

This talk is concerned with the following inverse problem for the wave equation:

Determine the variable wave speed from data gathered by a collection of sensors, which emit probing signals and measure the generated backscattered waves. Inverse backscattering is an interdisciplinary…

Seminar page.

We study the CP^2-slicing number of knots, which is by definition the smallest integer m such that the given knot bounds a properly embedded, null-homologous disk in m(CP^2) minus a ball. We give a lower bound on the smooth CP^2-slicing number and an upper bound on the topological CP…

Early algebraic forms of Euler's recursion include the Girard–Newton–Waring identities between coefficients of a polynomial and sums of powers of its roots. As a matter of analysis, the exp-log recursion appears in Euler's calculus text of 1755. With suitable parameters, this recursion generates…