Thursday, February 23, 2023
Time  Items 

All day 

4:00pm 
02/23/2023  4:00pm The Galois group of an additive polynomial over a finite field is contained in a finite general linear group. We will discuss three different probability distributions on these polynomials, and estimate the probability that a random additive polynomial has a “large” Galois group. Our computations use a trick that gives us characteristic polynomials of elements of the Galois group, so we may use our knowledge of the maximal subgroups of GL(n,q). This is joint work with Lior BarySoroker and Alexei Entin.
Location:
LOM 215
02/23/2023  4:00pm I will discuss joint work with Jonas Luhrmann and SungJin Oh on the stability of the catenoid, which is a minimal surface, viewed as a stationary solution to the hyperbolic vanishing mean curvature equation in Minkowski space. The latter is a quasilinear wave equation that constitutes the hyperbolic counterpart of the minimal surface equation in Euclidean space. Our main result is the nonlinear asymptotic stability, modulo suitable translation and boost (i.e., modulation), of the ndimensional catenoid with respect to a codimension one set of initial data perturbations without any symmetry assumptions, for $n\geq 5$. The modulation and the codimension one restriction on the data are necessary and optimal in view of the kernel and the unique simple eigenvalue, respectively, of the stability operator of the catenoid. In a broader context, this work fits in the long tradition of studies of soliton stability problems. From this viewpoint, our aim is to tackle some new issues that arise due to the quasilinear nature of the underlying hyperbolic equation. Location:
LOM 205
