# Seminars and Colloquia

### Upcoming Seminars

CAMS Seminar
Every other Monday at 3:30pm in Rolla G5

Hyperspace and Topology Seminar
3-5 PM on selected Mondays in Rolla G4
3-5 PM on selected Wednesdays in 103 Centennial

Analysis Seminar
Every other Monday at 3:30pm in Rolla G5

Time Scales Seminar
Wednesdays at noon in Rolla G5

### Ingram Lectureship

After he retired following the Fall 2002 semester, Professor W.T. Ingram, who was department chair from 1989-1998, generously set up an endowed fund to be used to bring well-known mathematical scientists to Rolla to give lectures on their work.  All Ingram Lectures are open to the entire S&T community, and are widely advertised on campus.  Visitors brought here under this program usually give two lectures, one of a general nature and accessible to students, and another more advanced aimed at faculty (though students are certainly welcome).

Presentations of Ingram Lectureship

## FALL 2018 Colloquia

Mean Curvature Flow and Variational Integrators

Yakov Berchenko-Kogan
Chauvenet Postdoctoral Lecturer
Department of Mathematics
Washington University in St. Louis

Friday, November 30
4:00-5:15 PM
Rolla Bldg G-5

Mean curvature flow is a well-studied geometric flow under which a surface moves in such a way as to decrease its area as fast as possible. Some surfaces, such as spheres and cylinders, evolve under mean curvature by dilations. Such surfaces, called self-shrinkers, are models for the singularities that can occur under mean curvature flow. The first nontrivial example of a self-shrinker was a torus proved to exist by Angenent in 1989. Self-shrinkers can be seen as the critical points of a weighted surface area functional called the entropy. There are simple formulas for the entropies of spheres and cylinders, but there is no such formula for the entropy of the Angenent torus, nor is their a formula describing the surface itself. The best previous result is a 2018 paper showing that the entropy of the Angenent torus is less than two. I numerically estimated the entropy of the Angenent torus to be 1.8512186, with an estimated accuracy of 0.0000019, using a variational numerical approach in order to facilitate future work on proving rigorous error bounds.

In this talk, I will introduce the basics of mean curvature flow and variational integrators and discuss how I used these ideas to numerically estimate the Angenent torus and its entropy. I will discuss numerical evidence for the error bounds of my estimate and describe a future strategy for rigorously proving such error bounds.

Host: He

Inviscid damping near Couette flow in a finite channel

Hao Jia
Assistant Professor
Department of Mathematics
University of Minnesota

Friday, October 26
4:00-5:15 PM
Rolla Bldg G-5

The two dimensional Euler equation is globally wellposed, but the long time behavior of solutions is not well understood. Generically, it is conjectured that the vorticity, due to mixing, should weakly but not strongly converge as $t\to\infty$. In an important work, Bedrossian and Masmoudi studied the perturbative regime near Couette flow $(y,0)$ on an infinite cylinder, and proved small perturbation in the Gevrey space relaxes to a nearby shear flow. In this talk, we will explain a recent extension to the case of a finite cylinder (i.e. a periodic channel) with perturbations in a critical Gevrey space for this problem. The main interest of this extension is to consider the natural boundary effects, and to ensure that the Couette flow in our domain has finite energy. Joint work with Alex Ionescu.

Hao Jia obtained his PhD in 2013 from University of Minnesota under the supervision of Vladimir Sverak. He was a Dickson Instructor in University of Chicago from 2013 to 2016, and spent one year as member in Institute for Advanced Study, Princeton. Dr. Jia is currently an assistant professor in University of Minnesota. His research interest is in the theory of partial differential equations, from fluids and waves.

Host: Murphy

Asymptotic behavior of quadratic Klein-Gordon equation in two dimensions

Satoshi Masaki
Associate Professor
Department of Systems Innovation
Graduate School of Engineering Science
Osaka University

Friday, September 21, 2018
4:00-5:15 PM
Rolla Bldg G-5

In this talk, we discuss asymptotic behavior of solutions to nonlinear Klein-Gordon equation with the gauge invariant power type nonlinearity of the critical order. By using the expansion of the nonlinearity, we see that there exist solutions which asymptotically behaves like a free solution with logarithmic phase correction. It will turn out that the behavior of a complex-valued solution is much complicated than that of a real-valued solution.

Dr. Masaki earned his PhD in Mathematics from Kyoto University in the Spring of 2009 under the supervision of Yoshio Tsutsumi. He began his career at Gakushuin University in Spring 2010 as an Assistant Professor. In Fall 2012, he moved to Hiroshima University as an Associate Professor. Since Spring 2016, he has been an Associate Professor at Osaka University. Dr. Masaki's main research interests lie in the areas of harmonic analysis and nonlinear dispersive equations, with a primary focus on the asymptotic behavior of solutions to nonlinear Schrödinger equations.

Host:  Murphy