Seminars and Colloquia Schedule

Knudsen layer: coupling fluids with kinetics

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 3, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Qin Li – UW-Madison –
Many kinetic equations have the corresponding fluid limits. In the zero limit of the Knudsen number, one derives the Euler equation out of the Boltzmann equation and the heat equation out of the radiative transfer equation. While there are good numerical solvers for both kinetic and fluid equations, it is not quite well-understood when the two regimes co-exist. In this talk, we model the layer between the fluid and the kinetic using a half-space equation, study the well-posedness, design a numerical solver, and utilize it to couple the two sets of equations that govern separate domains. It is a joint work with Jianfeng Lu and Weiran Sun.

Hypersurfaces with central convex cross sections

Series
Geometry Topology Seminar
Time
Monday, October 3, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alper Gur – Indiana University –
The compact transverse cross-sections of a cylinder over a central ovaloid in Rn, n ≥ 3, with hyperplanes are central ovaloids. A similar result holds for quadrics (level sets of quadratic polynomials in Rn, n ≥ 3). Their compact transverse cross-sections with hyperplanes are ellipsoids, which are central ovaloids. In R3, Blaschke, Brunn, and Olovjanischnikoff found results for compact convex surfaces that motivated B. Solomon to prove that these two kinds of examples provide the only complete, connected, smooth surfaces in R3, whose ovaloid cross sections are central. We generalize that result to all higher dimensions, proving: If M^(n-1), n >= 4, is a complete, connected smooth hypersurface of R^n, which intersects at least one hyperplane transversally along an ovaloid, and every such ovaloid on M is central, then M is either a cylinder over a central ovaloid or a quadric.

Boltzmann's equation and its entropy inequality

Series
Non-Equilibrium Statistical Mechanics Reading Group
Time
Monday, October 3, 2016 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zaher Hani – GeorgiaTech –
We continue our discussion, started last week, on what we called the "Boltzmann approach" to non-equilibrium statistical physics. We shall start with some remarks concerning the derivation and regimes of validity of the Boltzmann equation for rarefied gases (the Boltzmann-Grad limit). Then we will consider Boltzmann kinetic equation, and prove its H-principle. This corresponds mainly to Chapters 1 and 2 of Dorfman "An introduction to Chaos in Non-equilibrium Statistical Mechanics".

Geometric Small Cancellation

Series
Geometry Topology Working Seminar
Time
Wednesday, October 5, 2016 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shane Scott – Georgia Tech
In this lecture series, held jointly (via video conference) with the University of Buffalo and the University of Arkansas, we aim to understand the lecture notes by Vincent Guirardel on geometric small cancellation. The lecture notes can be found here: https://perso.univ-rennes1.fr/vincent.guirardel/papiers/lecture_notes_pcmi.pdf This week we will begin Lecture 4.

Algorithms in Combinatorial Topology

Series
Research Horizons Seminar
Time
Wednesday, October 5, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Dan Margalit – Department of Mathematics, Georgia Institute of Technology –

Food and Drinks will be provided before the seminar.

For every surface (sphere, torus, etc.) there is an associated graph called the curve graph. The vertices are curves in the surface and two vertices are connected by an edge if the curves are disjoint. The curve graph turns out to be very important in the study of surfaces. Even though it is well-studied, it is quite mysterious. Here are two sample problems: If you draw two curves on a surface, how far apart are they as edges of the curve graph? If I hand you a surface, can you draw two curves that have distance bigger than three? We'll start from the beginning and discuss these problems and some related computational problems on surfaces.

Math research in the age of Google Scholar and the revolutionary library

Series
Research Horizons Seminar
Time
Wednesday, October 5, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Liz Holdsworth – Georgia Institute of Technology
If Google Scholar gives you everything you want, what could Georgia Tech Library possibly do for you? Come learn how to better leverage the tools you know and discover some resources you may not. Get to know your tireless Math Librarian and figure out how to navigate the changes coming with Library Next. This is also an opportunity to have a voice in the Library’s future, so bring ideas for discussion.

Subgraphs of the curve graph

Series
Geometry Topology Student Seminar
Time
Wednesday, October 5, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin Lanier – Georgia Tech
Given a surface, intersection information about the simple closed curves on the surface is encoded in its curve graph. Vertices are homotopy classes of curves, and edges connect vertices corresponding to curves with disjoint representatives. We can wonder what subgraphs of the curve graph are possible for a given surface. For example, if we fix a surface, then a graph with sufficiently large clique number cannot be a subgraph of its curve graph. This is because there are only so many distinct and mutually disjoint curves in a given surface. We will discuss a new obstruction to a graph being a subgraph of individual curve graphs given recently by Bering, Conant, and Gaster.

Weak limits of optimal discrete measures for Riesz potentials

Series
Analysis Seminar
Time
Wednesday, October 5, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sasha Reznikov – Vanderbilt –
The problem in the talk is motivated by the following problem. Suppose we need to place sprinklers on a field to ensure that every point of the field gets certain minimal amount of water. We would like to find optimal places for these sprinklers, if we know which amount of water a point $y$ receives from a sprinkler placed at a point $x$; i.e., we know the potential $K(x,y)$. This problem is also known as finding the $N$-th Chebyshev constant of a compact set $A$. We study how the distribution of $N$ optimal points (sprinklers) looks when $N$ is large. Solving such a problem also provides an algorithm to approximate certain given distributions with discrete ones. We discuss connections of this problem to minimal discrete energy and to potential theory.

Notions of knot concordance

Series
Geometry Topology Working Seminar
Time
Friday, October 7, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jennifer Hom – Georgia Tech
The knot concordance group consists of knots in the three-sphere modulo the equivalence relation of smooth concordance. We will discuss varies ways to weaken the equivalence relation (e.g., considering locally flat concordances or concordances in more general four-manifolds) and what is known and unknown about the differences between the resulting groups.

Automorphisms of Strongly Regular Graphs

Series
Combinatorics Seminar
Time
Friday, October 7, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
John Wilmes – Georgia Tech
A graph is ``strongly regular'' (SRG) if it is $k$-regular, and every pair of adjacent (resp. nonadjacent) vertices has exactly $\lambda$ (resp. $\mu$) common neighbors. Paradoxically, the high degree of regularity in SRGs inhibits their symmetry. Although the line-graphs of the complete graph and complete bipartite graph give examples of SRGs with $\exp(\Omega(\sqrt{n}))$ automorphisms, where $n$ is the number of vertices, all other SRGs have much fewer---the best bound is currently $\exp(\tilde{O}(n^{9/37}))$ (Chen--Sun--Teng, 2013), and Babai conjectures that in fact all primitive SRGs besides the two exceptional line-graph families have only quasipolynomially-many automorphisms. In joint work with Babai, Chen, Sun, and Teng, we make progress toward this conjecture by giving a quasipolynomial bound on the number of automorphisms for valencies $k > n^{5/6}$. Our proof relies on bounds on the vertex expansion of SRGs to show that a polylogarithmic number of randomly chosen vertices form a base for the automorphism group with high probability.

"If I say KAM, what do you say?"

Series
Dynamical Systems Working Seminar
Time
Friday, October 7, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 170
Speaker
Livia Corsi – Georgia Tech
The aim of this talk is to give a general overview of KAM theory, starting from its early stages untill the modern era, including infinite dimensional cases. I'll try to present the main ideas with as little technicalities as possible, and if I have time I'll also discuss some open problems in the field.

Mathematical results in quantum physics

Series
Other Talks
Time
Saturday, October 8, 2016 - 09:34 for 8 hours (full day)
Location
CULC and Skiles
Speaker
see http://qmath13.gatech.edu/ – various
THis is an international meeting that will take place 8-11 October. See http://qmath13.gatech.edu/ for more details.