Seminars and Colloquia by Series

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.

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.

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.

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 –

Please Note: 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.

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.

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".

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.

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.

NumericalImplicitization for Macaulay2

Series
Algebra Seminar
Time
Friday, September 30, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Justin Chen – UC Berkeley

Please Note: Many varieties of interest in algebraic geometry and applications are given as images of regular maps, i.e. via a parametrization. Implicitization is the process of converting a parametric description of a variety into an intrinsic (i.e. implicit) one. Theoretically, implicitization is done by computing (a Grobner basis for) the kernel of a ring map, but this can be extremely time-consuming -- even so, one would often like to know basic information about the image variety. The purpose of the NumericalImplicitization package is to allow for user-friendly computation of the basic numerical invariants of a parametrized variety, such as dimension, degree, and Hilbert function values, especially when Grobner basis methods take prohibitively long.

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