Seminars and Colloquia by Series

Notions of knot concordance II

Series
Geometry Topology Working Seminar
Time
Friday, October 14, 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 two concordance invariants coming from knot Floer homology: tau and epsilon.

Approximately Sampling Elements with Fixed Rank in Graded Posets

Series
ACO Student Seminar
Time
Friday, October 14, 2016 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matthew Fahrbach – College of Computing, Georgia Tech
Graded posets are partially ordered sets equipped with a unique rank function that respects the partial order and such that neighboring elements in the Hasse diagram have ranks that differ by one. We frequently find them throughout combinatorics, including the canonical partial order on Young diagrams and plane partitions, where their respective rank functions are the area and volume under the configuration. We ask when it is possible to efficiently sample elements with a fixed rank in a graded poset. We show that for certain classes of posets, a biased Markov chain that connects elements in the Hasse diagram allows us to approximately generate samples from any fixed rank in expected polynomial time. While varying a bias parameter to increase the likelihood of a sample of a desired size is common in statistical physics, one typically needs properties such as log-concavity in the number of elements of each size to generate desired samples with sufficiently high probability. Here we do not even require unimodality in order to guarantee that the algorithm succeeds in generating samples of the desired rank efficiently. This joint work with Prateek Bhakta, Ben Cousins, and Dana Randall will appear at SODA 2017.

Graph Hausdorff dimension, Kolmogorov complexity and construction of fractal graphs

Series
Graph Theory Seminar
Time
Thursday, October 13, 2016 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Pavel Skums – Department of Computer Science, Georgia State University
Lately there was a growing interest in studying self-similarity and fractal properties of graphs, which is largely inspired by applications in biology, sociology and chemistry. Such studies often employ statistical physics methods that borrow some ideas from graph theory and general topology, but are not intended to approach the problems under consideration in a rigorous mathematical way. To the best of our knowledge, a rigorous combinatorial theory that defines and studies graph-theoretical analogues of topological fractals still has not been developed. In this paper we introduce and study discrete analogues of Lebesgue and Hausdorff dimensions for graphs. It turned out that they are closely related to well-known graph characteristics such as rank dimension and Prague (or Nesetril-Rodl) dimension. It allowed us to formally define fractal graphs and establish fractality of some graph classes. We show, how Hausdorff dimension of graphs is related to their Kolmogorov complexity. We also demonstrate fruitfulness of this interdisciplinary approach by discover a novel property of general compact metric spaces using ideas from hypergraphs theory and by proving an estimation for Prague dimension of almost all graphs using methods from algorithmic information theory.

New Applications of the Polynomial Method to Problems in Combinatorics

Series
School of Mathematics Colloquium
Time
Thursday, October 13, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ernie Croot – Georgia Tech
In this talk I will discuss some new applications of the polynomial method to some classical problems in combinatorics, in particular the Cap-Set Problem. The Cap-Set Problem is to determine the size of the largest subset A of F_p^n having no three-term arithmetic progressions, which are triples of vectors x,y,z satisfying x+y=2z. I will discuss an analogue of this problem for Z_4^n and the recent progress on it due to myself, Seva Lev and Peter Pach; and will discuss the work of Ellenberg and Gijswijt, and of Tao, on the F_p^n version (the original context of the problem).

Academic Webpage Workshop

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

Please Note: Refreshments will be provided before the seminar.

It's important to have a personal academic webpage—one that is up-to-date, informative, and easy to navigate. This workshop will be a hands-on guide to making an academic webpage and hosting it on the School of Math website. Webpage templates will be provided. Please bring a laptop if you have one, as well as a photograph of yourself for your new website. Come and get the help you need to create a great webpage!

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.

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.

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