Seminars and Colloquia by Series

TBA by Chun-Hung Liu

Series
Graph Theory Seminar
Time
Tuesday, December 8, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Chun-Hung LiuTexas A&M University

TBA

TBA by Taísa Martins

Series
Graph Theory Seminar
Time
Tuesday, November 24, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Taísa MartinsUniversidade Federal Fluminense

TBA

TBA by Theo Molla

Series
Graph Theory Seminar
Time
Tuesday, November 17, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Theo MollaUniversity of South Florida

TBA

TBA by Louis Esperet

Series
Graph Theory Seminar
Time
Tuesday, November 10, 2020 - 12:30 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Louis EsperetUniversité Grenoble Alpes

Please Note: Note the unusual time!

TBA

TBA by Ruth Luo

Series
Graph Theory Seminar
Time
Tuesday, November 3, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Ruth LuoUniversity of California, San Diego

TBA

TBA by Éva Czabarka

Series
Graph Theory Seminar
Time
Tuesday, October 27, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Éva CzabarkaUniversity of South Carolina

TBA

Generalized sum-product phenomena and a related coloring problem

Series
Graph Theory Seminar
Time
Tuesday, October 20, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Yifan JingUniversity of Illinois at Urbana-Champaign

In the first part of the talk, I will show that for two bivariate polynomials $P(x,y)$ and $Q(x,y)$ with coefficients in fields with char 0 to simultaneously exhibit small expansion, they must exploit the underlying additive or multiplicative structure of the field in nearly identical fashion. This in particular generalizes the main result of Shen and yields an Elekes-Ronyai type structural result for symmetric nonexpanders, resolving a question mentioned by de Zeeuw (Joint with S. Roy and C-M. Tran). In the second part of the talk, I will show how this sum-product phenomena helps us avoid color-isomorphic even cycles in proper edge colorings of complete graphs (Joint with G. Ge, Z. Xu, and T. Zhang).

Perfect matchings in random hypergraphs

Series
Graph Theory Seminar
Time
Tuesday, October 13, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Matthew KwanStanford University

For positive integers $d < k$ and $n$ divisible by $k$, let $m_d(k,n)$ be the minimum $d$-degree ensuring the existence of a perfect matching in a $k$-uniform hypergraph. In the graph case (where $k=2$), a classical theorem of Dirac says that $m_1(2,n) = \lceil n/2\rceil$. However, in general, our understanding of the values of $m_d(k,n)$ is still very limited, and it is an active topic of research to determine or approximate these values. In the first part of this talk, we discuss a new "transference" theorem for Dirac-type results relative to random hypergraphs. Specifically, we prove that a random $k$-uniform hypergraph $G$ with $n$ vertices and "not too small" edge probability $p$ typically has the property that every spanning subgraph with minimum $d$-degree at least $(1+\varepsilon)m_d(k,n)p$ has a perfect matching. One interesting aspect of our proof is a "non-constructive" application of the absorbing method, which allows us to prove a bound in terms of $m_d(k,n)$ without actually knowing its value.

The ideas in our work are quite powerful and can be applied to other problems: in the second part of this talk we highlight a recent application of these ideas to random designs, proving that a random Steiner triple system typically admits a decomposition of almost all its triples into perfect matchings (that is to say, it is almost resolvable).

Joint work with Asaf Ferber.

Inducibility of graphs and tournaments

Series
Graph Theory Seminar
Time
Tuesday, October 6, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Florian PfenderUniversity of Colorado Denver

A classical question in extremal graph theory asks to maximize the number of induced copies of a given graph or tournament in a large host graph, often expressed as a density. A simple averaging argument shows that the limit of this density exists as the host graph is allowed to grow. Razborov's flag algebra method is well suited to generate bounds on these quantities with the help of semidefinite programming. We will explore this method for a few small examples, and see how to modify it to fit our questions. The extremal graphs show some beautiful structures, sometimes fractal like, sometimes quasi random and sometimes even a combination of both.

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