## Seminars and Colloquia Schedule

### Fractional chromatic number of graphs of bounded maximum degree

Series
Graph Theory Seminar
Time
Tuesday, February 16, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Zdeněk DvořákCharles University

By the well-known theorem of Brooks, every graph of maximum degree Δ ≥ 3 and clique number at most Δ has chromatic number at most Delta. It is natural to ask (and is the subject of a conjecture of Borodin and Kostochka) whether this bound can be improved for graphs of clique number at most Δ - 1. While there has been little progress on this conjecture, there is a number of interesting results on the analogous question for the fractional chromatic number. We will report on some of them, including a result by myself Bernard Lidický and Luke Postle that except for a finite number of counterexamples, every connected subcubic triangle-free graph has fractional chromatic number at most 11/4.

### Mathematical modeling of the COVID-19 pandemic: an outsider's perspective

Series
School of Mathematics Colloquium
Time
Thursday, February 18, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
Speaker
Wesley PegdenCarnegie Mellon University

In this talk we will discuss epidemic modeling in the context of COVID-19.  We will review the basics of classical epidemic models, and present joint work with Maria Chikina on the use of age-targeted strategies in the context of a COVID-19-like epidemic.  We will also discuss the broader roles epidemic modeling has played over the past year, and the limitations it as presented as a primary lens through which to understand the pandemic.

### Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology

Series
CDSNS Colloquium
Time
Friday, February 19, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Speaker
Surena HozooriGeorgia Tech

We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and set up a framework to use tools from contact and symplectic geometry and topology in the study of questions about Anosov dynamics. If time permits, we will discuss a characterization of Anosovity based on Reeb flows and its consequences.

### The minimum degree of minimal Ramsey graphs for cliques

Series
Combinatorics Seminar
Time
Friday, February 19, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
We prove a new upper bound of $s_r(K_k) = O(k^5 r^{5/2})$ on the Ramsey parameter $s_r(K_k)$ introduced by Burr, Erd\H{o}s and Lov\'{a}sz in 1976, which is defined as the smallest minimum degree of a graph $G$ such that any $r$-colouring of the edges of $G$ contains a monochromatic $K_k$, whereas no proper subgraph of $G$ has this property. This improves the previous upper bound of $s_r(K_k) = O(k^6 r^3)$ proved by Fox et al. The construction used in our proof relies on a group theoretic model of generalised quadrangles introduced by Kantor in 1980.