## Seminars and Colloquia Schedule

### Normal surface theory and colored Khovanov homology

Series
Geometry Topology Seminar
Time
Monday, May 3, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Christine Ruey Shan LeeUniversity of South Alabama

The colored Jones polynomial is a generalization of the Jones polynomial from the finite-dimensional representations of Uq(sl2). One motivating question in quantum topology is to understand how the polynomial relates to other knot invariants. An interesting example is the strong slope conjecture, which relates the asymptotics of the degree of the polynomial to the slopes of essential surfaces of a knot. Motivated by the recent progress on the conjecture, we discuss a connection from the colored Jones polynomial of a knot to the normal surface theory of its complement. We give a map relating generators of a state-sum expansion of the polynomial to normal subsets of a triangulation of the knot complement. Besides direct applications to the slope conjecture, we will also discuss applications to colored Khovanov homology.

### Constructing non-bipartite $k$-common graphs

Series
Graph Theory Seminar
Time
Tuesday, May 4, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Fan WeiPrinceton University

A graph $H$ is $k$-common if the number of monochromatic copies of $H$ in a $k$-edge-coloring of $K_n$ is asymptotically minimized by a random coloring. For every $k$, we construct a connected non-bipartite $k$-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason. We also show that a graph $H$ is $k$-common for every $k$ if and only if $H$ is Sidorenko and that $H$ is locally $k$-common for every $k$ if and only if H is locally Sidorenko.

### A proof of the Erdős–Faber–Lovász conjecture

Series
School of Mathematics Colloquium
Time
Thursday, May 6, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/87011170680?pwd=ektPOWtkN1U0TW5ETFcrVDNTL1V1QT09
Speaker
Tom KellyUniversity of Birmingham

The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$.  In joint work with Dong Yeap Kang, Daniela Kühn, Abhishek Methuku, and Deryk Osthus, we proved this conjecture for every sufficiently large $n$.  In this talk, I will present the history of this conjecture and sketch our proof in a special case.

### Persistence of Invariant Objects under Delay Perturbations

Series
Dissertation Defense
Time
Thursday, May 6, 2021 - 16:00 for 1 hour (actually 50 minutes)
Location
ONLINE at https://bluejeans.com/137621769
Speaker
Jiaqi YangGeorgia Tech

We consider functional differential equations which come from adding delay-related perturbations to ODEs or evolutionary PDEs, which is a singular perturbation problem. We prove that for small enough perturbations, some invariant objects (e.g. periodic orbits, slow stable manifolds) of the unperturbed equations persist and depend on the parameters with high regularity. The results apply to state-dependent delay equations and equations which arise in electrodynamics. We formulate results in a posteriori format. The proof is constructive and leads to algorithms.

This is based on joint works with Joan Gimeno and Rafael de la Llave.