Speaker: Trung Chau (UM)
Title: Multiplicity of negative one of independence polynomials of graphs
Time: 2:30pm
Room: 225 St Paul's College
Zoom link: https://umanitoba.zoom.us/j/63619782230 password the first 6 Fibonacci numbers (starting with 11...)
Abstract: We will discuss a small study of the multiplicity of negative one of independence polynomials of graphs. In commutative algebra, this invariant equals the a-invariant of the corresponding edge ideals. In graph theory, this invariant has not been studied as a topic on its own, but much work has been done on whether this invariant is equal to or larger than zero, as this is related to the reduced Euler characteristic of the independence complex of a graph. This is joint work with Om Prakash Bradwaj, Sayeed Ikram, Gargi Lather, Vasudeva Nanjangud, and Chitra Venugopal.
Speaker: Sophie Spirkl (Waterloo)
Title: Cliques and colouring in tournaments
Time: 2:30pm
Room: 225 St Paul's College
Zoom link: https://umanitoba.zoom.us/j/63619782230 password the first 6 Fibonacci numbers (starting with 11...)
Abstract: Tournaments are orientations of complete graphs, and many graph theory questions — in particular, from the world of induced subgraphs — have analogues in tournaments. In particular, notions of colouring (due to Neumann-Lara) and clique number (Aboulker, Aubian, Charbit, Lopes) exist. I will tell you what these are, as well as some of what we know about them, and questions that remain.
Speaker: Sean Longbrake (Emory University)
Title: An extremal result for powers of trees
Time: 2:30pm
Room: 225 St Paul's College
Zoom link: https://umanitoba.zoom.us/j/63619782230 password the first 6 Fibonacci numbers (starting with 11...)
Abstract: Given a graph $H$, the extremal number $\ex(n,H)$ is the maximum number of edges in an $n$-vertex
graph not containing $H$ as a subgraph. For nonbipartite graphs, this function is well-understood, but for bipartite graphs, little is known in the general case.
One motivating conjecture in the field is the following of Bukh and Conlon. Let $T^p$ be the graph formed by taking $p$ copies of $T$ which agree on their leaf set and are otherwise disjoint. Let $\ell(T)$ be the number of leaves of $T$. For certain so-called balanced trees T, Bukh and Conlon conjectured $\ex(n, T^p) = O(n^{2 - (v(T) - \ell(T))/e(T)})$.
Conlon and Janzer proved this theorem for the height two-tree $F_{r, s}$ formed by taking an $K_{1, r}$ and adding to leaf $s$ new neighbors, as long as $r \geq s + 2$. In joint work with Jiang and Yepremyan, we proved the Bukh and Conlon conjecture for the subdivision of $F_{r, s}$, formed by replacing each edge of $F_{r, s}$ with a path with two edges, as long as $r \geq 2s + 3$.
In this talk, I will give some background on this problem and its origins, as well as give some intuition on the structure of the proof.
Speaker: Tatsuhiro Suga (Tohoku University)
Title: TBA
Time: 2:30pm
Room: 225 St Paul's College
Zoom link: https://umanitoba.zoom.us/j/63619782230 password the first 6 Fibonacci numbers (starting with 11...)
Abstract: TBA
Speaker: Jimmy Zhu (UM CS)
Title: TBA
Time: 2:30pm
Room: 225 St Paul's College
Zoom link: https://umanitoba.zoom.us/j/63619782230 password the first 6 Fibonacci numbers (starting with 11...)
Abstract: TBA
Speaker: Lila Crew (Waterloo)
Title: TBA
Time: 2:30pm
Room: 225 St Paul's College
Zoom link: https://umanitoba.zoom.us/j/63619782230 password the first 6 Fibonacci numbers (starting with 11...)
Abstract: TBA
Speaker: Colin Desmarais (TU Wien)
Title: TBA
Time: 2:30pm
Room: 225 St Paul's College
Zoom link: https://umanitoba.zoom.us/j/63619782230 password the first 6 Fibonacci numbers (starting with 11...)
Abstract: TBA