## Seminars and Colloquia Schedule

### Contact surgery numbers

Series
Geometry Topology Seminar
Time
Monday, July 22, 2024 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rima ChatterjeeUniversity of Cologne

A fundamental result in 3-dimensional contact topology due to Ding-Geiges tells us that any contact 3-manifold can be obtained via doing a surgery on a Legendrian link in the standard contact 3-sphere. So it's natural to ask how simple or complicated a surgery diagram could be for a given contact manifold? Contact surgery number is a measure of  this complexity. In this talk, I will discuss this notion of complexity along with some examples. This is joint work with Marc Kegel.

### Induction for 4-connected Matroids and Graphs (Xiangqian Joseph Zhou, Wright State University)

Series
Graph Theory Seminar
Time
Tuesday, July 23, 2024 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xiangqian Joseph ZhouWright State University

A matroid $M$ is a pair $(E, \mathcal{I})$ where $E$ is a finite set, called the {\em ground set} of $M$, and $\mathcal{I}$ is a non-empty collection of subsets of $E$, called {\em independent sets} of $M$, such that (1) a subset of an independent set is independent; and (2) if $I$ and $J$ are independent sets with $|I| < |J|$, then exists $x \in J \backslash I$ such that $I \cup \{x\}$ is independent.

A graph $G$ gives rise to a matroid $M(G)$ where the ground set is $E(G)$ and a subset of $E(G)$ is independent if it spans a forest. Another example is a matroid that comes from a matrix over a field $F$: the ground set $E$ is the set of all columns and a subset of $E$ is independent if it is linearly independent over $F$.

Tutte's Wheel and Whirl Theorem and Seymour's Splitter Theorem are two well-known inductive tools for proving results for 3-connected graphs and matroids. In this talk, we will give a survey on induction theorems for various versions of 4-connected matroids and graphs.