## Seminars and Colloquia Schedule

### Unavoidable dense induced subgraphs

Series
Graph Theory Seminar
Time
Tuesday, September 8, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Rose McCartyUniversity of Waterloo

Thomassen conjectures that every graph of sufficiently large average degree has a subgraph of average degree at least d and girth at least k, for any d and k. What if we want the subgraph to be induced? Large cliques and bicliques are the obvious obstructions; we conjecture there are no others. We survey results in this direction, and we prove that every bipartite graph of sufficiently large average degree has either K_{d,d} or an induced subgraph of average degree at least d and girth at least 6.

### Knot Concordance

Series
Geometry Topology Student Seminar
Time
Wednesday, September 9, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Hugo ZhouGeorgia Tech

Two knots are concordant to each other if they cobound an annulus in the product of S^3. We will discuss a few basic facts about knot concordance and look at J. Levine’s classical result on the knot concordance group.

### Singularity of sparse Bernoulli matrices with$p$ is close to $\log(n)/n$.

Series
High Dimensional Seminar
Time
Wednesday, September 9, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Join Zoom Meeting https://us02web.zoom.us/j/88203571169 Meeting ID: 882 0357 1169
Speaker
Han HuangGeorgia Tech

It has been conjectured that for a sufficiently large $n$, and $p = p_n \in [\log(n)/n, 1/2)$, the probability that a $n\times n$ Bernoulli($p$) matrix $A$ is singular equals to the probability that $A$ contains of a zero row or zero column up to a negligible error.

This conjecture has been recently proved by Litvak-Tikhomirov in the regime $C\log(n)/ n < p < 1/C$ for some universal constant $C>1$ with their new tool. While for $p = (1+o(1)) \log(n) /n$, it also holds due to a result of Basak-Rudelson. In this talk, we will discuss how to extend their results to fill the gap between these two regions. ( $1\le pn/\log(n) <\infty$ )

### Couplings of Markov chain Monte Carlo and their uses

Series
Stochastics Seminar
Time
Thursday, September 10, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/83378796301
Speaker
Pierre JacobHarvard University

Markov chain Monte Carlo (MCMC) methods are state-of-the-art techniques for numerical integration. MCMC methods yield estimators that converge to integrals of interest in the limit of the number of iterations, obtained from Markov chains that converge to stationarity. This iterative asymptotic justification is not ideal. Indeed the literature offers little practical guidance on how many iterations should be performed, despite decades of research on the topic. This talk will describe a computational approach to address some of these issues. The key idea, pioneered by Glynn and Rhee in 2014, is to generate couplings of Markov chains, whereby pairs of chains contract, coalesce or even "meet" after a random number of iterations; we will see that these meeting times, which can be simulated in many practical settings, contain useful information about the finite-time marginal distributions of the chains. This talk will provide an overview of this line of research, joint work with John O'Leary, Yves Atchadé and various collaborators.

### TBA by Tianyi Zhang

Series
Student Algebraic Geometry Seminar
Time
Friday, September 11, 2020 - 09:00 for 1 hour (actually 50 minutes)
Location
Microsoft Teams Meeting
Speaker
Tianyi ZhangGeorgia Tech

### Online Selection with Cardinality Constraints under Bias

Series
ACO Student Seminar
Time
Friday, September 11, 2020 - 13:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/264244877/0166
Speaker

Optimization and machine learning algorithms often use real-world data that has been generated through complex socio-economic and behavioral processes. This data, however, is noisy, and naturally encodes difficult-to-quantify systemic biases. In this work, we model and address bias in the secretary problem, which has applications in hiring. We assume that utilities of candidates are scaled by unknown bias factors, perhaps depending on demographic information, and show that bias-agnostic algorithms are suboptimal in terms of utility and fairness. We propose bias-aware algorithms that achieve certain notions of fairness, while achieving order-optimal competitive ratios in several settings.

### The chromatic number of a random lift of K_d

Series
Combinatorics Seminar
Time
Friday, September 11, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location