Events

Title: Optimization in Data Analysis: Some Recent Developments

Abstract:

Optimization is vital to the modern revolution in data science, and techniques from optimization have become essential in formulating and solving a wide variety of data analysis problems. In turn, data science has caused a ferment of new research activity in optimization by posing challenging new problems and new contexts.

Title: On the average size of independent sets in triangle-free graphs

Abstract:

Some of the results that we've seen in this reading group have been improved recently using the "hard-core model" from statistical physics.

Title: Decomposing graphs into rooted odd trails

Abstract:

We give a precise characterization of when the edge set of a graph can be partitioned into k trails so that every trail begins and ends at a specified vertex v and has an odd number of edges.

Joint work with Jim Geelen and Paul Wollan.

Title: Not colouring the 3-sphere

Abstract:

Let S(3) be the graph formed by the unit vectors in R³, two vectors adjacent if they are orthogonal. I will prove that S(3) has no 3-colouring.

Title: High-dimensional probability: Bernstein's Inequality

Abstract:

We will extend our study of concentration inequalities so far to random matrices.

Title: Using Lasserre Hierarchy for Graph Coloring  

Abstract:

In this talk, I will go over a technique introduced by Arora and Ge for coloring 3-colorable graphs having low threshold rank (i.e., graphs with few eigenvalues below certain negative constant).

Title: Toward a Theory of Crossing-Critical Graphs

Abstract: 

The crossing number of a graph is defined as the minimum number of crossings of edges in a drawing of the graph in the plane. In his seminal 1970 paper Toward a Theory of Crossing Numbers, Tutte made a fundamental contribution by proving what is known today as the Hanani-Tutte Theorem.

Title: IETF encryption standards post-TLS 1.3

Abstract:

TLS is one of the most important security protocols online. It’s most famously used in web browsing, providing the S in HTTPS.

Title: A proof of the Hell-Nešetřil Dichotomy via Siggers Polymorphisms

Abstract:

In 2017, the constraint satisfaction dichotomy was proven via techniques from universal algebra. If we restrict this theorem to graphs, we get the Hell-Nešetřil Dichotomy, which is a statement about colouring graphs.

Title: High dimensional probability: Estimation in high dimensions

Abstract:

In this talk, we discuss high dimensional estimation problems. The aim is to estimate some point x in a given ambient bounded space K using a small number of independent random observations.