Future students

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: 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: 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: Introduction to Quantum Cocliques

Abstract:

Quantum coclique is a generalisation of the notion of classical coclique.

Title: The Iterated Local Model for Social Networks

Abstract:

On-line social networks such as Facebook and Twitter are often studied through friendships between users. Adversarial relationships also play an important role in the structure of these social networks.

Title: High-dimensional probability: Random vectors in high dimensions

Abstract:

In this talk, I will finish our discussion of concentration inequalities, particularly, I will discuss the sub-exponential distribution and state Bernstein’s inequality; thereby completing our study of large deviations.

Title: Hypergraphs, Entropy, and Inequalities

Abstract:

In this talk, we discuss a generalization of Shearer's entropy lemma for weighted hypergraphs due to Friedgut (2004).

Title: Is any knot not the unknot?

Abstract:

Ever wanted to learn something about knots? This is your chance! We'll talk about some basics of knot theory, including how to prove some intuitively `obvious' but mathematically tricky results. 

Title: Counting maximal independent sets in the hypercube

Abstract:

In this talk we count the number of maximal independent set in the hypercube. It is not hard to see that the n-dimensional hypercube contains at least 2^(n-2) maximal independent sets.