Events

Title: Applications of the entropy method: Counting proper colorings of a regular graph

Abstract: Following Section 6 of Galvin's notes on Entropy and Counting, we will explore Galvin and Tetali’s tight upper bound

Title: Cyclic flat approach to matroid base polytopes

Abstract: Ardila, Benedetti and Doker realised matroid polytopes as generalized permutohedra, and using the work of Postnikov,

Title: Difference-of-SOS and Difference-of-Convex-SOS Decomposition Techniques for Polynomials

Abstract:

We are interested in polynomial decomposition techniques for reformulating any multivariate polynomial into difference-of-sums-of-squares (DSOS) and difference-of-convex-sums-of-squares (DCSOS) polynomials.

Title: Fixed-parameter tractability with respect to tree-widt

Abstract: Courcelle’s Theorem says that a very general class of decision problems on graphs is FPT with

Title: MAD and Local Versions of Reed's Conjecture

Abstract:

Graph coloring is a widely studied area of graph theory dating from the time of the Four Color Conjecture (now theorem).

Title: Entropy and the Upper Matching Conjecture

Abstract: In this talk we examine the 2013 work of Ilinca and Kahn,

Title: Free subshifts and the Local Lemma

Abstract: The purpose of this talk is to demonstrate how combinatorial tools and techniques can be used to tackle problems in other areas of mathematics, specifically,

Title: Introduction to high-dimensional probability: some basic concentration inequalities and useful distributions

Abstract: In this seminar, we introduce important tools from high-dimensional probability useful in studying applications in data science such as covariance estimation, matrix completion,

Title: On the Hardness of 4-coloring a 3-colorable graph

Abstract: A consequence of the PCP theorem is that it is NP-hard to approximate the chromatic number of a general graph to within \n^{1-\eps} for any constant epsilon.

Title: From graph theory to set theory and back

Abstract:

Many results in finite combinatorics can be extended to infinite structures via compactness---but this transfer is powered by the Axiom of Choice and leads, in general, to highly "pathological" objects.