Events

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.

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.

Title: Ideal clutters and k-wise intersecting families

Abstract:

A clutter is *ideal* if the corresponding set covering polyhedron has no fractional vertices, and it is *k-wise intersecting* if the members don’t have a common element but every k members do. 

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: Approximate Coloring of 2-Colorable 4-Uniform Hypergraphs

Abstract:

In this talk, we discuss several inapproximability results of Bhangale for 2-colorable 4-uniform hypergraphs.

Title: Ideal matrices

Abstract:

A 0,1 matrix M is *ideal* if the set covering system Mx>=1, x>=0 gives an integral polyhedron.