Events

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.

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: 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: 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.