Current students

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: 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: 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: Ideal matrices

Abstract:

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

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: 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: 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: 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.