Current students

Title: Greedy Heuristic for Maximizing Submodular Set Functions

Abstract:

Several hard combinatorial optimization problems can be posed in the following framework: maximize a submodular function over its domain subject to a cardinality constraint.

Title: Discrete diffusion on graphs and real hyperplane arrangements

Abstract:

In 2016, Duffy et al. introduced the following process on a graph.  Initially, each vertex has some integer number of ``chips'' placed there (possibly negative). 

Title: LP bounds and the addition formula

Abstract:

I will show how we can derive useful bounds on the size of codes and designs, using linear programming and the addition formula.

Title: Chord diagrams, generating functions, and qft

Abstract:

I'll talk about some joint work with Julien Courtiel where some nice enumerative combinatorics tells us something about how gauge theories are such special quantum field theories.

Title: Improving Implementations of CSIDH

Abstract: 

I will present on some papers related to implementations of CSIDH [1].

Title: Orthogonal Polynomials and the Addition Formula

Abstract:

Many questions about designs and codes in the unit sphere can be reduced to questions about members of a family of orthogonal polynomials, the so-called Gegenbauer polynomials.

Title: Undermining key exchange

Abstract:

There are many ways to undermine systems that rely on cryptography. An attacker could of course try to find flaws in the hardware and software implementing the system, or find mathematical weaknesses in the cryptographic algorithms.

Title: The sparsest matroids omitting an independent flat

Abstract:

Given integers $k,r \ge 1$, what is the smallest a rank-$r$ matroid can be that does not contain a $k$-element independent set that is also a flat? I will answer this question, characterize the extremal examples, and draw parallels with a problem in graph theory.

Title: Submodular function maximization

Abstract:

I will give the introductory talk for this term's topic for the Combinatorial-Optimization Reading group, namely submodular function maximization. Submodular functions arise in diverse contexts in combinatorial optimization.

Title: When are two Schur functions the same?

Abstract: 

A pair of skew shapes are said to be (skew) equivalent if they admit the same number of semistandard tableaux of any weight; i.e. if their associated skew Schur functions are equal.