Future students

Title: Extending drawings of K(n) to pseudolines and pseudocircles

Abstract:

In the early part of the 21st century, it was shown that the number of crossings in a straight-line drawing of K(n) is at least the number H(n), which is conjectured to be the crossing number of K(n). In fact, it is now known that, for n at least 10, the inequality is strict.

Title: Type II Matrices

Abstract:

   In 1867,  Sylvester defined an {\sl inverse orthogonal matrix} as an $n\times n$ complex matrix $W$ satisfying

Title: 

Abstract:

There are several different notions of what it means for a graph to converge. One popular notion for sparse graphs is Benjamini-Schramm convergence which focuses on local properties of the graphs.

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.