Seminar

Title: A Pseudoforest Analogue of the Strong Nine Dragon Tree Conjecture

Abstract:

In 2016, Jiang and Yang proved the Nine Dragon Tree Conjecture, a strengthening of the classical arboricity result of Nash-Williams (1964). On the way to developing this proof, Fan, Lim Song, and Yang proved an analogous result for decomposing graphs into pseudoforests, which is a strengthening of Hakimi’s Theorem.

Title: Maximizing a Monotone Submodular Function subject to a Matroid Constraint

Abstract:

Based on the paper by Calinescu, Chekuri, Pál, and Vondrák of the same title. We will study a randomized $(1-\frac{1}{e})$-approximation algorithm for the titular problem. 

Title: Scattering amplitudes and associahedra

Abstract:

The classic approach to scattering amplitudes sums a contribution from a (potentially very large) number of Feynman diagrams.

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.