Current students

Title: Algorithms for Rank-1 Bimatrix Games

Abstract:

The rank of a bimatrix game is the matrix rank of the sum of the two payoff matrices.

Title: The geometry of matroids

Abstract:

Matroid theory is a combinatorial theory of independence which has its origins in linear algebra and graph theory, and turns out to have deep connections with many other fields.

Title: Periodicity on Oriented Graphs by way of Transcendental Number Theory

Abstract: Using the adjacency matrix of a graph, it is straightforward to show that perfect state transfer between two vertices at some time t implies that both vertices will be periodic at time 2t.

Title: Gaps in the crossing numbers of drawings of the complete graph

Abstract: In the late 1990’s, a 5-author manuscript circulated proving the existence of intervals of integers that connot occur as the crossing number of a “good” drawing of the complete graph. 

Title:Generalizing the problem of packing disjoint cycles

Abstract: A classic result of Erdos and Posa states that there exists a function f such that for all k,

Title: Edge State Transfer

Abstract: Most research about quantum state transfer on graphs use adjacency matrices as their Hamiltonians and investigate the transfers between single vertex states.

Title: The coloring problem for restricted graph classes

Abstract:

Let L be a set of graphs. Free(L) is the set of graphs that do not contain any graph in L as an induced subgraph.

Title: The Many Faces of Circulation Algebras

Abstract:  The circulation algebra is a commutative graded algebra associated to a graph, introduced by Wagner in 1998 to study flows.

Title: The c₂ invariant at p=2 by counting edge bipartitions

Abstract:

Since no one provided a visitor or volunteered for this week, I will explain how to prove a special case of a conjecture about the c₂ invariant. 

Title: Stretching drawings of graphs

Abstract: Given a drawing D of a graph (where vertices are dots in the plane and edges are arbitrary curves connecting some pairs of dots),