Current students

Title: Counting Pentagons in Triangle-free Binary Matroids

Abstract:

Every triangle-free graph with n vertices contains at most (n/5)^5 cycles of length five, and this value is attained by the balanced blowup of the 5-cycle.

Title: Circuit-hyperplane relaxation and matroid representation

Abstract:

Relaxing a circuit-hyperplane in a representable matroid can destroy representability.

Title: Maximizing non-monotone submodular functions

Abstract:

Optimization of non-monotone submodular functions has applications in the maximum cut and maximum directed cut problems for graphs.

Title: Cutting a square into triangles of equal area

Abstract:

Suppose you are given a square and asked to cut it into n triangles of equal area. If n is even the problem is almost trivial, but when n is odd the problem becomes much harder.

Title: Perfect state transfer on Cayley graphs

Abstract:

Perfect state transfer on Cayley graphs

Title: Edge-maximal graphs on surfaces

Abstract:

It is straightforward to show that, with the exception of small complete graphs, every edge-maximal planar graph triangulates the plane.

Title: A Quantum Query Complexity Trichotomy for Regular Languages

Abstract:

We consider the quantum query complexity of regular languages and discover a surprising trichotomy: each regular language has query complexity either Theta(1), ~Theta(sqrt(n)) or Theta(n). 

Title: Interpolated versions of the Central Limit Theorem, and crossings of pair-partitions

Abstract:

Title: Perfect state transfer on Hadamard diagonalizable graphs

Abstract:

A (weighted) graph whose Laplacian matrix is diagonalizable by a Hadamard matrix is said to be Hadamard diagonalizable.

Title: Sublinear separators in intersection graphs of convex shapes

Abstract: 

A balanced separator of an n-vertex graph is set of vertices whose deletion leaves only components of size at most 2n/3.