Future students

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.

Title: Boundary measurement and sign variation in real projective space

Abstract:

Title: Discrete quantum walks, embeddings and designs

Abstract:

We construct a quantum walk from an embedding of a graph.

Title: Quantum Colouring and Derangements

Abstract:

Work in quantum information has lead to the introduction of quantum colourings.

Title: On the depth of cutting planesOn the depth of cutting planes

Abstract:

We tackle one of the most important open problems in computational integer programming: cut selection.

For four decades, cutting planes were believed to be useful only for structured combinatorial problems. This changed in 1995 when Balas, Ceria and Cornuéjols showed that Gomory cuts could helpfully strengthen the formulation of general integer programming problems. Since then, many other cut generation techniques have been developed, but their practical success has been moderate at best.

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.