Events by month

Title: Type II Matrices

Abstract:

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

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: 

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: 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: Quantum Colouring and Derangements

Abstract:

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

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: 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: 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: Discrete quantum walks, embeddings and designs

Abstract:

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

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: Boundary measurement and sign variation in real projective space

Abstract:

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

Abstract:

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.