Current students

Title: Some matrix problems in quantum information science

Abstract:

In this talk, we present  some matrix results and techniques in solving certain optimization problems arising  in quantum information science.

No quantum mechanics background is required.

Title: The Paulsen problem, continuous operator scaling, and smoothed analysis

Abstract:

The Paulsen problem is a basic open problem in operator theory: Given vectors u_1, ..., u_n in R^d that are eps-nearly satisfying the Parseval's condition and the equal norm condition, is it close to a set of vectors v_1, ..., v_n in R^d that exactly satisfy the Parseval's condition and the
equal norm condition? Given u_1,..., u_n, we consider the squared distance to the set of exact solutions.

Title: Sequences: random, structured or something in between?

Abstract:

There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation.  Typical problems include finding or avoiding patterns; testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc.

Title: A Short Introduction to Projective Geometry

Abstract:

Basically, see the title. I will be considering the real and complex cases mainly, because that is
what is needed in quantum physics.

Title: RSKy Business

Abstract:

We sketch the Robinson-Schensted-Knuth algorithm, then use it to glimpse into the representation theory of some classical combinatorial objects.

Title: I'll prove the Fundamental Theorem of Algebra

Abstract:

Gauss proved that complex polynomials always admit a root. I'll explain how he came to that conclusion and present a proof that rigorizes his argument in a nice way. You will only need to know a little vector calculus and the intermediate value theorem.

Title: The 8-connected excluded minors for the class of quasi-graphic matroids

Abstract:

The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle, is minor closed and contains both lifted-graphic matroids and frame matroids, each of which generalises the class of graphic matroids.

Title: Enumeration in quantum algebras

Abstract:

Many of the classical algebras that occur in algebraic geometry and other mathematical fields have natural quantizations; that is, one can deform the multiplication rule using a parameter q, which has the property that when we specialize q at 1 we recover the classical object.  As part of the general goal of understanding the representation theory of these rings, one often wants to understand the prime spectra of these algebras, that is, the collection of prime ideals in these rigs. 

Title: The 1,2,3-Conjecture and a related problem for bipartite graphs

Abstract:

Title: Quantum Walks and State Transfer

Abstract:

Quantum walks are the quantum analogues of classical random walks and can be used to model quantum computations. If a quantum walker starts at a vertex of a graph and after some length of time, has probability 1 of being found at a different vertex, we say there is perfect state transfer between the two vertices.