Current students

Title: Traveling Salesman Problems

Abstract:

We discuss open research questions, both theoretical and computational, surrounding the traveling salesman problem.

Title: Random Networks: Enumeration, Generation, and Universality

Abstract:

Large networks appear in almost all branches of the sciences and in everyday life, and they are often modeled by random graphs. Among the various random graph models, random graphs with specified degrees are particularly important in modelling and analyzing real-world networks.

Title: An introduction to gammoids

Abstract:

A gammoid is a matroid that is defined via vertex connectivity in a graph.

Title: Comprehensive robust counterparts of uncertain problems

Abstract:

We continue our study of Robust Optimization by discussing the paper by Ben-Tal,  Boyd and Nemirovski, "Extending scope of robust optimization: comprehensive robust counterparts of uncertain problems."

Title: Mixing in Discrete-Time Quantum Walks

Abstract:

Discrete-time quantum walks are building blocks for quantum algorithms. There are some parameters of a quantum walk that affect the performance of a quantum algorithm, such as the (time-averaged) limiting distribution and the mixing time.

Title: Tangent Lines and the equation 28 = 7 × 4

Abstract:

I will discuss combinatorial aspects of tangent lines to curves and planar graphs. In algebraic geometry, every smooth plane curve has finitely many lines that are tangent to it at two separate points.

Title: An introduction to vertex minors

Abstract:

This introductory lecture on vertex minors of graphs will highlight the similarities and differences with minors of graphs. We will also discuss the main conjectures relating to vertex minors.

Title: Robust Convex Optimization 

Abstract:

We continue our study of convex optimization problems with uncertain data by discussing the paper by Ben-Tal and Nemirovski, 'Robust Convex Optimization'.

Title: An Introduction to Quantum Graphs, Chromatic Numbers and Lovász Inequalties

Abstract:

Quantum graph theory, also known as non-commutative graph theory, is an operator system generalization of graph theory. Quantum graphs were first used to extend the notion of one-shot-zero-error capacity of a "Noisy Channel" to "Quantum Channels". 

Title: Post-Quantum Group-based Cryptography

Abstract:

The National Security Agency (NSA) in August 2015 announced plans to transition to post-quantum algorithms