Seminar

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 

Title: Constructing Graphs Pseudo-Similar Vertices

Abstract:

Let G be a graph. Let a and b be vertices in G, then a and b are pseudo-similar if G\a is isomorphic to G\b, but there's no automorphism of G that maps a onto b.

Title: Algorithms and complexity for quantum advantage

Abstract:

There is strong evidence that a sufficiently large fault-tolerant quantum computer would solve certain computational problems exponentially faster than any classical computer. How can quantum algorithms and complexity theory help guide the way forward in our current era of small and noisy quantum computers?

Title: ALBANIS: A brief overview of Lattice-Based NIST Submissions

Abstract:

Now that the NIST competition is in the first round of the review process, it is our turn to take a look at the submissions (at least, briefly).

Title: Polynomial systems: Graphical structure, Geometry, and Applications

Abstract:

Various problems in areas such as robotics, power systems, computer vision, cryptography, and chemical reaction networks, can be modeled by systems of polynomial equations, and in many cases the resulting systems have a simple sparsity structure.