Current students

Title: Are cryptosystems based on ideal lattices quantum-safe ?

Abstract:

Shor's algorithm factors RSA integers and solves the Discrete Logarithm Problem (DLP) in quantum polynomial time. Therefore, alternatives to these cryptosystems must be developed to replace the current cryptographic schemes. One of the most interesting family of schemes that have been proposed for the replacement of RSA-based and DLP-based primitives relies on the hardness of finding short vectors in Euclidean lattices.

Title: Stochastic algorithms for distributed optimization and machine learning

Abstract:

In the big data era, machine learning acts as a powerful tool to transform data into knowledge that helps us make predictions and decisions. It has strong ties to the field of optimization, in the way the latter provides methods and theory.

Title: Next-generation authentication and key exchange protocols

Abstract:

Key exchange and authentication are at the heart of protocols for establishing secure communication on the Internet and other communication channels.  In this talk, I'll discuss ways in which key exchange is evolving to meet new security demands and deliver new functionality. 

Title: Towards Large-Scale Nonconvex/Stochastic Discrete Optimization

Abstract:

Modern data analytics is powered by scalable mathematical optimization methods. For decision-making, we want to be able to solve large-scale mathematical problems that include discrete choices or structures. These can already be very challenging to solve exactly even when the objective and feasible region are convex.

Title: Generalized Conditional Gradient for Sparse Estimation

Abstract:

We will be discussing the paper (bearing the same title) of Yaoliang Yu, Xinhua Zhang, and Dale Schuurmans.  Structured sparsity is an important modelling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design.

Title: Continuous Quantum Walks and Symmetric Powers

Abstract:

The k-th symmetric power of a graph X has the k-subsets of V(X) as its vertices, and two k-subsets are adjacent if their symmetric difference is an edge in X. A continuous quantum walk on a graph gives rise in a natural walk to walks on it symmetric powers.

Title: Signal Recovery by Proximal Forward-Backward Splitting

Abstract:

We will be discussing the paper (bearing the same title) of Patrick Combettes and Valérie Wajs.  We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties.

Title: Turan problems for matroids

Abstract:

Given a fixed simple binary matroid N, what is the maximum size of a simple rank-r binary matroid that does not contain N a restriction?

Title: Asymmetric Latin squares, Steiner triple systems, and 1-factorizations

Abstract:

We outline how the Van der Waerden permanent theorem can be used to show that almost all Latin squares, Steiner triple systems, and 1-factorizations of the complete graph admit only trivial automorphisms. 

Title: Fragility and circuit-hyperplane relaxation

Abstract:

I will briefly discuss the problem of trying to determine the excluded minors for the class of GF(5)-representable matroids, highlighting the roles of N-fragility and of circuit-hyperplane relaxations.