Future students

Title: Type-II Matrices

Abstract:

The Schur product M o N of two matrices M and N is the usual entrywise product. The matrix N is the Schur inverse of M if M o N = J. Denote the Schur inverse of M by M(-). An n x n matrix is a type-II matrix if
WW^(-)T = nI.

Title: Sparse graphs with forbidden induced subgraphs and the Erdos-Hajnal conjecture

Abstract:

A graph G is called H-free if it does not contain H as an induced subgraph, i.e. H cannot be obtained from G by deleting vertices. A famous conjecture due to Erdos and Hajnal states that for every graph H, there is a constant c > 0 such that in every n-vertex H-free graph G, there is a set of n^c vertices that are either all pairwise adjacent or all pairwise non-adjacent.

Title: Principled algorithms for finding local minima

Abstract:

Convex optimization is the cornerstone of continuous optimization, but many real problems are nonconvex: neural networks, airplane design, water network management, etc. This two part talk explores my work developing algorithms for finding local minima of nonconvex functions.

Title: Quantum Latin Squares and Magic Unitaries

Abstract:

A quantum Latin square is an n x n array of vectors such that vectors in any row or any column form an orthonormal basis for Cⁿ. A magic unitary matrix is an n x n array of projections such that each row and column sums to I.

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.