Current students

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.

Title: Robust counterpart approximations of scalar chance constraints

Abstract:

We will cover section 2.1, section 2.2 and part of section 2.3 of the book Robust Optimization by Ben-Tal et al.

Title: On Pretty Good State Transfer, Entanglement, and Spin Chains

Abstract: 

We discuss the Vieira and Rigolin paper “Almost perfect transport of an entangled two-qubit state through a spin chain”,

Title: The Douglas-Rachford splitting algorithm for inconsistent minimization problems

Abstract:

The Douglas--Rachford (DR) method is one of the most popular splitting methods in optimization. The method was first introduced in 1956 to numerically solve certain types of heat equations.

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: Reading Seminar "Robust Optimization"

Abstract:

In this reading seminar, we will go through Section 1. 2-1. 3 of Chapter 1 in the book 'Robust Optimization'

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.