The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with
respect to the positive semidefinite order. This operator concavity property leads to numerous …

We study the convex hull of $SO(n)$, the set of $n\times n$ orthogonal matrices with unit
determinant, from the point of view of semidefinite programming. We show that the convex hull …

Let G be a finite abelian group. This paper is concerned with nonnegative functions on G
that are sparse with respect to the Fourier basis. We establish combinatorial conditions on …

In this paper we establish links between, and new results for, three problems that are not
usually considered together. The first is a matrix decomposition problem that arises in areas …

We describe a new approach to certifying the global nonnegativity of multivariate polynomials
by solving hyperbolic optimization problems---a class of convex optimization problems that …

It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program
(SDP) of a particular structure and that therein lies the computational bottleneck for SOS …

In this thesis we consider convex optimization-based approaches to the classical problem of
identifying a subspace from noisy measurements of a random process taking values in the …

We consider the problem of finding sum of squares (sos) expressions to establish the non-negativity
of a symmetric polynomial over a discrete hypercube whose coordinates are …

Sampling inference methods are computationally difficult to scale for many models in part
because global dependencies can reduce opportunities for parallel computation. Without strict …

Synchronous Condensers (SynCons) offer voltage regulation, inertia, and fault current
contribution to solve the challenges of voltage and frequency instability introduced by the high …