Bio: I was born in Romania in 1958, attended the West University of Timisoara, where I got my Bachelor of Science in 1982. After that, I attended the University of Bucharest and I got my Master of Science in 1983. During the period 1983-1991, I was researcher at the Institute of Mathematics of the Romanian Academy (former INCREST). During this time, I was awarded the Simion Stoillov prize of the Romanian Academy of Sciences (1989) for my work in Noncommutative Multivariable Operator Theory.

In 1991, I came to Texas A&M University where, under the direction of Professor Carl Pearcy, I got my PhD in Mathematics in 1993.

Since the Fall 1993, I have been at the University of Texas San Antonio (UTSA), where, initially, I got a job as a lecturer. I was promoted to full Professor in 2000, received the President’s Distinguished Achievement Award for Research Excellence in 2004, and inducted in the Academy of Distinguished researchers at UTSA in 2018. I have received NSF support for over 25 years.

I have published over 100 papers, some of them in top journals in mathematics, such as: Advances in Mathematics, Journal of Functional Analysis, Proceedings of the London Mathematical Society, Mathematische Annalen, Journal fur die Reine und Angewandte Mathematik, Analysis and PDE, Transactions of the American Mathematical Society, and many others. 
 I have written three research books published in the Memoirs of the American Mathematical Society, namely: Entropy and multivariable interpolation, 2006. 
 Unitary invariants in multivariable operator theory, 2009. Operator theory on noncommutative domains, 2010. 


Abstract

We present the structure of the k-tuples of doubly $\mathcal{U}$-commuting row isometries and the $C^{\ast }$-algebras they generate, where $\mathcal{U}$ is a set of commuting unitary operators on a Hilbert space. We obtain Wold decompositions and use them to classify the $k$-tuples of doubly $\mathcal{U}$-commuting row isometries up to a unitary equivalence. This study leads to the development of a dilation theory on the regular $\mathcal{U}$-twisted polyball ${\mathbf{B}}_{\mathcal{U}}(\mathcal{H})$, which is the set of all $k$-tuples $T:=(T_1,\dots ,T_k)$of row contractions $T_i:=[T_{i,1}\cdots T_{i,n_i}]$ on a Hilbert space $\mathcal{H}$ satisfying certain positivity condition on the defect operator ${\mathrm{\Delta }}_T(I)$ and $\mathcal{U}$-commutation relations. It is shown that many of the classical results concerning the dilation theory of contractions on Hilbert spaces have analogues for $\mathcal{U}$-twisted polyballs. This includes: Sz.-Nagy dilation theorem, von Neumann inequality, Ito and Brehmer dilations for commuting isometries and contractions, respectively, and Beurling characterization of the invariant subspaces for the unilateral shift on the Hardy space $H^2$.