Professor
Arcadia University
Glenside, PA
Professor in the mathematics and computer science department

I am interested in theoretical computer science and in applications of model theory to different areas of mathematics as well as in other fields.   Currently I am working in descriptive complexity theory, which is an area of theoretical computer science that studies computational complexity classes from the point of view of  finite model theory.  My work  focuses on developing tools to achieve separation of complexity classes by studying the model theory of finite-model logics associated with these classes. Some of my papers on this topic are: 1. Expressive Power and Complexity of a Logic with Quantifiers that Count Proportions of Sets, with A. Arratia, Journal of Logic and Computation, 16 (2006), 817-840, 2. First Order Extensions of Residue Classes and Uniform Circuit Complexity, with A. Arratia, Logic, Language, Information and Computation, WoLLIC 2013, Lecture Notes in Computer Sciences (L. Libkin et al editors), 8071 (2013), 49-63. I am also looking into  applications of logic to classical mathematical fields. For my dissertation I explored the model theory of analytic structures by studying the possibility of obtaining classical model theoretic results, such as the Omitting Types Theorem, in a very expressive infinitary logic that includes negation, infinite conjunction and existential quantification over infinitely many variables. The main tool that I developed was the notion of approximate formulas for the formulas in this logic. Some of the results obtained can be found in:  1. An Omitting Types Theorem for Normed Spaces”, a paper that studies the existence of a powerful Omitting Types Theorem for the logic of approximate formulas in normed spaces. This paper appeared in the Annals of Pure and Applied Logic, 108 (2001), 2. "Uniform Versions of Infinitary Properties in Banach Spaces", a paper that studies the following situation: Suppose that there is a statement P true in all the metric structures of a class, under which conditions do we know that the "uniform version" of this statement holds? And what is the "uniform version"? The answer is that this situation holds for a very large set of properties (namely, the ones that are expressible in an infinitary language L).  In this paper I also obtain a general recipe to obtain the “uniform” version of the formulas in the language L. I have also done work in applications of mathematical logic to diverse fields such as Finance Theory and Genomics. With my colleagues at Arcadia we have also reflected on the internationalization of the mathematics curriculum at college level.