Algebra and Number Theory
The Department of Mathematics at Temple University has a strong tradition of research in algebra and number theory. Under the leadership of Emil Grosswald, a member of our faculty from 1968 to 1980, research in our department developed a particular focus in analytic number theory. Grosswald's memory is honored by our ongoing distinguished lecturer series which carries his name. More recently, research in the algebra and number theory group has diversified and acquired further strengths in several other areas, notably in noncommutative algebra.
Faculty
Boris Datskovsky's research interests lie in algebraic and analytic number theory. He has worked on the distribution of discriminants of abelian and nonabelian extensions of an algebraic number field, the theory of zeta functions associated with prehomogeneous vector spaces, and arithmetic aspects of the theory of modular forms.
Vasily Dolgushev's research interests are in noncommutative geometry, homological algebra, category theory and mathematical physics. Most of the problems he is working on are motivated by questions in mathematical physics. His approach to these problems often involves higher algebraic structures such as homotopy algebras, higher operads, and higher categories. The solutions of these problems are applied to questions in Lie theory, algebraic geometry, and algebraic topology. Vasily's most recent works are on formality theorems and versions of the Deligne conjecture for Hochschild complexes.
Marvin Knopp has worked in the area of modular functions and forms for the past 50 years, his first paper on the subject having been published in 1960. His book, "Modular functions in analytic number theory," appeared in 1970, with a second edition in 1993 (Chelsea-AMS). In 2008 he published a book, jointly with Bruce Berndt, on "Hecke's theory of modular forms and Dirichlet series". He is currently preparing a sequel to the latter work. As well, he has done extensive work in the theory of modular integrals and Eichler cohomology. For the past 10 years or so, he has been studying (jointly with Geoffrey Mason) vector-valued modular forms, objects which arise naturally in the rational conformal field theory. He has been an editor of the Ramanujan Journal since its founding (1996).
Edward Letzter's research interest is in noncommutative rings, their representations (i.e, actions by linear transformations on vector spaces) and internal structure (primarily two-sided ideal theory). His most recent work concerns the structure of skew power series rings. He has also recently studied algorithmic aspects of finite dimensional representations.
Seymour Lipschutz is currently mainly doing research in two areas: (1) Gray code loopless algorithms which list the elements of various combinatorial families, and (2) generalizations of Stallings' pregroup.
Martin Lorenz's research interests encompass several areas of noncommutative algebra. He has worked on topics in ring theory, group theory, Hopf algebras, algebraic K-theory and other fields. For about ten years, Lorenz's research was focused on multiplicative invariant theory. His monograph with that title was published by Springer-Verlag in 2005. Subsequently, Lorenz has worked on applications of Koszul algebras to algebraic combinatoris and, most recently, on algebraic group actions on noncommutative spaces. Lorenz has served as Coordinating Editor of the Proceedings of the American Mathematical Society for algebra, number theory, combinatorics, and logic from 2006 to 2010.
Research Profile
The Algebra and Number Theory group is active in a variety of research areas including:
- analytic number theory, especially modular functions and forms
- algebraic number theory
- combinatorial group theory
- algorithmic approaches to finite-dimensional representation theory
- noetherian rings
- multiplicative invariant theory
- actions of algebraic transformation groups on noncommutative spaces
- applications of Koszul algebras to algebraic combinatorics
- ring-theoretic structure of quantum groups and related algebras
Seminars
Graduate Studies in Algebra and Number Theory
Several graduate students have completed Ph.D.s in algebra and number theory in recent years. Interested graduate students are encouraged to take advanced topics courses in these and related areas and to attend the above listed weekly seminars. Summer research stipends (from the NSA) are currently available for eligible graduate students.
General information about graduate study in mathematics at Temple, including course descriptions, can be found on the graduate program website.