Algebra Group

The algebra group in the Department of Mathematical Sciences conducts research in several areas of algebra; some of these including invariant theory, commutative algebra, valuation theory, central simple algebras, module theory, representation theory, and Leibniz homology.

There has been a weekly algebra seminar in the department for many years. Faculty participants of the algebra seminar include Louiza Fouli, Pat Morandi, Bruce Olberding, and Susana Salamanca-Riba. The department has hosted several distinguished visiting professors and Holiday Symposia speakers in algebra since 1990. They include Georgia Benkart, David Eisenbud, Ed Green, Derek Holt, and Bernd Sturmfels.

Faculty Interest 

Louiza Fouli

Commutative Algebra. My research interests lie in the area of Commutative Algebra and its interactions with Algebraic Geometry, Homological Algebra, and Combinatorics. Research Topics: Rees algebras, residual intersection theory, edge ideals of graphs, the core of ideals, study of systems of parameters, tight closure, and integral closure.

Some of my recent projects involve the study of the core of ideals, the study of the tight closure core and the study of the core of edge ideals of graphs. I have also been interested in studying the depth of powers of edge ideals. Recently, I have collaborated with Craig Huneke in a study of systems of parameters in Noetherian rings. Some of my recent collaborators are Craig Huneke (University of Kansas), Susan Morey (Texas State University), Claudia Poilini (University of Notre Dame), Bernd Ulrich (Purdue University), Janet Vassilev (University of New Mexico) and Adela Vraciu (University of South Carolina).

Bruce Olberding

Commutative Algebra and Module Theory. Recent research topics: valuation theory, integrally closed overrings of two-dimensional Noetherian domains, generic formal fibers of Noetherian rings, constructing rings from derivations, stable rings, ideal decompositions, and colon and injective properties of ideals integral domains.

Other research interests include Prufer domains, holomorphy rings in function fields, ultraproducts of commutative rings, and decompositions of torsion-free modules. Some of my recent collaborators include Pat Goeters, Bill Heinzer, Laszlo Fuchs, Moshe Roitman, Serpil Saydam and Jay Shapiro.

Emeritus Faculty

Patrick Morandi

Rings of continuous functions, pointfree topology, duality theory.

My early research was concerned with developing and using valuation theory in the study of finite dimensional division algebras and algebras with involution. My current research considers bounded archimedean lattice-ordered algebras, often on questions motivated from rings of continuous functions. I also work in frame theory and dualities involving compact Hausdorff spaces, including generalizations of Stone, Priestley, and de Vries duality. My work is joint with Guram Bezhanishvili, and also with Bruce Olberding and Luca Carai.

Susana Salamanca-Riba

Representation Theory of Real Lie groups and Lie algebras: My research focuses on the study of the unitary representations of real reductive Lie groups, and Leibniz Homology of affine Lie algebras. I study the unitary representations via the analogous problem of classifying the unitarizable Harish Chandra modules of G. My current research includes a program to reduce the classification of the unitary dual to a smaller set of representations. In particular, my most recent work concerns such program for a special class of representations of the Metaplectic group and the double cover of the unitary groups. I am also interested in the Leibniz Homology of the affine simple Lie algebras.

My most recent collaborators are Alessandra Pantano, Annegret Paul, and David Vogan. I am also a team member in the Atlas of Lie groups and Representations project (http://www.liegroups.org), whose goal is to make available information about representations of reductive algebraic groups like SL(n) or Sp(2n), in order to support research in the field and to aid graduate students and young researchers in the learning of the subject. The people involved in this project now are Jeffrey Adams, Dan Barbasch, Birne Binegar, Bill Casselman, Dan Ciubotaru, Scott Crofts, Tatiana Howard, Monty McGovern, Alfred Noel, Alessandra Pantano, Annegret Paul, Patrick Polo, Siddharta Sahi, John Stembridge, Peter Trapa, Marc van Leeuwen, David Vogan, Wei-ling Yee and myself.