Research Topics: My research focuses on the study of the unitary representations of real reductive Lie groups. This subject has applications to number theory, automorphic forms, class field theory, mathematical physics, control theory and many other areas of research. The field intertwines ideas of harmonic analysis, algebra, geometry and topology.
I study these representations via the equivalent problem of
the unitarizable Harish Chandra modules of G. these are
of both, the Lie algebra of G and of a maximally compact subgroup K of
My current research includes a program proposed in collaboration with David Vogan to reduce the classification of the unitary dual to a smaller set of representations and a program proposed by and in collaboration with Dan Barbasch and David Vogan and Jeff Adams to generalize Barbasch's classification of the Spherical unitary dual for Split real and p-adic groups.
Recently I have become involved in the Atlas of Lie groups and Representations project (see http://www.math.umd.edu/~jda/atlas/) This is a project, in collaboration with several colleagues, to make available information about representations of non-compact semi-simple Lie groups (and related groups over local fields). One of the goals of the Atlas is to put together such a data base for groups like SL(n, R ) or Sp(2n, R), that will be available for use in other fields of research like automorphic forms, class field theory, etc.
The people involved in this project now are Jeffrey Adams, Dan
Dan Ciubotaru, Fokko du Cloux, Anthony Knapp, Annegret Paul, Siddharta
Sahi, John Stembridge, Peter Trapa, Marc van Leeuwen, David Vogan,
Yu and myself.
Teaching: For general information about the Mathematical Sciences Department courses please see NMSU Math Department
Courses: For information, syllabi, etc on the following
click on the links below