**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
classifying
the unitarizable Harish Chandra modules of G. these are
representations
of both, the Lie algebra of G and of a maximally compact subgroup K of
G.

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
Barbasch,
Dan Ciubotaru, Fokko du Cloux, Anthony Knapp, Annegret Paul, Siddharta
Sahi, John Stembridge, Peter Trapa, Marc van Leeuwen, David Vogan,
Jiu-Kang
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
courses
click on the links below

Fall 2007

- Math 481/525 Section 1. Meets TR
10:20-11:35

Fall 2006

- Math 471 Section 1. Meets MWF 10:30
to 11:20 AM in Room SH109

Please send mail to ssalaman@nmsu.edu if you have any comments.