Distinguished Professor of Arts and Sciences in Mathematics
Lie groups, automorphic forms, representation theory
I am interested in the representation theory of reductive Lie groups, the cohomology of arithmetic groups and automorphic forms. Most of my work is related to geometric and topological properties of locally symmetric spaces. Recently worked on branching laws for the restriction of infinite dimensional representations of a reductive Lie group to a non compact subgroup and applications to automorphic forms, for example to the Gross Prasad conjectures.
- Symmetry Breaking for Representations of Rank One Orthogonal Groups II (with T. Kobayashi), Lecture Notes in Mathematics 2234, 367 pages, Springer Lecture Notes (2018), ISBN: 978-981-13-2900-5
- Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad (with T. Kobayashi), in Geometric Aspects of the Trace For- mula, Simons Symposia, Springer Verlag (2018), 245-266.
- Symmetry Breaking for Representations of Rank One Orthogonal Groups (with T. Kobayashi), Mem. Amer. Math. Soc., 238, Amer. Math. Soc., Providence, RI, (2015), v+112 pp., ISBN: 978-1-4704-1922-6. ISBNs: 978-1- 4704-1922-6
- Discrete components of some complementary series (with T.N. Venkataramana), Forum Math. 23 (2011), no. 6, 11591187
- Pseudo-Eisenstein forms and cohomology of arithmetic groups III: Residual classes and applications (with J. Rohlfs), in On certain L-functions Clay Mathematics Proceedings, vol 13 , 2011
- A Plancherel formula for L2(G/H) for almost symmetric subgroups (with B. Orsted), Pacific Journal (2016 ).