department of mathematics
Professor and Department Chair
Ph.D. University of Chicago
Honors and Awards
- NATO Postdoctoral Fellowship in Science, 1985-86
- Indo-American (Fullbright) Fellowship, 1987-88
- Sloan Fellowship, 1989-92
- MAA Northeastern Section Award for Distinguished College or University Teaching, 2009
Automorphic forms are functions which encode number theoretic or representation-theoretic information. These functions give rise to further functions called L-functions. The study of the interplay between automorphic forms, L-functions and representation theory is an important part of modern number theory, and is at the heart of my research interests. Over the past two decades, I have shown that it is possible to systematically study families of L-functions using certain functions in several complex variables, multiple Dirichlet series. Recently, my collaborators and I have established surprising links between these objects and combinatorial representation theory, quantum groups and statistical mechanics.
- Gauss sum combinatorics and metaplectic Eisenstein series,
with B. Brubaker and D. Bump, in Automorphic Forms and L-functions I: Global Aspects,
Contemporary Mathematics 488, Amer. Math.Soc., 2009, pp. 61–81.
- On the p-parts of quadratic Weyl group multiple Dirichlet series,,
with G. Chinta and P.E. Gunnells, Crelle’s journal 623 (2008), pp.1–23 .
- Weyl group multiple Dirichlet series III: Eisenstein series and twisted unstable Ar,
with B. Brubaker, D. Bump, J. Hoffstein, Annals of Mathematics 166 (2007), 293–316.
- Hecke L-functions and the distribution of totally positive integers,
with A. Ash, Canadian Journal of Mathematics 59, (2007), 673–695.
- Lifting automorphic representations on the double covers of orthogonal groups,
with D. Bump and D. Ginzburg, Duke Mathematical Journal 131 (2006)
- Weyl group multiple Dirichlet series II: the stable case,
with B. Brubaker and D. Bump, Inventiones Math. 165 (2006), 325–355