### ## Joseph Hundley SIUC, Mathematics

Assistant Professor

Ph.D. Columbia University, 2002

Representation Theory, Automorphic Forms
and L-functions

Office: Neckers A 381
Office Phone: 618-453-6570
Email: jhundley at math.siu.edu
Web Page: www.math.siu.edu/hundley/
www.math.siu.edu/hundley/personal/html

## Research Interests

The bulk of my work is in the Rankin-Selberg method, and much of it is joint with David Ginzburg. The Rankin-Selberg method is a method of studying the Dirichlet series with Euler product, known as L functions, which were attached by Langlands to automorphic representations of adele groups. Global applications to functoriality often involve characterizing the image of functorial lifts. My main current project with Ginzburg is an ambitious survey of the exceptional groups for such constructions. It is aided by some computer tools which I developed with my student Joe Pleso. In addition, I have recently completed an introductory textbook on automorphic forms on GL(n), with Dorian Goldfeld, and, together with E. Sayag, generalized the "functorial descent" construction of Ginzburg-Rallis-Soudry from representations which are isomorphic to their own contragredients to representations which are isomorphic to twists of their own contragredients.

## Selected Publications

1. (with D. Ginzburg) On certain Rankin-Selberg integrals on ${\rm GE}\sb 6$. Nagoya Math. J. 191 (2008), 21-78.
2. Spin L-functions for GSO(10) and GSO(12), Israel J. Math. 165 (2008), 103-132.
3. (with D. Ginzburg) On Spin L functions for GSO(10) J. Reine Angew. Math. 603 (2007) pp 183-213.
4. Siegel zeros of Eisenstein series, Acta Arith. 126 (2007), No. 4, pp.341-356
5. (with W.T. Gan) The spin L-function of quasi-split D4. IMRP Int. Math. Res. Pap. 2006, Art. ID 68213, 74 pp.