# Jeffrey Adler Professor Mathematics & Statistics

- Degrees
- PhD, Mathematics, The University of Chicago
- Bio
- Jeffrey Adler conducts research mainly in harmonic analysis and representation theory (which can be thought of as the study of symmetry from a formal point of view), and also occasionally supervises undergraduate research projects in other areas. Among his non-professional interests are string quartets, urban development, etc.

- See Also
- Department of Mathematics and Statistics
- Jeff Adler's personal page
- For the Media
- To request an interview for a news story, call AU Communications at 202-885-5950 or submit a request.

## Teaching

### Spring 2019

### Fall 2019

## Partnerships & Affiliations

## Scholarly, Creative & Professional Activities

### Honors, Awards, and Fellowships

- Paul Halmos Visiting Professor, University of Michigan, Fall, 2015.

### Professional Presentations

[Past few years only]

"Self-dual cuspidal and supercuspidal representations",

- Colloquium, Tata Institute of Fundamental Research, Mumbai, June 13, 2019.
- Number Theory Seminar, Cambridge University, May 21, 2019.
- Representation Theory Seminar, Oxford University, May 16, 2019.

"Multiplicity upon restriction to the derived subgroup", Mathematics Colloquium, Tata Institute of Fundamental Research, Mumbai, India, July 5, 2018.

"P-adic groups: what and why?", Joint Colloquium, Chebyshev Laboratory and the Laboratory for Modern Algebra and Applications, Saint-Petersburg State University, Saint-Petersburg, Russia, June 7, 2018. (Video)

"Root data with group actions", Workshop and Conference on Representation Theory
of *p*-adic Groups, IISER Pune, July 18, 2017.

"The Kostant section and topologically nilpotent elements", AMS Special Session on recent developments in automorphic forms and representation theory, Hunter College, New York, May 6, 2017.

"Transferring representations between finite reductive groups",

- Workshop on
*p*-adic Groups, Radboud Universiteit, Nijmegen, Netherlands, March 17, 2017. - University of East Anglia, Norwich, England, May 9, 2016.
- Secret Automorphic Seminar, Ben Gurion University of the Negev, Beer Sheva, Israel, April 14, 2016.
- Algebra Seminar, Technion, Haifa, Israel, April 7, 2016.
- Institute for Mathematical Sciences, Chinese University of Hong Kong, March 30, 2016.
- New Developments in Representation Theory, Institute for Mathematical Sciences, National University of Singapore, March 24, 2016.
- Group, Lie, and Number Theory Seminar, University of Michigan, November 17, 2015.
- Paul J. Sally Midwest Representation Theory Conference Columbia, MO, November 13, 2015.

"Representations of *p*-adic GL(2)", a 9-hour minicourse given at IISER Pune, January 15-February 9, 2016.

"Nonstandard analysis", Math Club, IISER Pune, January 29, 2016.

"An education reform that passed the test of time", Mathematics Education Seminar, University of Toronto, October 20, 2015.

"Lifting representations of finite reductive groups", Mathematics Seminar, IISER Pune, July 30, 2014.

### Work In Progress

- Liftings of representations of finite groups (with Joshua Lansky)
- Structure of Bernstein blocks (with Manish Mishra)
- Relative harmonic analysis (with Eitan Sayag and Sandeep Varma)
- Tamely ramified tori in p-adic groups (with Stephen DeBacker)

### Research Interests

Adler studies harmonic analysis on reductive p-adic groups, a subject that is closely connected to number theory. He also occasionally directs undergraduate research projects.

### Grants and Sponsored Research

- American Institute of Mathematics, "SQuaRE with Character", 2018-2020. This grant supports week-long annual meetings for a group of six people for three years.
- National Security Agency, "Liftings and symmetric spaces over p-adic fields", 9/2013-8/2015, $145,723 (jointly with Professors Hakim and Lansky).
- National Science Foundation, "Characters, liftings, and types", 9/2009-8/2012, $521,588 (jointly with Professors Hakim and Lansky).
- National Security Agency, "Aspects of harmonic analysis on p-adic groups", 2007–09.
- National Science Foundation, "Algebra, Number Theory, and Applications: a research experience for undergraduates", 2005–08.
- National Security Agency, "Depth-zero base change", 2005–07.
- Office of Naval Research, "N03-T004: Optimizing Human Resource Management Models", July, 2003.
- National Security Agency, "Representations of p-adic groups", 2002–04.
- American Mathematical Society, Mathematical Challenges Travel Grant, August, 2000.

### Selected Publications

- On Kostant sections and topological nilpotence (with Jessica Fintzen and Sandeep Varma), J. London Math. Soc., 97 (2018), pp. 325-351. E-print available at arXiv:1611.08566.
- Character relations for a lifting of representations of finite reductive groups (with Michael Cassel, Joshua Lansky, Emma Morgan, and Yifei Zhao), Involve 9 (2016) no. 5, pp. 805-812.
- Liftings of representations of finite reductive groups I: semisimple conjugacy classes (with Joshua Lansky), Canadian J. Math 66 (2014), pp. 1201-1224.
- Extensions of representations of p -adic groups, (with Dipendra Prasad), Nagoya Math. J. 208 (2012), pp. 171-199. E-print available at arXiv:1108.3668.
- Depth-zero base change for ramified U(2,1) (with Joshua Lansky), Trans. Amer. Math. Soc., 362 (2010), pp. 5569-5599. E-print available at arXiv:0807.1528.
- Supercuspidal characters of reductive p-adic groups (with Loren Spice), Amer. J. Math. 131 (2009), pp. 1137-1210. E-print available at arXiv:0707.3313.
- Reading encrypted diplomatic correspondence: An undergraduate research project, (with Ryan Fuoss, Michael Levin, and Amanda Youell), Cryptologia,32 (2008), Issue 1, pp. 1–12.
- Good product expansions for tame elements of p-adic groups (with Loren Spice), Int. Math. Res. Pap. vol. 2008, 95 pages.
- The local character expansion near a tame, semisimple element (with Jonathan Korman), Amer. J. Math., 129 (2007), no. 2, 381–403.
- On certain multiplicity one theorems (with Dipendra Prasad), Israel J. Math, 153 (2006), 221–245.
- Depth-zero base change for unramified U(2, 1), (with Joshua Lansky), J. Number Theory 114 (2005), no. 2, pp. 324–360. Printer’s error corrected in vol. 121 (2006), no. 1, 186.
- Murnaghan-Kirillov theory for supercuspidal representations of tame general linear groups, (with Stephen DeBacker), J. Reine Angew. Math. 575 (2004), 1–35.
- Some applications of Bruhat-Tits theory to harmonic analysis on the Lie algebra of a reductive p-adic group (with Stephen DeBacker), Mich. J. Math. 50 (2002), No. 2, 263–286.
- Refined anisotropic K-types and supercuspidal representations, Pacific J. Math., 185 (1998), no. 1, 1–32.