# Jeffrey Adler Professor Department of Mathematics and 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.

## Partnerships & Affiliations

## Scholarly, Creative & Professional Activities

### Honors, Awards, and Fellowships

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

### Work In Progress

- Liftings of representations of finite groups (with Joshua Lansky)
- Multiplicity upon restriction (with Dipendra Prasad)
- Relative harmonic analysis (with Eitan Sayag and Sandeep Varma)
- Tamely ramified tori in p-adic groups (with Stephen DeBacker)

### Grants and Sponsored Research

- 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.

### 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.

### 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.

### Professional Presentations

[Past few years only]

"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.

"Representation theory and p-adic numbers: What and why?",

- Mathematics Colloquium, IISER Pune, July 24, 2014.
- Frank Stones Lecture, Texas Christian University, March 10, 2011.

"The dual of a reductive group",

- Special Session on Recent Progress in the Langlands Program, Joint Mathematics Meetings, Baltimore, January 15, 2014.
- Session on Harmonic Analysis on Groups over Local Fields, 2013 Canadian Mathematical Society Winter Meeting, Ottawa, December 6--9, 2013.

"Towards a lifting of representations of finite reductive groups",

- Algebra and Combinatorics Seminar, North Carolina State University, March 11, 2013.
- Lie Theory Seminar, University of Minnesota, April 8, 2011.

"Liftings and Deligne-Lusztig theory", Conference on Representation Theory of Finite Groups of Lie Type: Deligne-Lusztig Theory, Tata Institute of Fundamental Research, Mumbai, India, December 16, 2011.

"Lifting representations of finite reductive groups", Representation Theory Seminar, University of Oklahoma, March 4, 2011.