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Jeffrey Adler Professor 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.

Teaching

Fall 2024

  • MATH-221 Calculus I

  • MATH-222 Calculus II

Spring 2025

  • MATH-221 Calculus I

  • MATH-221 Calculus I

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]

"Hecke algebra isomorphisms for tame types", Anaparastaseis: Orbits, Hecke algebras, and representations, Nisyros, Greece, July 15, 2023.

"Finite-group actions on reductive groups and buildings II: The unauthorized sequel",

  • Representations and Characters: Revisiting some aspects of the works of Harish-Chandra and Weil, a satellite conference of the International Congress of Mathematicians, National University of Singapore, July 7, 2022. (Video)
  • Seminar, Tata Institute of Fundamental Research, Mumbai, India, August 23, 2022.
  • Number theory seminar, Indian Institute of Science, Bangalore, India, August 29, 2022.
  • Arbeitsgemeinschaft Arithmetische Geometrie, Max Planck Institute for Mathematics, Bonn, Germany, November 15, 2022.

"P-adic groups: what and why?",

  • Colloquium, Indian Institute of Technology (Bombay), Mumbai, India, August 17, 2022.
  • Colloquium, Indian Institute for Science Education and Research, Pune, India, September 20, 2022.

"Regular Bernstein blocks", Special Session on Representations of p-adic groups and Langlands correspondences, 75th+1 Anniversary Meeting, Canadian Mathematical Society, June 10, 2021.

"Self-dual cuspidal and supercuspidal representations",

  • Number Theory Seminar, Johns Hopkins University, February 12, 2020.
  • 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.

Grants and Sponsored Research

  • American Institute of Mathematics, "SQuaRE with Character", 2018-2020.  This grant supported 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.
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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.

Work In Progress

  • Liftings of representations of finite groups (with Joshua Lansky)
  • Actions of groups on reductive groups and buildings (with Joshua Lansky and Loren Spice)
  • Relative harmonic analysis (with Eitan Sayag and Sandeep Varma)

Selected Publications

  • Reduction to depth zero for tame p-adic groups via Hecke algebra isomorphisms (with Jessica Fintzen, Manish Mishra, and Kazuma Ohara), August, 2024.  E-print available at arXiv:2024.07805.
  • Structure of Hecke algebras arising from types (with Jessica Fintzen, Manish Mishra, and Kazuma Ohara), August, 2024.  E-print available at arXiv:2024.07801.
  • Liftings of representations of finite reductive groups II: Explicit conorm functions (with Joshua Lansky), J. Algebra 631 (2023), pp. 610-657.  E-print available at arXiv:1109.0794.
  • Self-dual cuspidal representations (with Manish Mishra), Represent. Theory 24 (2020), pp. 210-228. E-print available at arXiv:1903.02770.
  • Multiplicity upon restriction to the derived subgroup (with Dipendra Prasad), Pacific J. Math., 301 (2019), pp. 1-14.  E-print available at arXiv:1806.03635.
  • 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.
  • 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.
  • The local character expansion near a tame, semisimple element (with Jonathan Korman), Amer. J. Math., 129 (2007), no. 2, 381–403.
  • 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.