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 nonprofessional 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 2028855950 or submit a request.
Teaching
Fall 2024

MATH221 Calculus I

MATH222 Calculus II
Spring 2025

MATH221 Calculus I

MATH221 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.
"Finitegroup actions on reductive groups and buildings II: The unauthorized sequel",
 Representations and Characters: Revisiting some aspects of the works of HarishChandra 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.
"Padic 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 padic groups and Langlands correspondences, 75th+1 Anniversary Meeting, Canadian Mathematical Society, June 10, 2021.
"Selfdual 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.
"Padic groups: what and why?", Joint Colloquium, Chebyshev Laboratory and the Laboratory for Modern Algebra and Applications, SaintPetersburg State University, SaintPetersburg, Russia, June 7, 2018. (Video)
"Root data with group actions", Workshop and Conference on Representation Theory of padic 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 padic 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 padic GL(2)", a 9hour minicourse given at IISER Pune, January 15February 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", 20182020. This grant supported weeklong annual meetings for a group of six people for three years.
 National Security Agency, "Liftings and symmetric spaces over padic fields", 9/20138/2015, $145,723 (jointly with Professors Hakim and Lansky).
 National Science Foundation, "Characters, liftings, and types", 9/20098/2012, $521,588 (jointly with Professors Hakim and Lansky).
 National Security Agency, "Aspects of harmonic analysis on padic groups", 2007–09.
 National Science Foundation, "Algebra, Number Theory, and Applications: a research experience for undergraduates", 2005–08.
 National Security Agency, "Depthzero base change", 2005–07.
 Office of Naval Research, "N03T004: Optimizing Human Resource Management Models", July, 2003.
 National Security Agency, "Representations of padic groups", 2002–04.
 American Mathematical Society, Mathematical Challenges Travel Grant, August, 2000.
Research Interests
Adler studies harmonic analysis on reductive padic 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 padic groups via Hecke algebra isomorphisms (with Jessica Fintzen, Manish Mishra, and Kazuma Ohara), August, 2024. Eprint available at arXiv:2024.07805.
 Structure of Hecke algebras arising from types (with Jessica Fintzen, Manish Mishra, and Kazuma Ohara), August, 2024. Eprint available at arXiv:2024.07801.
 Liftings of representations of finite reductive groups II: Explicit conorm functions (with Joshua Lansky), J. Algebra 631 (2023), pp. 610657. Eprint available at arXiv:1109.0794.
 Selfdual cuspidal representations (with Manish Mishra), Represent. Theory 24 (2020), pp. 210228. Eprint available at arXiv:1903.02770.
 Multiplicity upon restriction to the derived subgroup (with Dipendra Prasad), Pacific J. Math., 301 (2019), pp. 114. Eprint 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. 805812.
 Liftings of representations of finite reductive groups I: semisimple conjugacy classes (with Joshua Lansky), Canadian J. Math 66 (2014), pp. 12011224.
 Depthzero base change for ramified U(2,1) (with Joshua Lansky), Trans. Amer. Math. Soc., 362 (2010), pp. 55695599. Eprint available at arXiv:0807.1528.
 Supercuspidal characters of reductive padic groups (with Loren Spice), Amer. J. Math. 131 (2009), pp. 11371210. Eprint 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.
 Depthzero 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.
 MurnaghanKirillov theory for supercuspidal representations of tame general linear groups, (with Stephen DeBacker), J. Reine Angew. Math. 575 (2004), 1–35.
 Some applications of BruhatTits theory to harmonic analysis on the Lie algebra of a reductive padic group (with Stephen DeBacker), Mich. J. Math. 50 (2002), No. 2, 263–286.
 Refined anisotropic Ktypes and supercuspidal representations, Pacific J. Math., 185 (1998), no. 1, 1–32.