Chair, Department of Mathematics and Statistics
Department of Mathematics and Statistics
- 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.
DegreesPhD, Mathematics, The University of Chicago
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- For Spring 2014: MTh 2:45-4:30; W 10:30-11:45; and by appointment.
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Scholarly, Creative & Professional Activities
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.
Honors, Awards, and Fellowships
- Buchtel College of Arts and Sciences Early Career Research Award, The University of Akron, April, 2004.
- Member, Institute for Mathematical Sciences, Singapore, August, 2002.
- “Supercuspidal characters and coadjoint orbits,” Mini-colloque: Harmonic analysis on p-adic groups, Institut Henri Poincaré, Paris, June, 2000.
- “Murnaghan-Kirillov Theory for supercuspidal representations,” Harmonische Analysis und Darstellungstheorie topologischer Gruppen, Mathematisches Forschungsinstitut Oberwolfach, Germany, July, 2000.
- “Supercuspidal character germs for classical groups”, PIMS Workshop on Representations of Reductive p-adic Groups, Banff, Canada, February, 2002.
- “Base change, with an example”, Institute for Mathematical Sciences, Singapore, 31 July, 2002.
- “Categorical properties of supercuspidal representations,” Purdue University, November, 2003.
- “The local character expansion near a tame, semisimple element”, Recent Trends in Endoscopy and Representation Theory (a conference in honor of E.-W. Zink), Berlin, October 20, 2005.
- “Connectedness of centralizers: work of Steinberg”, Harish-Chandra Research Institute, Allahabad, India, November 9–10, 2005.
- “Representations of nilpotent groups”, Colloquium: Tata Institute of Fundamental Research, Mumbai, India, November 17, 2005.
- “Multiplicity one upon restriction”, Fields Institute Workshop on the Representation Theory of Reductive Algebraic Groups, University of Ottawa, January 21, 2007.
- “Towards a lifting of representations of finite reductive groups”, Special Session on p-adic Groups and Automorphic Forms, AMS Meeting #1041, Vancouver, Canada, October 4–5, 2008.
- "Tamely ramified tori", Special Session on harmonic analysis and representations of reductive p-adic groups, Joint Mathematics Meetings, San Francisco, January 16, 2010.
- "Towards a lifting of representations of reductive p-adic groups", 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.
- Refined anisotropic K-types and supercuspidal representations, Pacific J. Math., 185 (1998), no. 1, 1–32.
- 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.
- Murnaghan-Kirillov theory for supercuspidal representations of tame general linear groups, (with Stephen DeBacker), J. Reine Angew. Math. 575 (2004), 1–35.
- Injectivity, projectivity, and supercuspidal representations, (with Alan Roche), J. London Math. Soc. (2) 70 (2004), no. 2, 356–368.
- 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.
- On certain multiplicity one theorems (with Dipendra Prasad), Israel J. Math, 153 (2006), 221–245.
- The local character expansion near a tame, semisimple element (with Jonathan Korman), Amer. J. Math., 129 (2007), no. 2, 381–403.
- Good product expansions for tame elements of p-adic groups (with Loren Spice), Int. Math. Res. Pap. vol. 2008, 95 pages.
- Reading encrypted diplomatic correspondence: An undergraduate research project, (with Ryan Fuoss, Michael Levin, and Amanda Youell), Cryptologia,32 (2008), Issue 1, pp. 1–12.
- 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.
- 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 SL(2) over a p-adic field (with Stephen DeBacker, Paul J. Sally, Jr., and Loren Spice), in Harmonic analysis on reductive p-adic groups (Robert S. Doran, Paul J. Sally, Jr., and Loren Spice, eds.), Contemp. Math., vol. 543, pp. 19-69, American Mathematical Society, 2011. Eprint available at arXiv:1012.5548.
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.
Work In Progress
- Liftings of representations of finite groups (with Joshua Lansky)
- Self-similar periodic tilings of nilpotent Lie groups (with Judith Palagallo et al.)
- Tamely ramified tori in p-adic groups (with Stephen DeBacker)
- Characters of p-adic division algebras (with Loren Spice)
AU News and Achievements
Math Students Play Crucial Role in Proving Theorem
Mike Cassel, Emma Morgan, and Yifei Zhao worked with AU professors this summer to prove new mathematical ...