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.

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.

Professional Presentations

• “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.

Selected Publications

• 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., to appear. E-print available at arXiv:0707.3313 (http://arxiv.org/abs/0707.3313).

Grants and Sponsored Research

• 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.)