Nir Avni

I am a Benjamin Pierce Lecturer in the Mathematics Department in Harvard University.

My email is: MyLastName(dot)MyFirstName(at)gmail(dot)com

Research Interests

• Representation Theory.
• Algebraic Groups.
• Motivic Integration.

Publications

Written

• Spectral and Mixing Properties of Actions of Amenable Groups. Electronic Research Anouncements of the American Mathematical Society 11 (2005), 57-63.
• Entropy Theory for Cross Sections. Geometric and Functional Analysis 19 (2010), 1515--1538.
• The Value Ring of Geometric Motivic Integration and the Iwahori Hecke Algebra of SL_2, By Ehud Hrushovski and David Kazhdan. Appendix by Nir Avni. Geometric and Functional Analysis 17(6) (2007), 1924-1967.
• Conjugacy Classes of 3 By 3 Matrices Over Local Rings, With Uri Onn, Amrithanshu Prasad and Leonid Vasserstein. Communications in Algebra, 37(8), 2601-2615 (2009).
• Connectivity of the Product Replacement Graph of Simple Groups of Bounded Lie Rank, With Shelly Garion. J. Algebra 320 (2008), 945-960.
• Arithmetic Groups Have Rational Representation Growth. Ta appear in Annals of Mathematics
• Generating Product Systems, With Benjamin Weiss. Journal of Modern Dynamics, 4 (2) 2010.
• Gelfand Pairs Over Close Fields, With Avraham Aizenbud and Dmitry Gurevich. To appear in Commentary Math. Helv.
• On Commensurator Growth, With Seonhee Lim and Eran Nevo. To appear in Israel Journal of Mathematics
• On Representation Zeta Functions of Groups, and a Conjecture of Larsen--Lubotzky, With Benjamin Klopsch, Uri Onn, and Christopher Voll. C. R. Math. Acad. Sci. Paris, Ser. I 348 (2010), 363 -- 367.
• Representation Zeta Functions Of Compact $p$-Adic Analytic Groups And Arithmetic Lattices. With Benjamin Klopsch, Uri Onn, and Christopher Voll.
• Representation zeta functions of some compact p-adic analytic groups . With Benjamin Klopsch, Uri Onn, and Christopher Voll.

In preparation

• Base Change and Representation Growth.