# Nir Avni

I am an Assistant Professor in the Mathematics Department in Northwestern 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. Annals of Mathematics (2) 174,
(2011), 1009-1056

- Generating Product
Systems, With Benjamin Weiss. Journal of Modern Dynamics, 4 (2)
2010.

- Gelfand
Pairs Over Close Fields, With Avraham Aizenbud and Dmitry
Gurevich. Commentary Math. Helv. 87, (2012), 929-962.

- On Commensurator
Growth, With Seonhee Lim and Eran Nevo. Israel Journal of
Mathematics 188, (2012), 259-279.

- 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. Duke Math. J. Volume 162, Number 1 (2013),
111-197.

- Representation zeta functions of some compact p-adic analytic groups . With Benjamin Klopsch, Uri Onn, and
Christopher Voll. Proceedings of Recent Trends on Zeta Functions in
Algebra and Geometry, 295-330, Contemp. Math., 566,
Amer. Math. Soc., Providence, RI, 2012.

- Arithmetic Groups, Base Change and
Representation Growth . With Benjamin Klopsch, Uri Onn, and
Christopher Voll.

- Word Values in
p-Adic and Adelic Groups . With Tsachik Gelander, Martin
Kassabov, and Aner Shalev. To appear in Bulletin of the LMS

- Representation Growth
and Rational Singularities of the Moduli Space of Local Systems
. With Avraham Aizenbud.

My CV