Research

I got my Ph.D. under supervision of Gregory Margulis, from Yale university. He and Alex Lubotzky had a great influence on my mathematical work.

I was a Veblen research instructor, from Sep 2006-Jun 2009, in the Mathematics department , Princeton University and Institute for Advanced Study.

I was an Assistant Professor, from July 2009-Jun 2011, in the Mathematics department, Princeton University. During this time, I also served as a placement officer, which means I helped students (mostly freshmen, sophomore and students from local high schools) to find a course which is challenging enough for them.

I was an Assistant Professor, from July 2011-Jun 2015, in UCSD.

I was an Associate Professor, from July 2015-Jun 2019, in UCSD.

My research is partially funded by NSF grants DMS-1602137 and DMS-1902090.

##### Interests
• Algebraic, arithmetic, and analytic properties of linear groups.
• Homogeneous dynamical systems.
##### Preprints
• (with K. Mallahi-Karai, A. Mohammadi) Locally random groups, preprint. pdf.
• (With B. Longo) Towards super-approximation in positive characteristic, preprint. pdf.
• (With A. Mohammadi, F. Thilmany) Diameter of homogeneous spaces: an effective account, preprint. pdf.
##### Publications
• (With X. Zhang) Inducing Super-approximation, accepted for publication in IMRN. pdf.
• Super-approximation, II: $$p$$-adic and bounded power of square-free integer cases, JEMS 21 (2019), no. 7, 2163-2232. pdf.
• Sum-product phenomena: the $$\mathfrak{p}$$-adic case, accepted for publication in Journal d'Analyse Mathematique. pdf.
• (With A. Mohammadi) Characteristic free measure rigidity for the action of solvable groups on homogeneous spaces, GAFA 28 (2018), no 1, 179--227 pdf.
• Super-approximation, I: $$p$$-adic semisimple, IMRN 2017, no 23, (2017) 7190-7263. pdf.
• (With R. Boutonnet, A. Ioana) Local spectral gap in simple Lie groups and applications, Inventiones mathematicae 208 , no 3, (2017) 715-802. pdf.
• (With A. Mohammadi) Translates of horospherical measure and counting problems, American Journal of Mathematics 136, no 5, (2014) 1301-1346. pdf
• Affine sieve and expanders, Thin Groups and Superstrong Approximation, (Editors: H. Oh, E. Breuillard), MSRI publication 61, Cambridge University Press, New York, NY, USA, 2014. pdf
• (With P. Sarnak) Affine Sieve, JAMS 26 no. 4 (2013) 1085-1105. pdf
• (With P. Varju) Expansion in perfect groups, GAFA 22 no. 6 (2012), 1832-1891. pdf
• Lattices of minimum covolume in positive characteristic are non-uniform, Israel Journal of Math. 196, no. 1, (2013) 363-373. pdf
• Counting lattices in simple Lie groups: the positive characteristic case, Duke Mathematical Journal 161, no. 3, (2012) 431-481. pdf
• (With A. Mohammadi) Discrete subgroups acting transitively on vertices of a Bruhat-Tits building, Duke Mathematical Journal 161 no. 3 (2012) 483-544. pdf
• (With A. Mohammadi) Simultaneous Diophantine approximation on non-degenerate p-adic analytic manifolds, Israel Journal of Math. 188, no. 1, (2012) 231-258. pdf
• (With A. Mohammadi) S-Arithmetic Khintchine-Type Theorem, GAFA 19 no. 4 (2009) 1147-1170. pdf
• Lattices of minimum covolume in Chevalley groups over local fields of positive Char., Duke Mathematical Journal 146 no. 2 (2009) 227-251. pdf
• Character degrees of p-groups and pro-p groups, Journal of Algebra 286 no.2 (2005) 476-491. pdf
• (With S.Akbari, R.Ebrahimian & H.Momenaee Kermani) Maximal subgroups of GLn(D), Journal of Algebra 259 no.1 (2003) 201-225. pdf
• (With S.Akbari, R.Ebrahimian & H.Momenaee Kermani) The group of units of an Artinian ring, Algebra Colloq. 9 (2002) 81-88.
##### Misc. Publication
• (With A. Khojastepour, S. Rangarajan) Towards an optimal beamforming algorithm for physical layer multicasting, IEEE information theory workshop 2011.
• (With A. Khojastepour and A. Keshavarz-Haddad) On capacity achieving property of rotational coding for acyclic deterministic wireless networks, WiOpt2010, 313-317. pdf