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.

My research is partially funded by NSF grant DMS-1160472 and I am an Alfred P. Sloan Research Fellow (Sep. 2012-Sep. 2016).

##### Interests
• Algebraic, arithmetic, and analytic properties of linear groups.
• Homogeneous dynamical systems.
##### Preprints
• Super-approximation, II: $$p$$-adic and bounded power of square-free integer cases, preprint. pdf.
• Sum-product phenomena: the $$\mathfrak{p}$$-adic case, preprint. pdf.
• (With X. Zhang) Inducing Super-approximation, preprint. pdf.
##### Publications
• (With A. Mohammadi) Characteristic free measure rigidity for the action of solvable groups on homogeneous spaces, accepted for publication in GAFA 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
##### Talks
• May 2015, Workshop: Advances in homogeneous dynamics, MSRI, Berkeley, CA.
• May 2015, Atkin memorial workshop: Expansion in linear groups, University of Illinois at Chicago, Chicago, IL.
• May 2015, Atkin memorial lecturer, University of Illinois at Chicago, Chicago, IL.
• April 2015, Open ended seminar, MSRI, Berkeley, CA.
• April 2015, Workshop: Dynamics on moduli spaces, MSRI, Berkeley, CA.
• February 2015, Zariski-dense Subgroups, Institute for Pure and Applied Mathematics, Los Angeles, CA.
• Jan 2015-May 2015, Geometric and Arithmetic Aspects of Homogeneous Dynamics, MSRI, Berkeley, CA, Jan 2015-May 2015. (Visiting Professor)
• July 2014, Groups, Numbers, and Dynamics, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
• June 2014, Interactions between Dynamics of Group Actions and Number Theory, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. (Visiting Fellowship)
• April 2013, Arithmetic Groups, Banff International Research Station, Banff, Alberta, Canada.
• November 2013, The Southwestern Group Theory Day, University of Arizona, Tucson, AZ. (Unable to attend)
• January 2013, Special session on Groups, Representations, and Applications, Joint AMS meeting, San Diego, CA
• December 2012, Conference in honor of Professor Siavash Shahshahani, Sharif University of Technology, Tehran, Iran.
• November 2012, Geometry, topology and dynamics, Paris 11, Orsay, France.
• November 2012, Algebra seminar, University of California, San Diego, CA.
• October 2012, Group actions and dynamical system, University of Texas, Austin, TX.
• April 2012, Southern California Algebra Conference, University of California, Los Angeles, CA.
• March 2012, Geometry and analysis of large networks, Vanderbilt University, Nashville, TN.
• February 2012, Hot Topics: Thin Groups and Super-strong Approximation, MSRI, Berkeley, CA.
• July 2011, Geometry and arithmetic of lattices, LMS-EPSRC Durham symposium, Durham University, Durham, UK.
• June 2011, Groups and additive combinatorics, Isaac Newton Institute for mathematical sciences, a satellite meeting at Gregynog hall, University of Wales, UK.
• April 2011, Special session on interactions between Dynamical Systems, Number Theory, and Combinatorics, AMS sectional meeting, Worcester, MA.
• March 2011, Number theory seminar, IAS/Princeton University, Princeton, NJ.
• March 2011, New York joint Number Theory Seminar, CUNY Graduate Center, New York, NY.
• March 2011, Group Actions, Dynamics and Geometry Seminar, Brown University, Providence, RI.
• February 2011, Geometry seminar, University of Michigan, Ann Arbor, MI.
• February 2011, Joint Topology and GLNT seminar, University of Michigan, Ann Arbor, MI.
• February 2011, Colloquium, Rutgers University, Piscataway, NJ.
• January 2011, Colloquium, UC, San Diego, CA.
• January 2011, Special session on Expanders Graphs in Pure and Applied Mathematics, Joint AMS meeting, New Orleans, LA.
• December 2010, Workshop on Arithmetic and Geometry, IPM, Tehran, Iran.
• December 2010, The Second Annual Manhattan Group Theory Day, CUNY Graduate Center, NewYork, NY.
• August 2010, Geometry, Topology and Dynamics in Negative Curvature, ICM 2010 Satellite conference, Bangalore, India. (Unable to attend)
• July 2010, Workshop on Homogeneous Dynamics and Number Theory, Oberwolfach, Germany. (Unable to attend)
• April 2010, Workshop on Arithmetic Groups and their Applications in Combinatorics, Geometry and Topology, University of Virginia, Charlottesville, VA.
• October 2009, Dynamics of group actions, Yale University, New Haven, CT.
• May 2009, Special Number Theory/Topology/Geometry Seminar, University of Texas, Austin, TX.
• April 2009, What is happening in Fine hall?, Princeton University, Princeton, NJ.
• April 2008, Group Actions: Dynamics, Geometry, Invariants Seminar, Yale University, New Haven, CT.
• April 2008, Algebra seminar, University of Virginia, Charlottesville, VA.
• April 2008, Colloquium, University of Virginia, Charlottesville, VA.
• April 2008, Number theory/Arithmetic geometry, UIC, Chicago, IL.
• March 2008, Topology and geometric group theory seminar, Cornell University, Ithaca,NY.
• February 2008, Algebra and Lie groups seminar, Yale University, New Haven, CT.
• November 2007, Group actions seminar, Brown University, Providence, RI.
• October 2007, Joint Algebra-Geometry seminar, Indiana University,Bloomington, IN.
• October 2007, Topology and geometric group theory seminar, Cornell University, Ithaca,NY.
• September 2007, Conference in honor of Zimmer's 60th birthday, University of Chicago, IL.
• November 2006, Geometry seminar, University of Michigan, Ann Arbor, MI.
• October 2006, Group and Lie theory seminar, University of Michigan, Ann Arbor, MI.
• October 2006, Number theory seminar, Princeton University/ IAS, Princeton, NJ.
• April 2006, Group theory seminar, Rutgers University, Piscataway, NJ.
• February 2006, Lie groups, representations and discrete math, IAS, Princeton, NJ.
• October 2005, Fellowship of the Ring, Brandies, Waltham, MA.
• May 2005, Lie Group Seminar, CalTech, Pasadena, CA.
• April 2005, Special Session on Arithmetic Lattices, AMS Sectional Meeting, Newark,DE.
• March 2005, Topology & Group Theory Seminar, Cornell University, Ithaca,NY.
• November 2004, Group Actions: Dynamics, Geometry, Invariants Seminar, Yale University, New Haven, CT.
• October 2004, Albany Group Theory Conference,Rensselaerville, NY.
• August 2004, Graduate Seminar,Yale University, New Haven, CT.