Amir Mohammadi

How to reach me

• Paper mail:
  Department of Mathematics
  970 Evans Hall, MC 3840
  Berkeley, CA 94720-3840
  USA
  
  
• Office: 839 Evans Hall
  
• E-mail: amirmo@math.berkeley.edu
  

Preprints and publications

• Polynomially effective equidistribution for unipotent orbits in products of SL₂ factors. pdf, (with E. Lindenstrauss and L. Yang). Preprint.
  
  
• Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms. pdf, (with E. Lindenstrauss, Z. Wang, and L. Yang). Preprint.
  
  
• Effective Equidistribution of semisimple adelic periods and representations of quadratic forms. pdf, (with M. Einsiedler, E. Lindenstrauss, and A. Wieser). Preprint.
  
  
• An effective closing lemma for unipotent flows. pdf, (with E. Lindenstrauss, G. Margulis, N. Shah, and A. Wieser). Journal d'Analyse, to appear.
  
  
• Spectral Independence. pdf, (with A. S. Golsefidy and K. Mallahi-Karai). Preprint.
  
  
• An effective version of the Oppenheim conjecture with a polynomial error rate. pdf, (with E. Lindenstrauss, Z. Wang, and L. Yang). Preprint.
  
  
• Quantitative equidistribution and the local statistics of the spectrum of a flat torus. pdf, (with E. Lindenstrauss and Z. Wang). Journal d'Analyse., 151 (2023), 181-234.
  
  
• Effective equidistribution for some one parameter unipotent flows. pdf, (with E. Lindenstrauss and Z. Wang). Ann. of Math., to appear.
  
  
• Polynomial effective equidistribution. pdf, (with E. Lindenstrauss and Z. Wang). C. R. Math., 361 (2023), 507-520.
  
  
• Polynomial effective density in quotients of H³ and H² × H². pdf, (with E. Lindenstrauss). Invent. Math., 231 (2023), 1141-1237.
  
  
• Finitary analysis in homogeneous spaces. pdf, Proceedings of the ICM 2022, Vol 5, 1300-1331.
  
  
• Property tau in positive characteristic. pdf, (with N. Tamam). Israel J. Math., 265 (2025), 569-604.
  
  
• Benjamini-Schramm convergence of periodic orbits. pdf, (with K. Rafi). Geom. Dedicatae, 216 (2022), 57-68.
  
  
• Locally random groups. pdf, (with K. Mallahi Karai and A. Salehi Golsefidy). Michigan Math. J., 72 (2022), 479-527.
  
  
• Isolations of geodesic planes in the frame bundle of a hyperbolic 3-manifold. pdf, (with H. Oh). Compositio Math., 159 (2023), 488-529.
  
  
• Effective counting of simple closed geodesics on hyperbolic surfaces. pdf, (with A. Eskin and M. Mirzakhani). Journal of European Math. Society, 24 (2022), 3059–3108.
  
  
• Quantitative behavior of unipotent flows and an effective avoidance principle. pdf, (with E. Lindenstrauss, G. Margulis, and N. Shah). Journal d'Analyse, 153 (2024), 1-61.
  
  
• Arithmeticity of hyperbolic 3-manifolds with infinitely many totally geodesic surfaces. pdf, (with G. Margulis). Ergodic Theory and Dynam. Systems, special volume in the memory of A. Katok, 42 (2022), 1188-1219.
  
  
• Diameter of homogeneuous spaces: An effective account. pdf, (with A. Salehi Golsefidy and F. Thilmany). Math. Ann., 385 (2023), 1973-2012.
  
  
• Effective arguments in unipotent dynamics. pdf, (with M. Einsiedler). In: Dynamics, Geometry, Number theory: The impact of Margulis on Modern Mathematics. University of Chicago Press, Chicago, IL, 2022, 426-451.
  
  
• Geodesic planes in the convex core of an acylindrical 3-manifold. pdf, (with C. McMullen and H. Oh). Duke Math. J., 171 (2022), 1029-1060.
  
  
• Diagonal actions in positive characteristic. pdf, (with M. Einsiedler and E. Lindenstrauss). Duke Math. J., 169 (2020), 117-175.
  
  
• Effective equidistribution and property tau. pdf, (with M. Einsiedler, G. Margulis, and A. Venkatesh). Journal of the AMS, 33 (2020), 223-289.
  
  
• On effective equidistribution for quotients of SL(d, R). pdf, (with M. Aka, M. Einsiedler, and H. Li). Israel J. of Math., 236 (2020), 365-391.
  
  
• Characteristic free measure rigidity for the action of solvable groups on homogeneous spaces. pdf, (with A. Salehi Golsefidy). Geom. and Func. Anal., 28 (2018), 179-227.
  
  
• Geodesic planes in hyperbolic 3-manifolds. pdf, (with C. McMullen and H. Oh). Invent. Math., 209 (2017), 425-461.
  
  
• Horocycles in hyperbolic 3-manifolds. pdf, (with C. McMullen and H. Oh). Geom. and Func. Anal., 26 (2016), 961-973.
  
  
• Invariant Radon measures for Unipotent flows and products of Kleinian groups. pdf, (with H. Oh). Proc. of the AMS, 146 (2018), 1469-1479.
  
  
• Closed geodesics and holonomies for Kleinian manifolds. pdf, (with G. Margulis and H. Oh). Geom. and Func. Anal., 24 (2014), 1608-1636.
  
  
• Classification of joinings for Kleinian groups. pdf, (with H. Oh). Duke Math. J., 165 (2016), 2155-2223.
  
  
• Isolation, equidistribution, and orbit closures for the SL(2, R) action on Moduli space. pdf, (with A. Eskin and M. Mirzakhani). Ann. of Math., 182 (2015), 673-721.
  
  
• Matrix coefficients, counting and primes for orbits of geometrically finite groups. pdf, (with H. Oh). Journal of European Math. Society, 17 (2015), 837-897.
  
  
• On ergodic properties of the Burger-Roblin measure. pdf, In "Thin groups and superstrong approximation", edited by E. Breuillard and H. Oh, Math. Sci. Res. Inst. Publ. 61, Cambridge Univ. Press. Cambridge 2014.
  
  
• Ergodicity of unipotent flows and Kleinian groups. pdf, (with H. Oh). Journal of the AMS, 28 (2015), 531-577.
  
  
• Logarithm laws for one parameter unipotent flows. pdf, (with D. Kelmer). Geom. and Func. Anal., 22 (2012), 756-784.
  
  
• On presentations of integer polynomial points of simple groups over number fields. pdf, (with K. Wortman). Geometriae Dedicata, 164 (2013), 131-137.
  
  
• A special case of effective equidistribution with explicit constants. pdf, Ergodic Theory Dynam. Systems, 32 (2012), 237-247.
  
  
• Measures invariant under horospherical subgroups in positive characteristic. pdf, J. Mod. Dynamics, 5 (2011), 237-254.
  
  
• The extremal symmetry of arithmetic simplicial complexes. pdf, (with B. Farb). Advances in Math., 231 (2012), 843-854.
  
  
• Quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms. pdf, (with G. A. Margulis). Duke Math. J., 158 (2011), 121-160.
  
  
• A joining classification and special case of Raghunathan's conjecture in positive characteristic. pdf, (with M. Einsideler, with an appendix by K. Wortman). J. D'Analyse Math., 116 (2012), 299-334.
  
  
• Discrete transitive actions on vertices of Bruhat-Tits buildings. pdf, (with A. Salehi Golsefidy). Duke Math. J., 161 (2012), 483-544.
  
  
• Translates of horospheres and counting problems. pdf, (with A. Salehi Golsefidy). American J. Math., 136 (2014), 1301-1346.
  
  
• Unipotent flows and isotropic quadratic forms in positive characteristic. pdf. Int. Math. Res. Notices, (2011), 4535-4554.
  
  
• Simultaneous Diophantine approximation on non-degenerate p-adic manifolds. pdf (with A. Salehi Golsefidy). Israel J. Math., 188 (2012), 231-258.
  
  
• S-Arithmetic Khintchine type theorem. pdf (with A. Salehi Golsefidy). Geom. and Func. Anal., 19 (2009), 1147-1170.
  
  
• SL(n, Z[t]) is not FP_n-1. pdf (with K. U. Bux and K.Wortman). Comm. Math. Helv., 85 (2010), 151-164.
  
  

Curriculum Vitae

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Research supported in parts by the NSF.