Akshay Venkatesh -- Research Interests

My research is in number theory and various related topics. I like problems where there is interesting interaction between analysis and algebra.

Older papers (sorry, there are quite a few journal links missing)

The pdf files are preliminary versions and usually differ from the (final) journal versions. I do not know of any significant mathematical errors in the preliminary versions, but you should use the journal versions if you have access to them; in some cases the results there are sharper.
Link to paper Title Coauthors Publication details
pdf, arxiv Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II. Jordan Ellenberg and Craig Westerland. Submitted
pdf, arxiv A torsion Jacquet-Langlands correspondence. (Book) F. Calegari. Submitted
pdf, arxiv Periods and harmonic analysis on spherical varieties Yiannis Sakellaridis
pdf A note on sphere packings in high dimension IMRN, to appear.
pdf The distribution of periodic torus orbits on homonegeous spaces II: Duke's theorem for quadratic fields. Manfred Einsiedler, Elon Lindenstrauss, Phlippe Michel. l'Enseignment Math. to appear.
pdf Modelling lambda invariants by p-adic random matrices Jordan Ellenberg and Sonal Jain to appear, Communications in Pure and Applied Math
pdf Statistics of number fields and function fields Jordan Ellenberg Proceedings ICM, to appear.
arxiv Asymptotic growth of torsion homology for arithmetic groups. N. Bergeron. JIMJ, to appear.
arxiv Linnik's ergodic method and the distribution of integer points on spheres. Jordan Ellenberg and Philippe Michel. to appear, proceedings, International Colloquium at the Tata Institute (2012)
arxiv Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields Jordan Ellenberg and Craig Westerland Submitted.
arxiv, journal. The subconvexity problem for GL(2) Ph. Michel Publications Math IHES.
pdf, journal Some effective results for xaxb Jean Bourgain, Elon Lindenstrauss and Philippe Michel Ergodic theory and dynamical systems
arxiv. The distribution of periodic torus orbits and Duke's theorem for cubic fields Manfred Einsiedler, Elon Lindenstrauss and Philippe Michel Annals of Mathematics, to appear.
journal, arxiv. Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces, Manfred Einsiedler and Gregory Margulis Inventiones (2009)
pdf Entropy bounds for Hecke eigenfunctions on division algebras Lior Silberman Accepted GAFA*
journal, pdf, The distribution of periodic torus orbits on homogeneous spaces Manfred Einsiedler, Elon Lindenstrauss and Philippe Michel DMJ (2009).
pdf How small must ill-distributed sets be? Harald Helfgott Analytic number theory: essays in honor of Klaus Roth. (2009)
journal, pdf The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture (none) Bulletin AMS, (2007).
journal, arxiv Local-global principles for representations of quadratic forms Jordan Ellenberg Inventiones (2008).
pdf , journal. Reflection principles and bounds for class group torsion J. Ellenberg IMRN (2007).
journal, arxiv. Quantum unique ergodicity on locally symmetric spaces L. Silberman GAFA (2007)
pdf of long form, Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik Ph. Michel Proceedings International Congress of Mathematicians 2006
journal, pdf (more recent), arxiv. Appendix to "Counting maximal arithmetic subgroup", by M. Belolipetsky J. Ellenberg Duke (2007).
arxiv , journal. Existence and Weyl's law for spherical cusp forms. E. Lindenstrauss GAFA (2007)
journal, PDF. Effective computation of Maass forms A. Booker and A. Strombergsson IMRN (2007).
arxiv, journal. Sparse equidistribution problems, period bounds, and subconvexity. (none) Annals (2010).
pdf. Heegner points and nonvanishing of Rankin-Selberg L-functions P. Michel Analytic number theory: a tribute to Gauss and Dirichlet (2006).
journal, pdf. Large sieve inequalities for GL(n) forms in the conductor aspect (none) Adv. Math (2006).
pdf, journal The Burger-Sarnak method and operations on the unitary dual of GL(n) (none) Representation Theory (2005).
journal, arxiv The number of extensions of number field with fixed degree and bounded discriminant J. Ellenberg Annals (2006).
arxiv. Integral points on elliptic curves and 3-torsion in class groups H. Helfgott JAMS (2006).
pdf. On uniform bounds for rational points on non-rational curves J. Ellenberg IMRN (2005)
pdf. Counting extensions of function fields with specified Galois group and bounded discriminant J. Ellenberg Geometric methods in algebra and number theory (2005).
pdf. Small solutions to linear congruences and Hecke equidistribution A. Strombergsson Acta Arithmetica 118 (2005).
journal, pdf, Beyond endoscopy and the classification of special forms on GL(2) (none) Crelle (2004)
journal; pdf Dimension of the space of cusp forms associated to 2-dimensional Galois representations P. Michel IMRN (2002).
pdf Limiting forms of the trace formula (none) Princeton thesis (2002).
Locally quasiprimitive graphs C. Prager, C.H. Li, S. Zhou Discrete Math (2002).

I would like to acknowledge the support of the National Science Foundation, the Alfred P. Sloan foundation, and the Packard foundation. Any opinions expressed in the above papers do not necessarily reflect the views of any sponsoring agency.