I'm a professor at the Institute for Advanced Study
in Princeton, NJ. My email is my first name at math.ias.edu.
Unfortunately, because of the volume of email I get,
I am often unable to respond to queries not directly related to research mathematics.
Here is a list of papers, together with links to (not always the most updated) versions. Please let me know if any links are broken.
Relative Langlands duality,
with David Ben-Zvi and Yiannis Sakellaridis. Preliminary version, comments appreciated.
Symplectic L-functions and symplectic Reidemeister torsion (mod squares), with Amina Abdurrahman.
Some thoughts on automation and mathematical research. Not intended for publication.
The derived Hecke algebra for dihedral weight one forms, with Henri Darmon, Michael Harris and Victor Rotger,
to appear, Michigan Math Journal.
- Sparsity of integral points on moduli spaces of varieties,
with Brian Lawrence and Jordan Ellenberg, , IMRN
- Heights of automorphic forms and motives, to appear, proceedings of 2019 Tata Colloquium on arithmetic geometry.
- Eisenstein cocycles in motivic cohomology, with Romyar Sharifi, submitted.
- The Galois action on symplectic K-theory, with Tony Feng and Soren Galatius, to appear, Inventiones.
- The orbit method and analysis of automorphic forms, with Paul Nelson, to appear, Acta Math (2021).
- Diophantine problems and p-adic period mappings, with Brian Lawrence, Inventiones, (2020).
- Action of motivic cohomology on cohomology of arithmetic groups:
- The behavior of random reduced bases, with
Seungki Kim, to appear, IMRN (2017).
- Effective equidistribution
and property (tau), with Manfred Einsiedler, Gregory Margulis,
Amir Mohammadi, to appear, JAMS
- Functoriality, Smith
theory, and the Brauer homomorphism, with David Treumann.
Torsion homology growth and
cycle complexity of arithmetic manifolds, with N. Bergeron and
Hurwitz monodromy and full
number fields, with D. Roberts. Algebra and number theory
A torsion Jacquet-Langlands
F. Calegari. A shortened version will appear in Asterisque; the shortened version omits some material, but corrects several minor errors in the original, so please use it where possible.
Periods and harmonic analysis on spherical varieties , with
Yiannis Sakellaridis Asterisque (2018).
- Homological stability for
Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
, with Jordan Ellenberg and Craig Westerland, Annals (2016).
[The sequel to the above paper, available here,
had a gap affecting the results on Cohen-Lenstra heuristics, affecting parts of the introduction, Section 6, and Section 12, and discussed in this
blog post. Many of the unaffected results may now be found in Melanie Wood's paper An algebraic lifting invariant....
While we were ablel to recover some of the original applications under extra restrictions on target group and boundary monodromy, we are currently not intending to write a new version.
A note on sphere packings in high dimension , IMRN.
Asymptotic growth of torsion
homology for arithmetic groups, with N. Bergeron, JIMJ
Linnik's ergodic method and the distribution of integer points on
Jordan Ellenberg and Philippe Michel, proceedings, International
Colloquium at the Tata Institute (2012).
Modelling lambda invariants by p-adic random matrices,
Jordan Ellenberg and Sonal Jain, Communications in Pure and Applied
- Statistics of number fields and function fields,
with Jordan Ellenberg, Proceedings of the 2010 ICM (2010).
How small must ill-distributed sets be?, with Harald Helfgott. Analytic
number theory: essays in honor of Klaus Roth (2009).
- Some effective results for xaxb, with Jean
Bourgain, Elon Lindenstrauss, Philippe Michel,
Ergodic theory and dynamical systems (2009).
- Distribution of periodic torus orbits:
The distribution of
periodic torus orbits on homogeneous spaces, with Manfred
Einsiedler, Elon Lindenstrauss and Philippe Michel, DMJ
The distribution of periodic torus orbits on
homogeneous spaces II: Duke's theorem for quadratic fields.
, with Manfred Einsiedler, Elon Lindenstrauss, Philippe Michel,
- The distribution of
periodic torus orbits and Duke's theorem for cubic fields,
with Manfred Einsiedler, Elon Lindenstrauss and Philippe Michel, Annals
of Mathematics (2011). Erratum to theorem 4.9.
- The subconvexity problem for
GL(2), with Philippe Michel,
Publications Math IHES (2010).
- Effective equidistribution
for closed orbits of semisimple groups on homogeneous spaces,,
Manfred Einsiedler and Gregory Margulis,
Local-global principles for representations of quadratic forms,
with Jordan Ellenberg, Inventiones,
Sparse equidistribution problems, period bounds, and subconvexity,
- Entropy bounds for Hecke eigenfunctions on
division algebras , with Lior Silberman.
Appendix to "Counting maximal arithmetic subgroup", by M.
Belolipetsky, with Jordan Ellenberg.
The work of Einsiedler, Katok and Lindenstrauss on the Littlewood
Bulletin AMS (2007).
- Quantum unique
ergodicity on locally symmetric spaces, with L. Silberman. GAFA
Existence and Weyl's law for spherical cusp forms,
with E. Lindenstrauss. GAFA
Reflection principles and bounds for class group torsion, with
Effective computation of Maass forms, with A.
Booker and A. Strombergsson journal,
- The number of
extensions of number field with fixed degree and bounded
discriminant, with J. Ellenberg, Annals
- Integral points on
elliptic curves and 3-torsion in class
groups, with H. Helfgott, JAMS (2006).
Equidistribution, L-functions and ergodic theory: on some problems of
Yu. V. Linnik, with Ph. Michel, Proceedings of the 2006 ICM.
This is a longer version than the published one.
Heegner points and nonvanishing of Rankin-Selberg L-functions,
with P. Michel
Analytic number theory: a tribute to Gauss and Dirichlet (2006).
Large sieve inequalities for GL(n) forms in the conductor aspect,
in Math, 2006.
The Burger-Sarnak method and operations on the unitary dual of GL(n),
Representation Theory (2005).
On uniform bounds for rational points on non-rational
curves, with J. Ellenberg, IMRN (2005).
Counting extensions of function fields with specified Galois group
and bounded discriminant, with J. Ellenberg, Geometric methods
in algebra and number theory (2005).
Small solutions to linear congruences
and Hecke equidistribution, with A. Strombergsson, Acta
Beyond endoscopy and the classification of special forms on
- Dimension of the space of cusp forms associated
to 2-dimensional Galois representations, with P. Michel, IMRN
fixing equation (3.4).
Limiting forms of the trace formula , my PhD thesis (2002).
- Locally quasiprimitive graphs, with C. Prager, C.H. Li, S. Zhou, Discrete
I would like to acknowledge the support of the National Science
the Alfred P. Sloan foundation, and the Packard foundation. Any opinions
expressed in the above papers do not necessarily reflect the views of any