Research Page

    I am interested in the problems at the intersection of the areas of automorphic forms and algebraic cycles.

    My research is currently supported by NSF grants DMS 2001293 and (RTG) DMS 1840234 .

    Previous support: NSF grants DMS 1600494, DMS 1160720, DMS 1015173, DMS 0801191, DMS 0854900.

    Note: Clicking on the link below should open up a pdf file with the most current version of the article.

  1. Integrality of a ratio of Petersson norms and level-lowering congruences , Ann. of Math., (2), 163 (2006), no. 3, pp. 901-967.

  2. Arithmetic properties of the theta correspondence and periods of modular forms , Eisenstein series and Applications, Progress in Math. 258, Birkhauser, 2008, pp. 251-269.

  3. Arithmetic properties of the Shimura-Shintani-Waldspurger correspondence (with an appendix by Brian Conrad) , Invent. Math. 176, p. pp. 521-600 (2009).

  4. On p-adic properties of central values of quadratic twists of an elliptic curve , Canad. J. Math. 62 (2010), no. 2, pp. 400-414.

  5. On the Fourier coefficients of modular forms of half-integral weight , Forum Math. 22 (2010), no. 1, pp. 153-177.

  6. Chow-Heegner points on CM elliptic curves and values of p-adic L-functions (with Massimo Bertolini and Henri Darmon), IMRN, appeared online doi:10.1093/imrn/rns237, print version:Vol. 2014 (2014) pp. 745-793.

  7. p-adic Rankin L-series and rational points on CM elliptic curves (with Massimo Bertolini and Henri Darmon), Pacific Journal of Mathematics (Jonathan Rogawski Memorial Issue), Vol. 260, No. 2, 2012, pp. 261-303.

  8. Generalized Heegner cycles and p-adic Rankin L-series (with Massimo Bertolini and Henri Darmon; and an appendix by Brian Conrad), Duke Math Journal, Vol. 162, No. 6, 2013, pp. 1033-1148.

  9. p-adic L-functions and the coniveau filtration on Chow groups (with Massimo Bertolini and Henri Darmon; and an appendix by Brian Conrad), J. Reine Angew. Math. 731 (2017), 21–86.

  10. p-adic L-functions and Euler systems (Survey article, with Massimo Bertolini, Francesc Castella, Henri Darmon, Samit Dasgupta, Victor Rotger), Proceedings of the 2011 LMS-EPSRC Durham Symposium on Automorphic forms and Galois representations.

  11. Generalised Heegner cycles and the complex Abel-Jacobi map (with Massimo Bertolini, Henri Darmon and David Lilienfeldt) Math. Z. 298 (2021), no. 1-2, 385-418.

  12. Periods of quaternionic Shimura varieties. I. (with Atsushi Ichino), Contemp. Math., 762, 2021, vi+214 pp.

  13. Automorphic cohomology, motivic cohomology and the adjoint L-function. (with Akshay Venkatesh), Asterisque(2021),no. 428, viii+132 pp.

  14. Hodge classes and the Jacquet-Langlands correspondence. (with Atsushi Ichino), Forum Math. Pi 11 (2023), Paper No. e22, 1-135.

  15. Motivic action for Siegel modular forms. (with Alex Horawa), Preprint 2023.