Ananth Shankar

Department of Mathematics

University of Wisconsin, Madison

ashankar@math.wisc.edu

I am an Assistant Professor at UW Madison. I graduated with a BSc in Mathematics and Computer Science from Chennai Mathematical Institute in August, 2012. I was a PhD student at Harvard University under the supervision of Mark Kisin, and graduated in May, 2017. Before joining Madison, I was at MIT as a CLE Moore Instructor until July 2020.

Research

My research is in arithmetic geometry and number theory. More specifically, I work in the following areas:

  • Arithmetic aspects of Shimura varieties.

  • The Grothendieck-Katz p-curvature conjecture.

  • Arithmetic Statistics.

Here are some of my research papers:

  1. Canonical Heights on Shimura Varieties and the André-Oort Conjecture
    With J. Pila and J. Tsimerman, and an appendix by H. Esnault and M. Groechenig.

  2. The existence of abelian varieties not isogenous to Jacobians over global fields.
    With J. Tsimerman,
    submitted.

  3. Finiteness of reductions of Hecke orbits.
    With M. Kisin, J.
    Lam and P. Srinivasan, submitted.
    My talk on this work.

  4. Picard Ranks of K3 surfaces and the Hecke orbit conjecture.
    With D. Maulik and Y. Tang, Inventiones.

  5. Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields.
    With Arul Shankar, Y. Tang and S. Tayou, submitted.

  6. The rank two p-curvature conjecture on generic curves.
    With A. Patel and J.P. Whang, Advances in Mathematics.

  7. Counting elliptic curves by conductor.
    With Arul Shankar and X.Wang, Compositio.

  8. Reductions of abelian surfaces over global function fields.
    With D. Maulik and Y. Tang, Compositio.

  9. Almost ordinary abelian varieties over finite fields.
    With A. Oswal, Journal of the London Mathematical Society.

  10. Exceptional splitting of reductions of abelian surfaces.
    With Y. Tang, Duke Mathematical Journal.

  11. Serre-Tate theory for Shimura variaties of Hodge type.
    With R. Zhou, Math Zeitschrift.
    My talk on this work.

  12. Unlikely intersections in finite characteristic.
    With J. Tsimerman, Forum of Mathematics, Sigma.

  13. The p-curvature conjecture and monodromy around simple closed loops.
    Duke Mathematical Journal.
    My talk on this work.

  14. The Hecke orbit conjecture for "modèles étranges".
    Preprint.

  15. 2-Selmer groups of hyperelliptic curves with marked points.
    Transactions of the AMS.



Seminars (co-)organized