# Ananth Shankar

Department of Mathematics

University of Wisconsin, Madison

ashankar@math.wisc.edu

I am an Assistant Professor at UW Madison. I was a PhD student at Harvard University under the supervision of Mark Kisin, and graduated in May, 2017. 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:

Finiteness theorems for reductions of Hecke orbits

With M. Kisin, J. Lam and P. Srinivasan,*in preparation*.

My talk on this work.Picard Ranks of K3 surfaces and the Hecke orbit conjecture.

With D. Maulik and Y. Tang,*submitted*.Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields.

With Arul Shankar, Y. Tang and S. Tayou,*submitted*.The rank two

*p*-curvature conjecture on generic curves.

With A. Patel and J.P. Whang,*submitted*.Counting elliptic curves by conductor.

With Arul Shankar and X.Wang,*to appear in Compositio*.Reductions of abelian surfaces over global function fields.

With D. Maulik and Y. Tang,*submitted.*Almost ordinary abelian varieties over finite fields.

With A. Oswal,*Journal of the London Mathematical Society.*Exceptional splitting of reductions of abelian surfaces.

With Y. Tang,*Duke Mathematical Journal.*Serre-Tate theory for Shimura variaties of Hodge type.

With R. Zhou,*Math Zeitschrift*.

My talk on this work.Unlikely intersections in finite characteristic.

With J. Tsimerman,*Forum of Mathematics, Sigma.*The

*p*-curvature conjecture and monodromy around simple closed loops.*Duke Mathematical Journal.*My talk on this work.The Hecke orbit conjecture for "modèles étranges".

*Preprint.*2-Selmer groups of hyperelliptic curves with marked points.

*Transactions of the AMS.*

### Seminars (co-)organized

I am a co-organizer of the UW Madison Number Theory Seminar.

I am a co-organizer of an online seminar series, New Developments in Number Theory.