Current work

I am currently an SNSF-funded professor and the head of the research group GR-JET in SMA/FSB. Some of my recent research projects include the following:

• Constructing an Euler system from higher dimensional cycles on unitary groups and using it to study the Bloch-Kato conjecture for automorphic representations for unitary groups.
• Constructing universal norms from special cycles in unitary Shimura varieties, proving non-triviality of these norms and Iwasawa theoretic applications (joint with Hunter Brooks and Reda Boumasmoud).
• Birch and Swinnerton-Dyer conjectural formula for elliptic curves of analytic rank 1 (joint with Christopher Skinner and Xin Wan).
• Computing cyclic isogenies for abelian varieties with real multiplication (joint with Alina Dudeanu and Damien Robert).
• Random self-reducibility of the discrete logarithm problem in genus 2 (joint with Benjamin Wesolowski).
• Structure of isogeny graphs of abelian surfaces and threefolds over finite fields (joint with H. Brooks and B. Wesolowski).

Biography

Currently, I am a Swiss National Science Foundation Professor in number theory, arithmetic algebraic geometry and mathematical cryptology at SMA, EPFL. I completed my PhD in number theory and arithmetic geometry at the University of California, Berkeley in 2008 under the supervision of Prof. Ken Ribet. I was then a post-doc at IHES, Bures-sur-Yvette as well as the Laboratory for Cryptologic Algorithms, LACAL at EPFL.

Teaching

• Spring 2017 - Anneaux et Corps
• Fall 2016 - Algebraic Curves and Cryptography
• String 2016 - Number Theory in Cryptography
• Fall 2015 - Algèbre Linéaire : IN/SC - Math 111-(e)
• Spring 2015 - Introduction to Bruhat-Tits theory
• Fall 2014 - Algèbre Linéaire : IN/SC - Math 111-(e)
• Spring 2014 - Introduction to Shimura Varieties
• Fall 2013 - Algèbre Linéaire : IN/SC - Math 111-(e)
• Fall 2011 - Advanced Topics in Cryptology (a course at IC with Prof. Arjen Lenstra)
• Fall 2010 - Algorithms in Public Key Cryptography (a course at IC with Prof. Arjen Lenstra)

EDUCATION

University of California at Berkeley, Ph.D., M.A. in mathematics, May 2008
Ph.D. Thesis: Heegner Points, Component groups, Kolyvagin systems and Selmer groups
Advisor: Prof. Kenneth A. Ribet

Harvard University, B.A. in mathematics, June 2004

RESEARCH INTERESTS

Elliptic curves, Selmer groups, Euler systems, special points, equidistribution, analytic and ergodic methods, mathematical foundations of cryptology, ECC, symmetric key cryptography, complexity analysis of cryptologic algorithms