Arithmetic Dynamics A/A, Algebraic number theory (local class field theory) A/A, An Introduction to the Shimura varieties A/A, Algebra I 19.8/20, Algebra III 18.3/20, Complex Analysis 19/20, Algebraic Topology 19/20, Riemann Surfaces 19.5/20, Quadratic Forms 17.5/20, Advanced Algebra 20/20, Linear Groups 20/20, Smooth Manifolds 20/20
I am currently a PhD student McGill under supervision of Professor Patrick Allen. I am working on Watkins conjecture in the theory of elliptic curves which asserts that the rank of a rational elliptic curve divides the degree of the modular parametrization of that elliptic curve by the modular curve. For this, one needs to study the geometry of the modular curves and their jacobians. I am particularly interested in finding possible ways to generalize the work already done by Ribet-Takahashi and Caro-Pasten to the more general situations like considering Shimura curves rather merely classical modular curves. To be more precise, an elliptic curve over a totally real field might be parametrized by two different Shimura curves and so we get two modular degrees. Now, one may ask is there any relation between these two degrees. My main goal is to give possible answers to such questions.
The Commissioner, 62nd International Mathematical Olympiad, St.Petersburg, Russia, 07/14/21 - 07/24/21 International Representative Member, Mirzakhani Foundation, Tehran, Iran, From 01/01/20 Mathematics Tutor, Website: Iranian Mathematicians, Tehran-Mashhad, Iran, 01/01/17 - 01/01/20