Mathematician Ananth Shankar has received the prestigious Faculty Early Career Development (CAREER) Award from the National Science Foundation (NSF), the foundation’s most prestigious honor for junior faculty members.
Shankar’s research is in number theory and arithmetic geometry, focusing mainly on Shimura varieties and abelian varieties. He studies the arithmetic of polynomial equations and their solutions, i.e. polynomial equations with integer and rational coefficients.
Shankar is an assistant professor of mathematics at Northwestern University. He will receive $494,290 over five years from NSF’s Division of Mathematical Sciences.
The CAREER Award is designed to support promising young faculty members who exemplify the role of teacher-scholar through the combination of outstanding research and education
Shankar’s CAREER project is titled “Algebraicity and Integral Models of Shimura Varieties.” With the NSF support, Shankar and his collaborators will work on the fundamental problems of studying integral models and the p-adic geometry of Shimura varieties.
Shimura varieties are geometric spaces that are defined as solutions to polynomial equations with rational coefficients. Shimura varieties have played a crucial role in settling several long-standing conjectures, including the Mordell conjecture. Shankar and his team will work on the question of finding polynomial equations with integer coefficients which define Shimura varieties. This question is fundamental to the study of number theory and arithmetic geometry and has broad applications to folklore conjectures.
In addition to mentoring graduate and undergraduate students, Shankar plans to organize an “arithmetic geometry bootcamp.” The target audience will be graduate students who have passed their qualifying exams. The aim will be to get these students in a place where they are ready to start reading papers in the field and thinking about research and thesis problems.