Akshay Venkatesh

Akshay Venkatesh ( born November 21, 1981 in New Delhi) is an Indian- Australian mathematician who deals with number theory, ergodic theory and automorphic forms.

Life

Venkatesh grew up in Australia in Perth. In 1994 he received a bronze medal at the International Mathematical Olympiad. From 1995, he studied mathematics at the University of Western Australia (Bachelor in 1997 with first class honors ). From 1998 he was at Princeton University with Peter Sarnak, where he was awarded his doctorate in 2002 (Limiting forms of the trace formula ). As a post-doc, he was Moore Instructor at Massachusetts Institute of Technology. From 2004 he was an associate professor at the Courant Institute of Mathematical Sciences of New York University and from 2008 professor at Stanford University.

2004 to 2006 he was Clay Research Fellow. In 2007 he was Packard Fellow and received the Salem Prize. In 2008 he won the SASTRA Ramanujan Prize.

In 2006 he gave a lecture at the International Congress of Mathematicians in Madrid ( Equidistribution, L -functions and ergodic theory: on some problems of Yuri Linnik, with Philippe Michel ) and 2010, he was invited speaker at the ICM in Hyderabad (Statistics of number fields and function fields with Jordan S. Ellenberg ).

Work

With Jordan S. Ellenberg, he turned to methods of ergodic theory to the question of the representation of integer quadratic forms by those with fewer variables and rejected the validity of a local-global principle (in the sense of Hasse ) to.

Partly with Elon Lindenstrauss, Manfred hermit and Grigory Margulis he dealt with equal distribution issues in homogeneous spaces.

With Lindenstrauss he proved the conjecture of Sarnak on the validity of Hermann Weyl 's law for cusp forms as eigenfunctions of the Laplacian in locally symmetric spaces. This law establishes a relationship between the number of eigenvalues ​​of the Laplace operator with the volume of the manifold in its original form by Weyl. Locally symmetric spaces are given by forming the quotient by a discrete subgroup in a large class of algebraic groups. He also scored with Lior Silberman progress with respect to another conjecture of Sarnak ( quantum unique ergodicity, guess with Zeev Rudnick ).

Also with Ellenberg he improved the upper bound ( asymptotically for large degrees ) the number of fixed -degree number fields with discriminant limited. Manjul Bhargava had previously treated the special case of number fields with degree less than 5.

In the analytic theory of automorphic forms, he scored (some with Philippe Michel ) progress on the issue of sub- convexity bounds for L-functions of automorphic representations on the critical line. The problem also has applications in equal distribution of questions in the geometry of numbers

With Harald Helfgott he gave to new bounds for the number of integer points on elliptic curves.