Title: Algebraic twists of GL(3)-modular forms

Speaker: Dr. Yongxiao Lin (école polytechnique fédérale de Lausanne) 

Time: 10:00-12:00 a.m., August 2

Location: Room 200-9, Sir Shaw Run Run Business Administration building, School of Mathematical Sciences, Yuquan Campus

Abstract: The subconvexity problem for GL(1)-twists of a fixed GL(3) cusp form is equivalent to establishing that Dirichlet characters /chi modulo q do not correlate with the Fourier--Whittaker coefficients of the given GL(3) form in the convexity range q^{3/2}. This was solved by R. Munshi (2015) by using a novel GL(2)-delta method. We will discuss several variants, simplifications and extensions of Munshi's result. In particular we will explain how one can replace the Dirichlet character /chi by a general trace function modulo q. This is joint work with E. Kowalski, Ph. Michel and W. Sawin.