Academics

A two term Kuznecov sum formula

Time:10:00-11:00 am, August 26th (Fri), 2022

Venue:Zoom: 618-038-6257, Password: SCMS

Organizer: Chen Xi (Fudan), Jin Long (Tsinghua)

Speaker:Xi Yakun(Zhejiang University)

Abstract

A period integral is the average of a Laplace eigenfunction over a compact submanifold. Much like for the Weyl law, one can obtain improved estimates on period integrals given geometric or dynamical assumptions on the geodesic flow. While there are many results improving bounds on period integrals, there have been none which improve the remainder of the corresponding sum formula. In this talk, we discuss a recent joint work with Emmett Wyman. We show that an improvement to the remainder term of this sum formula reveals a lower-order oscillating term whose behavior can be described by the dynamics of the geodesic flow. Moreover, this oscillating second term illuminates bounds on period integrals.



DATEAugust 24, 2022
SHARE
Related News
    • 0

      Road to conquer the hardness - solving hard computational problems with generic tensor networks

      AbstractI will introduce a tensor network-based method to compute the solution space properties of a broad class of combinatorial optimization problems (e.g. spin glasses and hard core lattice gases). These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the hard core latt...

    • 1

      From condensed matter theory to sub-wavelength physics

      Abstract:The ability to manipulate and control waves at scales much smaller than their wavelengths is revolutionizing nanotechnology. The speaker will present a mathematical framework for this emerging field of physics and elucidate its duality with condensed matter theory.About SpeakerHabib Ammari is a Professor of Applied Mathematics at ETH Zürich. Habib Ammari is a world leading expert in w...