Zeroes and Nodal Lines of Modular Forms: a colloquium by the 2011 Mahler Lecturer

Speaker: 

Peter Sarnak, the 2011 Mahler Lecturer

Affiliation: 

Princeton University/IAS

Date: 

Fri, 26/08/2011 - 2:30pm to 3:30pm

Venue: 

Room 175 Carslaw Building, University of Sydney

Abstract: 

One of the consequences of the recent proof by Holowinski and Soundararajan of the holomorphic "Quantum Unique Ergodicity Conjecture" is that the zeros of a classical holomorphic hecke cusp forms become equidistributed as the weight of the form goes to infinity. We review this as well as some finer features (first discovered numerically) concerning the locations of the zeros as well as of the nodal lines of the analogous Maass forms. The latter behave like ovals of random real projective plane curves, a topic of independent interest.

At 12pm on the same day, also at the University of Sydney, Prof. Marston Conder (Auckland) will give a Joint Colloquium talk.

School Seminar Series: