## UNIVERSITY OF PENNSYLVANIA

## Department of Mathematics

Fall 2014 -Hans Rademacher Lectures in Mathematics

Andre Neves

## Imperial College London

will speak on

Min-max methods in Geometry: Introduction

Will survey several applications of Min-max methods in Geometry, starting with Birkhoff's work and ending with recent applications found by Fernando Marques and Andre Neves

Monday....November 3, 2014....4:30pm....A8 DRL

Min-max methods in Geometry: Part I

Will review Lusternick-Schnirelman classical result on the existence of three simple closed geodesics on 2-spheres

Tuesday....November 4, 2014....4:30pm....A2 DRL

Min-max methods in Geometry: Part II

Will explain why ambient manifolds (with dimension between 3 and 7) with positive Ricci curvature metrics admit an infinite number of minimal embedded hypersurfaces. This is joint work with Fernando Marques

Wednesday....November 5, 2014....4:30pm....A6 DRL

Min-max methods in Geometry: Parti III

Will explain how min-max methods can be used to solve the Willmore conjecture, which states that the L^2-norm of the mean curvature on any torus is never smaller than 2\pi^2. This is joint work with Fernando Marques

Thursday....November 6, 2014....4:30pm....A7 DRL

Lectures will be held in the David Rittenhouse Laboratory (DRL),

S.E. corner of 33rd and Walnut Streets, Philadelphia, PA.

Tea: preceding the lectures at 4:00pm in 4E17 DRL.

For further information, please call the Department of Mathematics at the University of Pennsylvania - 215-898-8627.