Está aqui

home / CMAF-CIO /
Voltar ao Topo

CMAF-CIO

Min-max theory in Geometry

André Neves
Imperial College London

Abstract: Min-max theory was recently used by myself and Fernando Marques to prove the Willmore Conjecture, the Freedman-He-Wang Conjecture, and the Yau Conjecture for metrics with positive Ricci curvature. I will survey those results and talk about new directions in the area.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.

Elementary approach to closed billiard trajectories in asymmetric normed spaces

Arseniy Akopyan
IST Austria

Abstract: We apply the technique of Karoly Bezdek and Daniel Bezdek to study the billiards in convex bodies, when the length is measured with a (possibly asymmetric) norm. We give elementary proofs of some known results and prove an estimate for the shortest closed billiard trajectory, related to the nonsymmetric Mahler problem. (joint work with A. M. Balitskiy, R. N. Karasev, and A. Sharipova).

Two functional interpretations of arithmetic: the ‘dialectica’ interpretation of Gödel and the monotone interpretation of Kohlenbach (conclusion)

Ana Borges
Instituto Superior Técnico, Universidade de Lisboa

In this talk we present two functional interpretations of arithmetic: Gödel's functional or `dialectica' interpretation and Kohlenbach's monotone functional interpretation, which is a modification of the first. On the way, we describe weakly extensional Heyting arithmetic in all finite types, Bezem's strong majorizability notion and Howard’s majorizability theorem.

Páginas