Continuous model theory and Banach space geometry: an introduction

Por Alexander Usvyatsov (Universidade de Lisboa, CMAF-CIO).

Abstract: These two talks are intended as a soft and not too technical introduction to model theory of metric structures, including a short history and motivating questions, with a particular emphasis on fundamentals of continuous first order logic. I will also mention a few successful applications to Banach space theory, as well as more recent promising directions. 

The regularity of solutions to the elasto-plastic problem and to variational problems of fast growth

Por Arrigo Cellina (Università di Milano-Bicocca).

Abstract: We consider the problem of the higher differentiability of solutions to some variational problems, characterized by the fast growth of the Lagrangian with respect to the variable gradient. In particular,  the case of the elasto-plastic problem, where the Lagrangian is an extended-valued function, will be discussed.

A quantitative analysis of a theorem by F.E.Browder guided by the bounded functional interpretation

Por Pedro Pinto (Universidade de Lisboa, CMAF-CIO).

Abstract: In [2], Kohlenbach did an analysis of the proof of Browder's theorem (in [1]) via the monotone functional interpretation. I will be following the same outline but guided by the bounded functional interpretation ([3], [4]). Although the bounds obtained are the same, this example provides a first look at how the bounded functional interpretation works in practice.