Colloquium De Giorgi 2013 and 2014

Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events.

Gives general viewpoints in recent research, accessible to non-experts in the field Includes expositions from eminent experts in the fields The various contributions usually provide an overview of both the past and the recent research in a field

Inhalt
Pierre Cartier: New Developments in Galois Theory.- Enrico Bombieri: The Mathematical Truth.- Alessio Figalli: Quantitative Stability Results for the Brunn-Minkowski Inequality.- Luc Illusie: Grothendieck at Pisa: crystals and Barsotti-Tate groups.- Étienne Fouvry, Emmanuel Kowalski and Philipper Michel: Trace functions over finite fields and their applications.- Michel Waldschmidt: Schanuel's Conjecture: algebraic independence of transcendental numbers.