Colloquium De Giorgi 2010-2012 (Publications of the Scuola Normale Superiore Book 4)

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. Front Matter....Pages i-xiv Galois theory beyond algebraic numbers and algebraic functions....Pages 1-7 Simple things we don’t know....Pages 9-16 Is laziness paying off? (“Absorbing” method)....Pages 17-34 Moduli of algebraic and tropical curves....Pages 35-47 Three projection operators in complex analysis....Pages 49-59 Congruent numbers and Heegner points....Pages 61-68 Back Matter....Pages 69-69 Edited By Umberto Zannier. Papers Presented At Conferences Organized By Scuola Normale Superiore Di Pisa. Includes Bibliographical References. Text In English.