Visions in Mathematics: GAFA 2000 Special Volume, Part II

ISBN-13: 9783034604246 / Angielski / Miękka / 2010 / 544 str.

Noga Alon; Jean Bourgain; Alain Connes

Opis

"Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a two-volume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future.

Spis treści

Foreword.- Algebraic and probabilistic methods in discrete mathematics (N. Alon).- Challenges in analysis (R. Coifman).- Noncommutative geometry - Year 2000 (A. Connes).- Indtroduction to symplectic field theory (Y. Eliashberg, A. Givental and H. Hofer).- Holomorphic curves and real three-dimensional dynamics (H. Hofer).- Perspectives on the analytic theory of L-functions (H. Iwaniec and P. Sarnak).- Combinatorics with a geometric flavor (G. Kalai).- Topics in asymptotic geometric analysis (V. Milman).- Quantum information theory: results and open problems (P. Shor).- Universality, phase transitions and statistical mechanics (T. Spencer).- How classical physics helps mathematics (V. Zakharov).- Addendum: Discussions at the Dead Sea.- Introduction.- Discussion on Mathematical Physics.- Discussion on Geometry.- Discussion on Mathematics in the Real World.- Discussion on Computer Science and Discrete Mathematics.- Reflections on the development of mathematics in the 20th century (D. Kazhdan).