####
Description

Visions in Mathematics Towards 2000
All videos playlist https://www.youtube.com/playlist?list=PLP0YToNcfAwLBd8yibTtjv3aHfcbT4GBA
The Proceeding of this conference was published by Birkhauser in two parts, and also represent the Volume 2000 of GAFA:
https://books.google.ru/books?id=kQtYL7pUWSwC&printsec=frontcover&hl=ru#v=onepage&q&f=false
https://books.google.ru/books?id=MNpJ4voD5PQC&printsec=frontcover&hl=ru#v=onepage&q&f=false
Wednesday, August 25, 1999, 9:15-15:00
1.0 Introduction by U.Liberman and V.Milman
1.1 M. Gromov : Geometry as the art of asking questions
1.2 H. Hofer : Holomorphic curves and real three-dimentional dynamics
1.3 Y. Eliashberg : Symplectic field theory
1.4 H. Furstenberg : Dynamical methods in Diophantine problems
Wednesday, August 25, 1999, 15:00-18:00
1.5 G. Margulis : Diophantine approximation, lattices and flows on homogeneous spaces
1.6 Y. Sinai : On some problems in the theory of dynamical systems and mathematical physics
1.7 Discussion of the subjects of lectures, Day August 25 with introduction by Y. Sinai (Zakharov, Shnirelman, Hofer)
Thursday, August 26, 1999, 9:00-12:00
2.1 J. Fröhlich: Large quantum systems
2.2 Y. Ne'eman : Physics as geometry – Plato vindicated
2.3 A. Connes : Non-commutative geometry
Thursday, August 26, 1999, 13:00-18:00
2.4 P. Shor : Mathematical problems in quantum information theory
2.5 A. Razborov : Complexity of proofs and computation
2.6 A. Wigderson : Some fundamental insights of computational complexity
2.7 M. Rabin : The mathematics of trust and adversity
Friday, August 27, 1999, 14:00-18:00, Moriah Hotel, Dead Sea
3.1 A. Jaffe : Mathematics of quantum fields
3.2 S. Novikov : Topological phenomena in real physics
3.3 Discussion on Mathematical Physics with introduction by A. Connes
3.4 Discussion on Geometry with introduction by M. Gromov
Sunday, August 29, 1999, 10:00-12:00, 14:00-16:00, Moriah Hotel, Dead Sea
4.1 Discussion on Mathematics in the Real World (image, applications etc.) with introduction by R. Coifman
4.2 Discussion on Computer Science and Discrete Mathematics with introduction by M. Rabin
Monday, August 30, 1999, 9:00-12:30
5.1 R. Coifman : Challenges in analysis 1
5.2 P. Jones : Challenges in analysis 2
5.3 E. Stein : Some geometrical concepts arising in harmonic analysis
5.4 Discussion of the subjects of lectures, Morning August 30
Monday, August 30, 1999, 14:30-18:00
5.5 H. Iwaniec : Automorphic forms in recent developments of analytic number theory
5.6 P. Sarnak : Some problems in number theory and analysis
5.7 D. Zagier : On "q" (or "Connections between modular forms, combinatorics and topology")
5.8 Discussion "The unreasonable effectiveness of modular forms" introduced by P. Sarnak
Tuesday, August 31, 1999, 9:00-13:00
6.1 L. Lovász : Discrete and continuous: two sides of phenomena
6.2 N. Alon : Probabilistic and algebraic methods in discrete mathematics
6.3 G. Kalai : An invitation to Tverberg's theorem
6.4 Discussion of the subjects of lectures, Morning August 31
Tuesday, August 31, 1999, 14:30-19:00
6.5 T. Gowers : Rough structure and crude classification
6.6 J. Bourgain : Some problems in Hamiltonian PDE's
6.7 V. Milman : Topics in geometric analysis
6.8 Discussion of the subjects of lectures, Evening August 31
Wednesday, September 1, 1999, 9:00-12:30
7.1 S. Bloch : Characteristic classes for linear differential equations
7.2 V. Voevodsky : Motivic homotopy types
7.3 D. Kazhdan : The lifting problems and crystal base
Wednesday, September 1, 1999, 14:30-18:40
7.4 A. Beilinson : Around geometric Langlands
7.5 J. Bernstein : Equivariant derived categories
7.6 V. Kac : Classification of infinite-dimensional simple groups of supersymetries and quantum field theory
7.7 Discussion of the subjects of lectures, Evening September 1
Thursday, September 2, 1999, 9:00-12:50
8.1 R. MacPherson : On the applications of topology
8.2 M. Kontsevich : Smooth and compact
8.3 D. Sullivan : String interactions in topology
8.4 Discussion of the subjects of lectures, Morning September 2
Thursday, September 2, 1999, 14:30-19:00
8.5 R.J. Aumann : Mathematical game theory: Looking backward and forward
8.6 E. Hrushovski : Logic and geometry
8.7 Discussion of the subjects of lectures, Evening September 2
8.8 Discussion "The role of homotopical algebra in physics" with introductions by D. Sullivan and M. Kontsevich
Friday, September 3, 1999, 9:00-13:30
9.1 T. Spencer : Universality and statistical mechanics
9.2 E. Lieb : The mathematics of the second law of thermodynamics
9.3 A. Kupiainen : Lessons for turbulence
9.4 S. Klainerman : Some general remarks concerning nonlinear PDE's
9.5 Discussion of the subjects of lectures, Day September 3

## Comments, questions and answers