November 23, 2000

Quasicrystals are nonperiodic configurations in space that have many properties of crystals (i.e., periodic configurations). An example is the famous Penrose's tiling discovered in 1973. These objects attracted attention of mathematicians and physicists. In 1984, physicists obtained quasicrystallic metallic alloys with 5th order symmetry which is forbidden for crystals. Very soon mathematicians discovered remarkable connections between quasicrystals and harmonic analysis, mathematical physics, number theory, mathematical logic, dynamical systems. Some aspects of this theory is the subject of the lecture.

November 21, 2000

1.

The talk presents the results of the joint work with A.Vershik and M.Yor. We define a sigma-finite measure on the space of discrete measures on a measurable space which is equivalent to the law of the classical gamma process and is invariant under an infinite-dimensional group of multiplicators. This measure was first discovered in the works by Gelfand--Graev--Vershik2.

on the representation theory of current groups, but we construct it explicitly using some properties of the gamma process. The above invariance property is a natural generalization of the corresponding property of the Lebesgue measure in R^{n}, and this allows us to call the constructed measure the infinite-dimensional Lebesgue measure. It enjoys many distinguished properties, some of them will be considered in the talk.

October 31, 2000

- An information system on special functions SFTools functioning
as an independent Knowledge Based dialogue system as well as in the other
modification as an educational client-server system is exposed. The mathematical
contents of SFTools is based on the book

The following special functions are presented in the system:

1) hypergeometric-type functions, 2) Heun functions,
3) Painleve transcendents, 4) orthogonal polynomials.

For these functions basic differential equations with
emphasize to singularities, integral relations, series expansions, Riemann's
P-symbols and other important characteristics are given. Output in TEX
format is available. The numerical values of functions can be computed
by Jaffe-Lay algorithm.

September 7, 2000.

A meeting dedicated to the memory of

Speakers:

May 30, 2000

April 14, 2000

April 11, 2000

A video about Erdos. Commentaries by

March 23, 2000

January 11, 2000

A meeting dedicated to the memory of

December 23, 1999

A lecture of the "Young Mathematician" Prize winner for 1999.

December 7, 1999

November 16, 1999

Speakers:

October 28, 1999

October 26, 1999

1.

2.

October 5, 1999

August 19-25, 1999

A conference "

June 1, 1999

May 25, 1999

Main speakers:

- May 18, 1999.

May 19.

May 20.

May 21.

April 27, 1999

April 13, 1999

March 30, 1999

January 12, 1999

Speakers:

1996 | 1997 | 1998 | 1999 | 2000 | Forthcoming

December 22, 1998.

October 22, 1998

October 13, 1998

September 22, 1998

(

May 12, 1998

April 28, 1998

April 7, 1998.

March 10, 1998

(Groups, Algorithms and Programming).

1996 | 1997 | 1998 | 1999 | 2000 | Forthcoming

December 16

1.

2.

3.

2.

December 11

December 13

November 11, 1997

October 16

June 24

April 15

March 25

February 18

1996 | 1997 | 1998 | 1999 | 2000 | Forthcoming

November, 19

October, 22

September, 24

April, 8

March, 5

February, 20

1996 | 1997 | 1998 | 1999 | 2000 | Forthcoming