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                          PROGRAMME OF THE CONFERENCE
                        "Fundamental Mathematics Today"
                  dedicated to the Xth Anniversary of IUM ***)

December, 26, Wednesday
 9.00--10.00: registration of participants
10.00--10.30: Opening speach of the President of IUM

                  PLENARY LECTURES
10.40--11.30: V.I.Arnold    Astroidal geometry and hyperbolic polynomials
11.30--11.50: Coffee break
11.50--12.40: A.Vershik   Metric classification of functions of several
                          arguments, random matrix and space of Polish spaces
12.50--13.40: L.D.Faddeev   Problem of mass for the quantum Yang-Mills
                            theory: what is it
13.40--15.30: Lunch
15.30--16.20: I.Krichever   Isospectral and isomondromy equations
                            on algebraic curves

                  SECTIONAL TALKS (see footnotes *, **)
 ______________________________________________________________________________
|Chairman    |A:R.MacPherson| B: P.Deligne  |  C: A.Vershik   | D: A.A.Belavin |
|____________|_____________|________________|_________________|________________|
|16.30-17.10 | Yu.Burman   | A.Skorobogatov | M.Blank         | S.Shlosman     |
|____________|_____________|________________|_________________|________________|
|Coffee break                                                                  |
|______________________________________________________________________________|
|17.30-18.10 | A.Skopenkov | F.L.Zak        | W.Faris         | A.Alexeevskii  |
|            |             |                |                 | S.Natanzon     |
|____________|_____________|________________|_________________|________________|
|Coffee break                                                                  |
|______________________________________________________________________________|
|18.30-19.10 | S.Duzhin    | A.G.Khovanski  | D.Kaledin       | M.Shubin       |
|____________|_____________|________________|_________________|________________|

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December, 27, Thursday

                     PLENARY LECTURES
10.00--10.50: R.MacPherson       Intersection homology and torus actions
11.00--11.50: A.Bolibrukh        Semistable Vector Bundles with Connections
                                 and the Riemann-Hilbert Problem
11.50--12.20: Coffee break
12.20--13.10: P.Cartier          Cosmos and atom : a revival of Hermann Weyl's
                                 ideas about gauge invariance
13.10--15.00: Lunch
15.00--15.50: E.Vinberg          The dual horospherical Radon transform
                                 for polynomials

                         SECTIONAL TALKS
 ______________________________________________________________________________
|Chairman    |A:R.MacPherson | B: P.Cartier    |C: A.Vershik   |D: A.A.Belavin |
|____________|_______________|_________________|_______________|_______________|
|16.00-16.40 | V.Timorin     | M.Tsfasman      | A.Eskin       | A.A.Belavin   |
|            |               |                 | A.Zorich      | A.V.Odesskii  |
|            |               |                 |               | R.A.Usmanov   |
|____________|_______________|_________________|_______________|_______________|
|Coffee break                                                                  |
|______________________________________________________________________________|
|17.00-17.40 | J.-M.Kantor   | V.Lunts         | A.Panov       | L.Chekhov     |
|____________|_______________|_________________|_______________|_______________|
|Coffee break                                                                  |
|______________________________________________________________________________|
|18.00-18.40 | O.Karpenkov   | S.Arkhipov      | A.Gorodetsky  | A.Sergeev     |
|____________|_______________|_________________|_______________|_______________|
|18.50-19.30 | S.Shadrin     | A.Braverman     |  S.Maksimenko | V.Gordin      |
|____________|___________ ___|_________________|_______________|_______________|

*****************************************************************************
December, 28, Friday

                     PLENARY LECTURES
10.00--10.50: V.Vassiljev     Combinatorial formulas for cohomology
                              of spaces of knots
11.00--11.50: A.A.Kirillov   Representations and orbits of triangular groups
11.50--12.20: Coffee break
12.20--13.10: V.M.Buchstaber  Symmetric powers as algebraic variety
13.10--15.00: Lunch
15.00--15.50: V.Ginzburg      Symplectic reflection algebras


                         SECTIONAL TALKS
 ______________________________________________________________________________
|Chairman    |A: S.P.Novikov| B: P.Cartier | C: V.Vassiliev   | D: L.D.Faddeev |
|____________|______________|_____________ |__________________|________________|
|16.00-16.40 | M.Kazarian   | L.Katzarkov  | S.Gusein-Zade    |I.Shchepochkina |
|____________|______________|______________|__________________|________________|
|Coffee break                                                                  |
|______________________________________________________________________________|
|17.00-17.40 | S.Lando      | A.Khelemski  | Yu. Ilyashenko   |  A.Rudakov     |
|____________|______________|______________|__________________|________________|
|Coffee break                                                                  |
|______________________________________________________________________________|
|18.00-18.40 | P.G.Grinevich|A.L.Gorodentsev|  G.Olshanskii   |  O.Sheinman    |
|            | S.P.Novikov  |               |                 |                |
|____________|______________|_______________|_________________|________________|
|18.50-19.30 | I.Dynnikov   | M.Verbitsky   | E.Polulyakh     |  S.Loktev      |
|____________|______________|_______________|_________________|________________|

*****************************************************************************
December, 29, Saturday

                     PLENARY LECTURES
10.00--10.50: S.P.Novikov     Discrete systems and integrabilty
11.00--11.50: P.Deligne       Tensor Categories
11.50--12.20: Coffee break
12.20--13.10: A.Katok         Nonuniform Hyperbolicity and Rigidity
13.10--15.00: Lunch
15.00--15.50: B.Dubrovin      From integrable systems to Gromov - Witten
                              invariants
15.50--16.10: Coffee break
16.10--17.00: B.Feigin         Vertex algebras and representations of
                               small quantum group

Celebrating of the forthcoming 70th birthday of N.N.Konstantinov
            (precise time to be announced)
_____________________________________________________________________________

              *)   TITLES OF SECTIONAL TALKS

A.Alexeevskii, S.Natanzon
Klein topological field theory and Hurwitz numbers of complex and
real algebraic curves

S.Arkhipov
A geometric realization of the category of modules over the small
quantum group

A.A.Belavin, A.V.Odesskii, R.A.Usmanov
New relations in the algebra of the Baxter Q-operators

M.Blank           Dynamical spectrum for random maps and Ulam conjecture

A.Braverman       Singularities of loop schemes and automorphic L-functions

Yu.Burman         Whitney index and Laplace integrals

L.Chekhov         Commutative and noncommutative Teichmuller spaces
                  via graphs

S.V.Duzhin        Decomposable skew-symmetric functions

I.Dynnikov        TBA

A.Eskin, A.Zorich   Billiards in rectangular polygons

W.Faris            Ornstein-Uhlenbeck and renormalization semigroups

V.A. Gordin        Eigen-value Functional Optimization in Mathematical
                   Physics and Stability Problems

A.L.Gorodentsev   Abelian Lagrangian Algebraic Geometry and ALAG-quantization

A.Gorodetskii      Stable nonhyperbolic properties of dynamical systems
                   and smooth realization of skew products

P.G.Grinevich, S.P.Novikov
Toplological charge of the finite-gap Sine-Gordon solutions

S.Gusein-Zade      Indices of 1-forms on an isolated complete intersection
                   singularity.

Yu.Iljyashenko     Centennial History of Hilbert's 16th problem

D.Kaledin          Symplectic singularities in algebraic geometry

J.-M.Kantor        Recent works on lattice polytopes

O.Karpenkov        Energy of a knot: variational principles

L.Katzarkov        Algebro Geometric methods in symplectic geometry

 M.Kazarian        Multisingularities and cobordisms

A.Khelemsky        Wedderburn-type theorems for operator algebras:
                   traditional and "quantum" homological approaches.

A.G.Khovanski      Parshin's symbols, toric geometry and product of the
                   roots of a system of equations

S.K.Lando          The Hurwitz problem and the geometry of spaces
                   of meromorphic functions

S.Loktev           Coinvariants of one-dimensional lattice VOAs

V.Lunts            Motivic measures and stable birational geometry
                   (joint work with M. Larsen)

S.Maksimenko       Smooth shifts along trajectories of flows

G.Olshanskii       Gelfand--Tsetlin schemes, measures of hypergeometric type,
                   and point processes

A.Panov            TBA

E.Polulyakh        Dynamical systems which admit periodical decompositions

A.Rudakov          Representations of infinitedimensional graded Lie
                   s-algebras with sl(3)timesаsl(2)timesаgl(1) as
                   the zero degree component

Shchepochkina, I.  Classification of the real simple Lie superalgebras
                   of vector fields (joint work with Dimitry Leites)

A.G.Sergeev        Seiberg--Witten equations and Abrikosov strings

S.Shadrin          Topological classification of unitary functions
                   of arbitrary genus

O.K.Sheinman       The second order casimirs for the affine
                   Krichever-Novikov algebras

S.B.Shlosman       Convex envelope of the Wiener loop

M.A.Shubin         Capacities in spectral theory of magnetic
                   Schroedinger operators

A. Skopenkov       The Whitehead link, the Hudson-Habegger invariant and
                   classification of embeddings $S^1times S^3toR^7$

A.Skorobogatov     Rational points on certain Kummer surfaces

V.Timorin          Four dimensional geometry of circles

M.A.Tsfasman       Asymptotic Properties of Global Fields

M.Verbitsky        Proof of Mukai conjecture

F.L.Zak            Order, rank, and class of projective algebraic varieties

             **) LIST OF SECTIONS
  A. Geometry & Topology
  B. Algebra, Algebraic Geometry & Number Theory
  C. Dynamical Systems & the Theory of Singularities
  D. Mathematical Physics

***) The Conference is supported by the Russian Foundation for Basic
Research, European Mathematical Union, and Steklov Mathematical
Institute of the Russian Academy of Sciences

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