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List of Talks

Program (in Russian)

Program (in English)

• B. B. Venkov "Dense euclidean lattices and the energy minimizations"
  

  The talk is about some recent interconnections of the Voronoi theory of perfect lattices and energy minimization problem for some geometric potentials. Spherical designs arise naturally in this context. There are relations to some classical problems of the number theory such as the distributions of zeros of zeta functions.  
  

• S. O. Gorchinsky "Adelic resolution and its applications"
  

  We discuss a new type of resolutions, called adelic resolutions, for a certain class of abelian sheaves on algebraic varieties. This class includes sheaves of K-groups. Adelic resolutions are multiplicative and contravariant (in contrast with the Gersten resolution). There is an explicit quasiisomorphism between the adelic and Gersten resolutions. In particular, this allows to describe (higher) products on Chow groups and biextensions over Chow groups in terms of the adelic resolution.  
  

• V. A. Gritsenko "The moduli spaces of polarised symplectic varieties"
  

  The first example of such varieties is a polarised K3 surface. In 1956 A. Weil formulated a program on the K3 surfaces an their moduli spaces. All questions of the program had been solved during the next 25 years except the problem on the birational type of the moduli space F(2d) of the polarized K3 surfaces of degree 2d. (F(2d)is quasi-projective variety of dimension 19).
  For d=1, 2, ..., 10, 12, 17, 19 the variety F(2d) is still unirational (Mukai). In this talk I present m joint result with K. Hulek (Hannover) and G. Sankaran (Bath) on the solution of the problem of the birational type. Using the theory of automorphic forms we proved that F(2d) is of general type, i. e., its Kodaira dimension is maximal, starting from d=46. Our method gives similar results for the moduli spaces (of dimension 20 and 21) of some polarised irreducible symplectic manifolds.  
  

• P. G. Zograf "Numeric" geometry on moduli spaces of curves"
  

  We describe a "fast" algorithm for computing intersection numbers on moduli spaces of complex algebraic curves. As an application, we compute the exact large genus asymptotics of symplectic volumes of moduli spaces.  
  

• R. O. Mikhailov "Derived functors in the sense of Dold and Puppe"
  

  The talk is about recent joint results with L. Breen related to the theory of derived functors of the non-additive functors in the category of abelian groups. The main problem in this area which we try to solve is to find a good functorial description of the homology of Eilenberg-MacLane spaces.  
  

• D. O. Orlov "Mirror symmetry and D-branes in Landau-Ginzburg models"  
  

• A. N. Parshin "Adelic groups (representation theory and related reasults)"
  

  We will consider the following issues: unramified nilpotent adelic groups related to algebraic surfaces, characters of their induced representations and modular forms, relations with L-functions of the surface.  
  

• V.L. Popov. "Is the field of functions on the Lie algebra pure over the invariant subfield?"
  

  Let G be a connected reductive algebraic group over a field k of characteristric zero and let Lie G be its Lie algebra. Let k(G) and k(Lie G) be the fields of rational functions on G and Lie G respectively.
  The conjugation action of G on itself and the adjoint action of G on Lie G determine the invariant subfields k(G)^G and k(Lie G)^G of k(G) and k(Lie G) respectively. In the talk the following problems will be addressed and answered:

  1. Is the field extension k(G)/k(G)^G pure (i.e., purely transcendental)? stably pure?
  2. The same questions for the field extension k(Lie G)/Lie(G)^G.
  These questions come up in connection with the counterexamples to the Gelfand--Kirillov conjecture and they are also naturally related to the birational counterpart of the classical classification problem of representations with free module of covariants. The talk is based on the joint results with J.-L.Colliot-Th'el`ene, B. Kunyavskii, and Z. Reichstein.  
  

• A. A. Suslin "Motivic complexes over nonperfect fields"