<Title and Abstract>
Michio Jimbo
Alexander Varchenko
I will define a class of line bundles on the scheme $\cup_{k=0}^n Ell_T(T^*Gr (k,n))$ such that the operator algebra of the elliptic dynamical quantum group $E_{\tau,h}(gl_2)$ will act on sections of those line bundles (a generator of the operator algebra will send a section of such a line bundle to a section of possibly another line bundle). That construction is an analog of the Yangian $Y(gl_2)$ action on the direct sum $\oplus_{k=0}^n H^*_T(T^*Gr(k,n))$ of equivariant cohomology.
This is a joint work with G.Felder and R.Rimanyi.
Morihiko Saito
1. Relation with D-modules generated by rational powers of a holomorphic function. 2. Relation between the microlocal V-filtration and the Hodge ideals. 3. Computation of the roots of b-function for a homogenous polynomial with one-dimensional singular locus using the pole order spectral sequence.
Takuro Mochizuki
We shall explain a theorem on the structure of the formal completion of vector bundles on $\overline{M}$ along the infinity, which is an analogue of the Hukuhara-Levelt-Turrittin theorem for meromorphic flat bundles on curves. It is motivated by the study of doubly periodic instantons, and we shall discuss something related.
Nikita Nekrasov
Aleksander A. Belavin
The massless sector of Superstring theory corresponds to the set of chiral fields of N=2 Super CFT and this sector is described by Topological CFT (TCFT). The properties of the Lagrangian of the corresponding sigma model for this massless sector are defined in terms of the mirror pairs of Calaby-Yau manifolds linked to the same TCFT. The explicit form of the flat coordinates is important also for the solution of the TCFT models related to the Gepner chiral rings which are a subset of Kazama--Suzuki connected with a certain class of the isolated singularities. Thus, the computation of the Flat coordinates and the Saito primitive form for Frobenius manifolds is the important part of the solution of the above mentioned physical problems. We propose a new simple method for computing flat coordinates on the Frobenius manifolds linked with TCFT. Approach is based on using a Conjecture about integral representations for the flat coordinates and on the Saito cohomology theory. It helps to reduce the problem of the computation of the flat coordinates to a simple linear problem.
Si Li
Shigeru Mukai Title: Enrique surfaces whose automorphism groups are virtually free Abstract: An Enriques surface is an algebraic surface obtained from a K3 surface taking quotient by a fixed point free involution. The automorphism group Aut(S) of an Enriques surface is always discrete, and shrinks from very infinite to mildly infinite and to finite under specialization, just like the Mordell Weil group of an elliptic fibration. In this talk I discuss the the virtual cohomological dimension (vcd) of Aut(S) and present some examples of Aut(S) with vcd 1 (and 0) using infinite Coxeter groups acting on the 9-dimensional hyperbolic space. This is a joint work with H. Ohashi.
Kentaro Hori
Yukinobu Toda
Alexey Bondal
Kyoji Saito
Hiroshi Iritani
We discuss the analyticity of the Saito structure and that the pairings match under mirror symmetry. This is based on joint work with Coates, Corti and Tseng.
Claus Hertling
There is a period map to a classifying space of Brieskorn lattices. Its injectivity is a Torelli type conjecture. It is proved for the singularities with modality 0,1,2. All this lifts old work to marked singularities. Partly it is joint work with F. Gauss. If time permits, also a natural hermitian form on the base space of a universal unfolding will be mentioned. |