[geometry-ml:01051] Workshop at IPMU 4/5-6 Recent Advances in Mathematics at IPMU, 2

[Satoshi Kondo]

Dear colleagues:

We announce the following workshop at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

Satoshi Kondo (IPMU)
http://ipmu.jp/

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Recent Advances in Mathematics at IPMU, 2.

Period :  5-6 April, 2010
Place: Seminar Room A
Organizers:  Alexey Bondal, Toshitake Kohno, Kyoji Saito

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Program

April 5

10:30 -- 12:00   Boris Venkov

13:30 -- 15:00   Tomoyuki Abe

15:30 -- 17:00   Alexandr Usnich

April 6

10:30 -- 12:00  Alexey Bondal

15:30 -- 17:00  Noriyuki Abe

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Tomoyuki Abe (University of Tokyo)

Title:
Differential equations over non-archimedean fields and the theory of
arithmetic D-modules.

Abstract:
In this talk, I will discuss a theory of linear differential equations
(L.D.E.) of one variable and a theory of arithmetic D-modules over
non-archimedean fields. I would like to start from reviewing what
non-archimedean fields are. The biggest difficulty of the theory of
L.D.E. over non-archimedean fields is that the radius of convergence of
the exponential function is small. However, by adding "Frobenius
structures", which are distinctive structures for L.D.E. over
non-archimedean fields of characteristic $p$, it is known that very
similar structure theorem holds. Now I would like to introduce the
theory of arithmetic D-modules due to Berthelot briefly, and summarize
main problems of the theory. Finally, I would like to state the main
theorem of this talk, which says that a kind of finiteness theorem holds
for overconvergent isocrystals (i.e. $p$-adic analog of local systems)
over curves even without Frobenius structures.

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Noriyuki Abe (University of Tokyo)

Title:
On the extensions between Verma modules.

Abstract:
Cartan-Weyl classified irreducible finite-dimensional representations of
a semisimple Lie algebra using highest weights of a representation.
After their work, Bernstein-Gelfand-Gelfand introduced the category O.
Roughly speaking, this is the category generated by highest weight
modules. There are important objects in O which are called Verma modules.
This modules represent the space of highest weight vectors.
In this talk, I discuss the first extension groups between Verma modules.
It relates the coefficients of R-polynomials.

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Alexey Bondal

Title: TBA

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Alexandr Usnich

Title:
Non-commutative cluster mutations.

Abstract:
We construct a birational invariant of algebraic varieties from its
derived category of coherent sheaves. Then we make this construction
explicit for rational surfaces to obtain an action of the Cremona group on
the non-commutative ring.  This result is then applied to deformation
quantization and to non-commutative cluster mutations.

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Boris Venkov

Title:
Strongly perfect lattice.

Abstract:
Strongly perfect lattices form an interesting subclass of locally dense
Euclidean lattices.  They are defined by purely combinatorial property,that
shortest vectors in it form a spherical 5-design. They also minimize energy
for some geometric potential.  There is relation with modular forms and
invariant theory.  Some classification results will be discussed.

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You can check the location from
http://www.ipmu.jp/access/img/KashiwaCampusMap.png

The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/