Friday, September 26, 2008

Presentation at the Mathematical Society of Japan, 2008 Fall

At the Tokyo Institute for Technology (TITech), a mathematics domestic conference is running. TITech is close to my home university, so that I did not reserve a hotel nor a flight.

My presentation was at the first of morning session of algebra session (Session I) at the following building. [see left]

The slides of this presentation are now uploaded at my official web-site, where there exist the ppt file as well as the pdf file. The slides are consisted of two-folds; one is on the gerbes of chiral differential operators and the other is more on recent developtment of mine on motivic nature of chiral algebras of Beilinson and Drinfeld. My points on quantum geometry were almost abbreviated, because the audience must be mostly interested in the chiral Hecke algberas of  algebro-geomteric nature; rather than generalized differential geometry.

At the afternoon, I heard two 1-hour talks of representation of W-algebras (by Arakawa), and of polylogs, Eisenstein classes, and p-adic L-functions (by Bannai). Arakawa's talk was on the non-linear vertex algebras and around, including the history such as Victor Kac, Igor Frenkel, Feigin-Frenkel, abd Miura pairs. This talk also emphasized the role of chiralization and Hamiltonian reduction. Bannai's talk was mostly on the movie like demostration of elementary theory of generalized polylogarithm well based on the classic work of Beilinson and Deligne, and the relation to local systems after the Riemann-Hilbert correspondence (but not on the monodromy problem so much). Bannai explained his personal motivation at his student period from the paper by Kazuya Kato on the absence of fundamental theorem.

By the way, the sound of bell-ring insect at night is getting louder in Japan.

Thursday, September 18, 2008

Third day of micro-local analysis

Today was my birthday.

After the Hilbert scheme and the Hamiltonian reduction of quiver variety and (particular) Frobenius action, Kashiwara's lecture was going on. For rational Cherednik algebra of type A, $A_c^{loc}, and e H_c e$, we were talking about something like a noncommutative coherent ring (finite represented but not always finitely generated).

We ate lunch at the cafeteria (to be the truth, there are 2 cafeterias), Leclerc explained his article (based on a proceeding of a conference).

1. Facts about the preprojective algebra

ADE (not $\hat$ case; we study finite-dimensional one of $\Lambda$'s, where $\Lambda := \mathbb{C} \bar{Q}$  /(Gelfand-Ponomarev equation)), $\Lambda$ is self-adjoint, and simple $\Lambda$-modules case.

2. Relation between mod $\Lambda$ and $\mathbb{C} [N]$
3. Mutation for rigid $\Lambda$-modules
Thm.[Geiss-Schr\"oer] and Thm[GLS].

I walked around and near the campus in the spare time, and there exists a park in front of the gate of the Kashiwa campus. It is said that new office building will be installed to the empty grass field.

Today was the end of the workshop on Micro-local analysis and Symplectic manifolds.

Wednesday, September 17, 2008

Second day of micro-local analysis

Today's talks were by Kashiwara, Leclerc, and Nagao. Masaki Kashiwara ("Quantization of symplectic manifolds") was on DGA (Differential Graded Algebra; and its localization algebra), the dualizing complex, Frobenius action, Beilinson-Bernstein theory, and a little bit of (spherical) rational Cherednik algebra of type $A_n$. Bernard Leclerc was on symmetric Kac-Moody algebras $\mathcal{g}$ of type ADE (and its maximal nilpotent subalgebra $\mathcal{n}$; tomorrow will be $A^{(i)}, D^{(i)})$), under the title "Nilpotent varieties and cluster algebras".

See you again.

Tuesday, September 16, 2008

IPMU (Institute for the Physics and Mathematics of the Universe) workshop on micro-local analysis

Today we have a workshop, which consists of review / lecture and original works of 3 speakers with about 20 participants. This workshop was mainly on the (complex) symplectic geometry of several (deformation / resolution) quantization procedures.
The atmosphere of the conference was informal, in the sense that the organizers encourage the questoions from the audience, from both technical and conceptual meanings.

By the way, the workshop residence was at the Kashiwa campus of the University of Tokyo. However, strictly speaking, Kashiwa is inside the Chiba prefecture, and is not in Tokyo. It takes about 2 hours from the center of Tokyo; although the "Tsukuba express" -- newly constructed modern railway -- is available.

The weather is getting better since the rainy season and Summer are over. We are awaiting for Autumn.

Wednesday, September 10, 2008

Back to home

For the moment, I do not go abroad. I stay at the mathematical science building in Komaba, the University of Tokyo.

Well, I am preparing for workshop presentations, seminars, and a paper submission. I hope I can do a good work.