SGAD2012 Geometrical perspective of topological modular forms

- A fusion of number theory and stable homotopy theory by utilizing the language and the concept of derived algebraic geometry -

Supported by

Grant-in-Aid for Scientific Research (B)
`Geometric structures and combinatorial structures of 3-manifolds'
Grant Number 22340013 (Makoto Sakuma)

Grant-in-Aid for Scientific Research (B)
`Reseach on algebraic cycles using cohomology'
Grant Number 23340003 (Kanetomo Sato)

Purpose: We plan to give a stimulus of inter-cultural communication to budding researchers, number theory, algebraic geometry, topology and so on, at home as well as abroad by enlightening about the brilliance of derived algebraic geometry.

Date: 12-16, November, 2012
Place: Graduate School of Mathematical Sciences, The University of Tokyo. (Access)
Speakers: Keisuke Arai, Tilman Bauer, David Gepner, Shin Hattori, Naoki Imai, Isamu Iwanari, Mariko Ohara, Yoshiyasu Ozeki, Yuki Kato, Ryo Kato, Sho Saito, Yuji Shimizu, Takahiro Tsushima, Takeshi Torii, Kentaro Nakamura, Norihiko Minami, Hirofumi Nakai, Nobuaki Yagita, Seidai Yasuda

Contents:
1. Prehistorical back grounds and vista of TMF
2. Foundations and relationship between formal groups and the cobordism theory saw through by Quillen
3. Moduli stacks of elliptic curves and modular forms
4. Local moduli of p-divisible groups, formal groups
5. Construction of TMF after Goerss-Hopkins-Miller, Behrens and Lurie

Program:
12, November
09:30 - 10:30 Norihiko Minami, Long and winding road to tmf
10:45 - 11:45 Yoshiyasu Ozeki, Basics on elliptic curves
14:00 - 15:00 Sho Saito, Generalized cohomology and spectra
15:15 - 16:15 Mariko Ohara, Complex oriented cohomology and formal group law
16:30 - 17:30 Masao Aoki, Algebraic stacks (slides)

13, November
09:30 - 10:30 Tilman Bauer, The construction of the descent spectral sequence
10:45 - 11:45 Shin Hattori, Formal group laws I
14:00 - 15:00 Nobuaki Yagita, Complex K-theory and complex cobordism
15:15 - 16:15 Yuki Kato, Quillen's theorem, moduli stack of formal groups and Adams-Novikov spectral sequence
16:30 - 17:30 Ryo Kato, Brown-Peterson, Morava E, K-theories

14, November
09:30 - 10:30 David Gepner, Higher stacks in derived algebraic geometry
10:45 - 11:45 Keisuke Arai, Moduli spaces of elliptic curves (note)
12:00 - 13:00 Takahiro Tsushima, Introduction to classical modular forms

15, November
09:30 - 10:30 Yuji Shimizu, D-modules in derived algebraic geometry
10:45 - 11:45 Tilman Bauer, The E2-term of the descent spectral sequence (slides)
14:00 - 15:00 Hirofumi Nakai, Landweber exact functor theorem
15:15 - 16:15 Kentaro Nakamura, Formal group laws II
16:30 - 17:30 Takeshi Torii, On K(1)-local topological modular forms

16, November
09:30 - 10:30 Naoki Imai, Local moduli of p-divisible groups
10:45 - 11:45 Seidai Yasuda, Shimura varieties and automorphic forms
14:00 - 15:00 Tilman Bauer, Differentials in the descent spectral sequence (slides)
15:15 - 16:15 David Gepner, Derived elliptic curves, orientations, and topological modular forms
16:30 - 17:30 Free discussion

Organizers: Isamu Iwanari, Toshiro Hiranouchi (hira at hiroshima-u.ac.jp) , Satoshi Mochizuki, Hirofumi Nakai, Seidai Yasuda

poster

Last update: 26 Nov., 2012