Workshop “Arithmetic Galois Theory and Related Moduli Spaces” October 23-27 & 30-31, 2006 Room 420 & 115, RIMS, Kyoto University Program Organizers P.Dèbes, M.Fried, J.Koenigsmann, H.Nakamura and K.Ribet

October 23 (Monday) Room 420 9:50 – 10:00 Hiroaki Nakamura (Okayama Univ.)

Opening Words and Facilities Information

10:00 – 11:00 Pierre Dèbes (Univ. Lille 1)

l-adic aspects of the modular tower program

11:15 – 12:15 Michel Emsalem (Univ. Lille 1)

l-adic points on a modular tower

14:00 – 15:00 Jakob Stix (IAS, Princeton)

Exploration of anabelian varieties in higher dimension

15:00 – 15:45 Tea 15:45 – 16:45 Makoto Matsumoto (Hiroshima Univ.)

Malcev completions of arithmetic mapping class groups

17:00 – 18:00 Michael Dettweiler (Heidelberg Univ.)

Motives with Galois group G_{2}

October 24 (Tuesday) Room 420 10:00 – 11:00 Jan Minác (Univ. of Western Ontario)

Galois cohomology, quotients of absolute Galois groups,

and a little modular representation theory

11:15 – 12:15 Stefan Wewers (Bonn Univ.)

Indigenous bundles, deformation data and Hurwitz curves

with bad reduction

14:00 – 15:00 Gerhard Frey (Univ. Duisburg-Essen)

Curves of genus 2 with elliptic differentials and associated Hurwitz spaces (joint work with E. Kani)

15:00 – 15:45 Tea 15:45 – 16:45 Tamás Szamuely (Alfréd Rényi Inst. Math., Hungarian Acad. Sci.)

Local-global principles for semiabelian varieties

17:00 – 18:00 Florian Pop (Univ. of Pennsylvania)

Meta-abelian anabelian geometry over algebraically closed base fields

October 25 (Wednesday) Room 420 10:00 – 11:00 Shreeram S. Abhyankar (Purdue Univ.)

Simultaneous surface resolution

11:15 – 12:15 David Harbater (Univ. of Pennsylvania)

On function fields with free absolute Galois groups Free afternoon

October 26 (Thursday) Room 420 10:00 – 11:00 Mike Fried (UC, Irvine emeriti / MSU-Billings)

How pure-cycle Nielsen classes test the Main Modular Tower Conjecture

11:15 – 12:15 Ki-ichiro Hashimoto (Waseda Univ.), Hiroshi Tsunogai (Sophia Univ.) Some recent results on Noether’s problem 14:00 – 15:00 Anna Cadoret (Univ. Bordeaux 1/RIMS, Kyoto Univ.)

Arithmetic properties of moduli spaces for p etale G covers and torsion on abelian varieties

15:00 – 15:45 Tea 15:45 – 16:45 Yasutaka Ihara (Chuo Univ. COE)

On Euler-Kronecker invariants of global fields

17:00 – 18:00 Michael Tsfasman (Indep. Univ. of Moscow / Univ. de Luminy)

Infinite global fields and their zeta functions Banquet and a tribute to the Conference

October 27 (Friday) Room 420 10:00 – 11:00 Darren Semmen (Univ. Southern California)

Duality groups and modular towers

11:15 – 12:15 Thomas Weigel (Univ. di Milano - Bicocca)

Class field theory and modular towers

14:00 – 15:00 Yuri Zarhin (Pennsylvania State Univ.)

Abelian varieties without homotheties

15:00 – 15:45 Tea 15:45 – 16:45 Yuichiro Hoshi (RIMS, Kyoto Univ.)

Cuspidalizations of fundamental groups of configuration spaces

17:00 – 18:00 Akio Tamagawa (RIMS, Kyoto Univ.)

The algebraic and anabelian geometry of configuration spaces (joint work with Shinichi Mochizuki)

October 30 (Monday) Room 115 10:00 – 11:00 Jochen Koenigsmann (MPIM, Bonn)

On birational anabelian geometry over almost arbitrary fields

11:15 – 12:15 Mohamed Saidi (Exeter Univ./RIMS, Kyoto Univ.)

A prime to p version of the Grothendieck anabelian conjecture in characteristic p (joint work with A.Tamagawa)

14:00 – 15:00 Jared Weinstein (UC, Berkeley)

Galois representations with prescribed ramification

15:00 – 15:45 Tea 15:45 – 16:45 Kinya Kimura (RIMS, Kyoto Univ.)

Modular towers of moduli stacks

17:00 – 18:00 Discussion on themes presented at this RIMS conference and possibilities for a 3rd Profinite Geometry Conference

October 31 (Tuesday) Room 115 10:00 – 11:00 Hidekazu Furusho (Nagoya Univ.)

Survey of Drinfel’d’s work on GT and its associated quantum groups

11:15 – 12:15 Hiroaki Nakamura (Okayama Univ.)

Profinite Grothendieck-Teichmüller parameters and a family of Mordell elliptic curves (joint work with H.Tsunogai)

14:00 – 15:00 Discussions: repository creation, exposition of braid software etc. 15:00 – 16:00 Tea

Special thanks to RIMS-International Project Research 2006 “Arithmetic Algebraic Geometry” at Kyoto University by Kazuya Kato, Hiroyuki Yoshida, Atsushi Moriwaki, Akio Tamagawa and Shinichi Mochizuki