This is the first of three planned conferences in Profinite Geometry
and Related Moduli spaces
Click on a blue-lit name in the participant list
to see abstracts and talk titles.
By the end of the Red Lodge meeting there was considerable planning for the meeting in RIMS (see Followup Conferences). Ken Ribet took two series of conference participant pictures: morning of the first conference day and many of the students and post-doctorals on the hike-excursion Wednesday, April 5. Stefan Wewers and Hidekazu Furusho also have series:
During the conference sessions and the
Friday night conference party, and during the Wednesday walk and the conference party.
TABLE OF CONTENTS:
I.
ATTENDEES
II. LOCATION AND LOGISTICS
III.
CONFERENCE THEME
IV. PROGRAM
V.
FOLLOWUP CONFERENCES
I.
ATTENDEES
Organizing Committee
Pierre Debes pde@ccr.jussieu.fr
(Survey: Intro to Modular Towers)
Mike Fried mfri4@aol.com (Survey:
(A meaning for the phrase "Profinite Arithmetic Geometry")
ribet@math.berkeley.edu (Survey: An introduction to Serre's work on Galois groups attached to division points on elliptic curves over number fields)
Not at this meeting: Hiroaki Nakamura h-naka@math.okayama-u.ac.jp
Senior Attendees
Fedor Bogomolov bogomolo@CIMS.nyu.edu
Armand Brumer brumer@fordham.edu
Ido Efrat efrat@math.bgu.ac.il
Michel Emsalem emsalem@math.univ-lille1.fr
Hidekazu Furusho furusho@math.nagoya-u.ac.jp
Adrian Vasiu adrian@math.arizona.edu
Thomas Weigel thomas.weigel@unimib.it
Stephan Wewers wewers@mpim-bonn.mpg.de
Yuri Zarhin zarhin@math.psu.edu
Student and Post-Doctorals Attendees
Reza Akbarpour akbarpur@uwo.ca
Anna Cadoret cadoret@math.jussieu.fr
(Survey: Abelianized Modular Towers)
Alina Cojocaru cojocaru@math.princeton.edu
Aji Dhillon adhill3@uwo.ca
Kinya Kimura Kinnyakim@aol.com
Grace Lyo gracelyo@math.berkeley.edu
Mihran Papikian papikian@math.stanford.edu
Andy Schultz aschultz@stanford.edu
Stanford
Darren Semmen dsemmen@gmail.com
Jared Weinstein jared@Math.Berkeley.EDU
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II. LOCATION AND LOGISTICS
Coordination Conference in Montana: April 3-7, 2006, in Red
Lodge, Montana. The entrance to Red Lodge is spectacular, especially in
springtime. The nearby Bear Tooth Highway climbs almost a mile through
Mesozoic archeological formations. This conference will have several
planning aspects, including fixing the global program, defining
the main problems, outlining significant approaches, and
structuring our RIMS meeting. Compatible with these goals, our invited
lecturers will aim to educate young people to tools and goals of the
conference series. A conference product will be an informal proceedings
that aims to
encourage research programs of conference attendees to contributing to
the
conference series goals.
Specific Items:
- Arrival location:
Logan Airport in Billings, Montana
- Getting to the conference
site: Shuttle arranged through Rock Creek Lodge and a rental from Thrify.
For most participants pick up will be from Hampton Inn at 8:15AM, Monday morning for transport to Rock Creek.
- Stay: Monday night
through Thursday night conference attendees will stay at the Rock Creek
Resort. Sunday night they will stay at the Hampton Inn (along Interstate 90 outside Billings)
and will be delivered in the morning to Rock Creek. Friday night we'll
stay at the Hampton Inn again, from which it is easy to get to
the airport by the Inn shuttle.
- Entertainment:
It's a beautiful place to walk, akin to Oberwolfach. Wednesday
afternoon we hope to have an excursion to Cody, Wyoming, the site of the Buffalo Bill (Historical Center) museum complex. The museum is mostly the creation of Gertrude Vanderbilt Whitney (the founder of the Whitney museum in New York; extremely wealthy, and equally elegant) and her son, who educated himself in sophisticated architecture so as to dedicate several of its wings to her memory and art. Further, it contains the works of several European artists who wanted to record the vanishing life of the Indians and Northwest plains. www.bbhc.org
- Conference Conclusion:
Friday night we'll have a conference party at Mike Fried's house in
Billings.
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III.
CONFERENCE THEME
Our series will combine moduli space ideas with profinite Galois and
group theory. Several speakers will aim to solve a list of well-known
problems ripe for new understanding. Several are from Fried-Jarden,
Field Arithmetic, whose second edition appeared in 2004, and still
unsolved since the 1986 first edition. Investigating
the structure of absolute Galois groups of fields, for example finding
their finite quotients (the Inverse Galois Problem), is a particular
major motivation. Others connect to conjectures limiting torsion points
on abelian varieties over a number field.
Some special topics we expect to appear in several talks, at Red
Lodge and/or at RIMS:
From Arithmetic: Strong Torsion Conjecture (on abelian varieties);
Serre's Open Image Theorem (a special case of annabelian problems) and
properties of l-adic representations; Detecting Rational Points;
Inverse Galois Problem; PAC and Ample Fields; Fried-Voelklein
generalization of Shafarevich's Conjecture.
From Moduli Spaces and Geometry: Degeneration at cusps; Stable
compactification; Fine moduli (for various moduli problems); Modular
curves generalizations such as Modular Towers and Shimura Varieties;
Properties of Curves embedded in their Jacobians
From Profinite Group Theory: Frattini covers; Schur-Zassenhaus; Etale
cohomology; Embedding problems and their obstructions; Groups of finite
cohomological dimenion, p-Poincare dual groups; Algebraic groups over
the p-adics
The conference will be a success if most attendees come away with the
value of joining Profinite Group Theory, Moduli Spaces and Arithmetic
Geometry, especially the interpretation of geometric properties using
homological algebra.
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IV.
PROGRAM
03/15/06: The abstracts and program have all been posted.
Program file: rr-prog.html
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V.
FOLLOWUP CONFERENCES
Presentation Conference at RIMS: Tentatively October 23-27, 2006. We
have been invited to organize a meeting within a year long international "Arithmetic algebraic geometry
project" run by Kazuya Kato, Akio Tamagawa and Shin Mochizuki.
Our part of this conference will be a public presentation of results to
a mature audience of related Arithmetic Geometry
researchers. The world at large will learn what we are doing. Our own
group will see the collective progress and bottlenecks in our
respective programs. We understand the
organizers here would like to see a production volume. This should not
interfere with the volume planned for the 3rd conference.
Final Results Conference at BANFF: Fall of 2007 or Spring of 2008, to
present final results. From this we expect a timely publication from
the whole conference series. Of course, Banff is spectacular, too, with
its
Cambrian rock formations.
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