Homotopical Group Theory and Topological Algebraic Geometry
WORKSHOP
This workshop is aimed at graduate students and young researchers, in
part as preparation for the
conference
at the Max Planck institute the following week. The
workshop, as well as conference, focuses on the new interactions of Algebraic Topology with
Group Theory, Algebraic Geometry and Mathematical Physics which come
from looking at these fields through the eye of a homotopy
theorist. It celebrates one of the contributors to the subject by
honoring the 60th birthday of Haynes Miller.
NEW (July 9,2008): Workshop pictures!!
Scientific Program
Minicourse by Bill Dwyer (Notre Dame): Homotopical group theory
(10 lectures of 45 minutes each).
Minicourse by Paul Goerss (Northwestern): Topological algebraic
geometry (10 lectures of 45 minutes each).
In addition to the lectures there will be scheduled problem sessions
each day on both topics. Several of the MPI speakers will be in
residence to answer questions (Behrens, Lurie...)
Lecture notes further down the page!
Getting to CabInn Scandinavia and the Univ. Copenhagen Math
Department/H.C.Ørsted Institute (in "Universitetsparken")
To get to CabInn
Scandinavia from the airport, take the frequent metro from the
airport terminal and get off at the stop "Forum" (17 minutes, 10 stops; every metro from the airport stops at
"Forum"). CabInn Scandinavia is now very close. For a map and more detailed directions see here.
You need to buy
a 3 zone ticket in the airport terminal before boarding the
metro (or buy and stamp a 10 journey 3-zone multijourney
ticket).
Getting from CabInn Scandinavia to the Math Department/The
H.C. Ørsted Institute (HCØ) is a
pleasant 30 minutes walk (metro/bus is also an option). See the directions page for a map.
Within HCØ, all lectures take place in the central Auditorium 1. A map of the HCØ
indicating the location of Auditorium 1 can
be found here
A more fancy google map, also showing bus stops and lunch places can
be found
HERE
(but don't worry, there
will also be signs, and 120 topologists running around).
Tentative daily schedule monday-friday (all activities in main Auditorium 1)
09:00-10:45 Dwyer HGT lectures
10:45-11:15 Coffee break
11:15-12:00 Independent study time
12:00-13:00 HGT exercise session
13:00-14:00 Lunch
14:00-15:45 Goerss TAG lectures
15:45-16:15 Coffee break
16:15-17:00 Independent study time
17:00-18:00 TAG exercise session
18:00-18:30 "Fyraftensbajer" (aka øl, pivo, cerveza..)
(18:30-01:00 study; 01:00-08:00 sleep; repeat...)
(Monday at 16:15 Y. Manin will give a general-audience talk about Euler
products during the independent study time.)
Course outlines
Homotopy theory and its application to classifying spaces (Bill Dwyer)
Synopsis: The lectures will introduce several tools that are widely
used in homotopy theory and discuss the role that some of these tools
play in the analysis of classifying spaces. Much of the course will
focus on unstable homotopy theory, and the intention will be to
emphasize common ideas rather than special cases. The topics covered
will include many if not all of the following.
(1) Homotopy theories, model categories, and examples (chain
complexes, topological spaces, simplicial sets, topological
groups, simplicial groups, spectra, diagrams).
(2) Functors, derived functors, and examples (tensor, hom,
abelianization, fixed point sets, orbits, limits, colimits,
left and right Kan extensions, ends and coends). Initial and
terminal functors. Function spaces.
(3) Completions, localizations, and examples (p-completion,
rationalizaton, general homology localization, localization
with respect to a map). The arithmetic square and its
extensions.
(4) Lannes theory, both algebra (the functor T) and geometry
(towers and their limits). Cohomology of function spaces and
homotopy fixed point sets.
(5) K(\pi,1)'s and maps between them. More general maps between
classifying spaces. Compact Lie groups, finite loop spaces,
p-compact groups.
(6) Homology decompositions, fusion systems, and p-local finite
groups.
Prerequisites: It will be assumed that the members of the audience
have a background in the basics of
homotopy theory.
NEW (6/2008): Lecture notes can be found here. The slides of the
lectures can be found here.
Topological algebraic geometry (Paul Goerss)
Synopsis: I would like to give a concise introduction to derived
algebraic geometry over the moduli stack of
formal groups. Put another way, I would like to discuss when
continuous families of Landweber exact homology
theories can be lifted to families of structured ring spectra. I would
also like to explain why we care:
this is part of long standing program (going back to Morava and
others) of using arithmetic algebraic
geometry to understand phenomena in stable homotopy theory. While very
much a developing theory, the work of
Hopkins, Miller, Lurie, Behrens, Lawson, and others over the last ten
or so years have given us very precise
tools. The theory and practice of these tools is the emphasis of these
lectures.
Topics we be a subset of the following list, depending on time and
the background of the audience.
1. Schemes, stacks, and algebraic stacks
2. Structured ring spectra and derived algebraic geometry
3. Formal groups, p-divisible groups, and their role in homotopy
theory
4. Derived stacks over the moduli stack of formal groups; Lurie's
Theorem
5. Deformations of formal groups and the Hopkins-Miller theorem
6. Examples: the Elliptic Case (Topological Modular Forms)
7. Examples: Shimura varieties (Topological Automorphic Forms)
Prerequisites: See
here for some recommended reading!.
HANDOUTS:
Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9+10
All lectures as one file
California: A musical
tribute to Haynes Miller
Registration & application for funding
THE REGISTRATION DEADLINE HAS NOW PASSED. See further down the page
for funding decisions.
A list of registred participants is available from the
Bonn
Conference website. (It should say "Yes" in the column
"Reg. CO" if you are registered for Copenhagen.)
Accomodation
Accomodation in Copenhagen will be at CABINN SCANDINAVIA. The
price is DKK 585/night for a single room and DKK 645/night (approx
EUR 86) for a double room, including breakfast.
A block of rooms has been reserved for 7 nights from Sunday June 15,
2008 to Sunday June 22, 2008. Note: Talks starts Monday morning
and end Friday afternoon; there will be a social program
Saturday.
**PARTICIPANTS ARE RESPONSIBLE FOR BOOKING THEIR OWN ACCOMODATION AT CABINN SCANDINAVIA** by calling (+45) 35 36 11 11 and citing the booking reference #100253.
Hotel space at Cab Inn only guaranteed until FEBRUARY 15, 2008.
As of late February there are still rooms available at CabInn. But
we cannot guarantee future availability, so please book today.
The website of CabInn is: www.cabinn.com, and click under CAB INN SCANDINAVIA. Warning: that CabInn Scandinavia is not the only CabInn hotel in the greater copenhagen area.
The address is:
CAB INN Scandinavia
Vodroffsvej 55
DK-1900 Frederiksberg C
Tlf: (+45) 35 36 11 11
Fax: (+45) 35 36 11 14
Email: scandinavia@cabinn.com
THE FUNDING DEADLINE HAS PASSED. Please see below for funding information, for those who applied.
Funding decision
If you applied for funding you should have received an email from the
Max Planck Institute with information.
Copenhagen Funding to those who applied:
We can offer 6 nights of shared double occupancy accomodation at
CabInn
Scandinavia, or 7 nights in a 3- or 4-person room. For single
occupancy we
can reimburse 3 nights if needed, but strongly encourage you to use
alternatively funding, since this will free up funds for younger
participants (120 people applied for funding). You are responsible for
booking your own room at CabInn Scandinavia using reference number
#100253, and finding your own roommates. Rooms booked any other way
cannot
be refunded. The granted nights will be deducted from your bill at
checkout; please also write an email to homotopical2008@math.ku.dk
stating
that you want to accept the funding. THE OFFICIAL HOLD-DATE ON THE
ROOMS
HAS PASSED SO IF YOU HAVE NOT BOOKED ALREADY CALL TODAY! We cannot
guarantee availability. A list of participants is linked from the
conference homepage http://www.ruhr-uni-bochum.de/topologie/conf08. If
you
cannot find a roommate you can write to homotopical2008@math.ku.dk,
and we
will try to offer a suggestion. (Note: Requests concerning the
conference in Bonn should be directed to MPI instead.)
Getting to and from Copenhagen
Arrival day is Sunday June 15, 2008. Lectures start Monday June 16,
2008 in the morning and end Friday June 20 in the
afternoon. There
will be optional social activities Saturday June 21, 2008 for the people staying
until Sunday.
For people traveling onwards to Bonn, there are frequent flights between Copenhagen (CPH)
and Cologne/Bonn (CGN), Frankfurt (FRA), or Dusseldorf
(DUS). Overseas participants attending both events may want to
consider buying an "open-jaw" ticket arriving in Copenhagen Sunday June 15 and
departing from e.g. Frankfurt Saturday June 29, and then buy the
one-way Copenhagen-Bonn on June 21 or 22 separately.
(See here for a listing of
the route network of low-cost carriers within Europe.)
Acknowledgement
The conference is partially supported by the DFG
Graduiertenkolleg 1150 "Homotopy and Cohomology" , the Max Planck Institute
Bonn., and the US National Science Foundation.
The workshop is supported by the
University of Copenhagen through a grant from the researcher training program
"Forskerskole i Matematik og anvendelser" and a Faculty of Science
grant, as well as a EURYI award from the ESF and Roemer
award from the Danish Natural Science Research Council.
Organization
The workshop is organized by the Copenhagen Topology
Group, in connection with the conference at MPI organized by Ando,
Grodal, Laures, and Shipley.
