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Seminar on topological
automorphic forms, 2009-11. This
is my attempt to understand Topological automorphic forms
by Mark
Behrens and Tyler Lawson. This 159 page memoir describes a
general construction which includes that of the theory of topological
modular forms (tmf) as a special case. It includes a lot of
number theory and algebraic geometry not familiar to most
topologists.
Before attempting to read it one should look at Lawson's
introduction, An overview of abelian varieties in homotopy
theory, 37 pages. It describes some of the backgroup and
motivation for the constructions and definitions in TAF.
Another useful introduction is Topological algebraic geometry by Paul Goerss.
This consists of over 100 slides for a series of lectures given in
Copenhagen in June, 2008. Here you can find quick discussions of schemes, sheaves, stacks, topoi and other
relevant notions from abstract algebraic geometry. For a record fast
description of the moduli stack of elliptic curves over the complex
numbers, see What is ... a stack?
Goerss' writeup of his March, 2009 Bourbaki talk Topological Modular
Forms [after Hopkins, Miller and Lurie], 33 pages, is the best
single account I have seen of the construction of
tmf. ArXiv link.
For a very concise introduction to the relevant facts about
elliptic curves and modular forms, see Appendix B (starting on page
53) of
Ando-Hopkins-Strickland.
Talks given in April, 2010, are based on Goerss'
paper Quasi-coherent
sheaves on the Moduli Stack of Formal Groups.
|
A collection of related
papers
Also see Nora
Ganter's Topological
modular forms literature list
Seminar meetings
The seminar did not meet in Fall 2010. In Spring 2011 it is being
run
by Don
Larson.
- Spring, 2011
- Schedule for future talks
- Friday, April 15, 2:00 in Hylan 1104.
Don
Larson will speak again on forms and involutions.
Ravenel's lecture notes
- Friday, March 25, 2:00 in Hylan 1104.
Don
Larson will pseak on forms and involutions.
Ravenel's lecture notes
- Friday, February 25, 2:00 in Hylan 1104.
Scott
Bailey will speak again on polarized abelian varieties.
Ravenel's lecture
notes
- Friday, February 18, 2:00 in Hylan 1104.
Scott
Bailey will speak on polarized abelian varieties.
Fili's lecture notes
- Friday, February 11, 2:00 in Hylan 1104.
Amanda
Beeson will finish the Honda-Tate classification and then cover
Chapter 3 on level structures.
Ravenel's lecture notes
- Friday, February 4, 2:00 in Hylan 1104.
Amanda
Beeson will briefly review $p$-divisible groups and then start
the Honda-Tate classification of
abelian varieties over finite fields. This material is from
chapters 1 and 2 of the Behrens-Lawson
manuscript.
Ravenel's lecture notes
- Friday, January 28, 4:00 in Hylan 1106A.
Survey talk by Don Larson. A good reference for this material
is Hopkins-Mahowald.
Paul Fili's lecture notes
- Spring, 2010
- Friday, April 30, 2:00 in Hylan 1106B. Scott Bailey will speak on
The Tangent Scheme and Derivations II.
The reference for this talk is pages 19-23 of Goerss' paper.
Ravenel's lecture notes
- Friday, April 23, 2:00 in Hylan 1106B. Scott Bailey will speak on
The Tangent Scheme and Derivations.
The reference for this talk is pages 19-23 of Goerss' paper.
Ravenel's lecture notes
- Friday, April 16, 2:00 in Hylan 1106B. Troy Winfree will speak on
Faithful flatness, descent, formal schemes and formal groups.
- No meeting on April 7.
- Friday, April 2, 2:00 in Hylan 1106B. Troy Winfree will speak on a simple introduction to sheaves over functors.
Ravenel's lecture notes
- Friday, March 26, 2:00 in Hylan 1106B. Paul
Synhavsky will speak again on Morava stabilizer groups, and I will talk about Greek letter elements.
Ravenel's lecture notes
- Friday, March 19, 2:00 in Hylan 1106B. Paul
Synhavsky will speak again on Morava stabilizer groups.
Ravenel's lecture notes
- No meetings on March 5 or 12.
- Friday, February 26, 2:00 in Hylan 1106B. Paul
Synhavsky will speak on Morava stabilizer groups.
- Friday, February 19, 2:00 in Hylan 1106B. Don
Larson will speak again on p-divisible groups.
Ravenel's lecture
notes
- No meeting on February 12.
- Friday, February 5. 2:00 in Hylan 1106B. Don
Larson will speak on p-divisible groups.
Ravenel's
lecture notes
-
Fall, 2009
- Friday, December 4. 2:00 in Hylan 1106B. I will
continue to speak on a talk Mark Behrens gave recently.
My notes on Behrens' talk of October
24, 2009.
- No meetings on November 20 or 27.
- Friday, November 13. 2:00 in Hylan 1106B. I will
speak on a talk Mark Behrens gave recently.
My notes on Behrens' talk of October
24, 2009.
- No meeting on November 6.
- Friday, October 30, 2:00 in Hylan 1106B. Nick
Rogers will speak on Shimura curves.
Ravenel's lecture notes
- No meetings on October 16 and October 23.
- Friday, October 9, 2:00 in Hylan 1106B. Scott
Bailey will speak the construction of tmf.
Ravenel's lecture notes
- Friday, October 2, 2:00 in Hylan 1106B. Don
Larson will speak on abstract algebraic geometry.
Ravenel's lecture notes
- Friday, September 25, 2:00 in Hylan 1106B. Doug
Haessig will speak on elliptic curves.
Ravenel's lecture notes
- Friday, September 18, 2:00 in Hylan 1106B.
Organizational meeting and introductory talk by me.
ABSTRACT: I
will give
- A very brief overview of the motivation and goal of TAF.
- A brief introduction to the theory of formal group laws.
- A brief discussion of the connection between formal
group laws and homotopy theory.
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Created September 14, 2009; last modified August 29,
2011.