Topological Modular Forms Seminar

University of Sheffield, 2015/16


This academic year we will study the construction of the tmf spectra following mainly the book of Douglas et al.[1]

The meetings will take place in room J-11 Hicks Building on Tuesdays at 4pm during the Spring.

A short note on the seminar can be found HERE.

Fall Talks:

Title: An overview of elliptic cohomology, I
Speaker: John Greenlees
Week: 5
Contents: Complex oriented cohomology theories, genera, complex cobordism, Quillen's theorem.

Title: An overview of elliptic cohomology, II
Speaker: John Greenlees
Week: 6
Contents: Formal groups laws associated to complex oriented cohomology theories, formal group laws coming from elliptic curves, Landweber exact theorem and the construction of elliptic cohomologies.

Title: Elliptic curves
Speakers: Haluk Sengun
Week: 8
Contents: Cover Chapter 2 of [1].

Title: Modular forms
Speakers: Haluk Sengun
Week: 9
Contents: Basic theory of modular forms, relation to modular forms and the ring structure.

Title: Moduli stack of elliptic curves, I
Speaker: Tom Bridgeland
Week: 10
Contents: This talk will serve as an introduction to stacks. Moduli stack of elliptic curves will be discussed.

Title: Moduli stack of elliptic curves, II
Speaker: Tom Bridgeland
Week: 11
Contents: Continuation of the previous talk.

Title: Formal groups and M_{FGL}
Speaker: Callan McGill
Week: 12
Contents: An extended discussion that covers the final part of Chapter 3 of [1].

Spring Talks:

Title: Sheaves in homotopy theory, I
Speaker: Dimitar Kodjabachev
Week: 3
Contents: An extended discussion that covers the final part of Chapter 5 of [1].


Title: Sheaves in homotopy theory, II
Speaker: Dimitar Kodjabachev
Week: 4
Contents: An extended discussion that covers the final part of Chapter 5 of [1].


Title: Landweber exact thorem
Speaker: John Greenlees
Week: 5
Contents: An extended discussion that covers the final part of Chapter 4 of [1].


Title:  Bousfield localization and the chromatic Hasse square
Speaker: Dimitar Kodjabachev
Week: 8

Title: TMF with level structures
Speaker: Lennart Meier (Bonn)
Week: 9

Materials:


[1] Douglas, Francis, Henriques and Hill. "Topological modular forms"

For a discussion of basic materials see the short note on our seminar.

For an extensive list, visit Tyler Lawson's tmf literature webpage.