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.