High dimensional cohomology of moduli spaces

 

 

University of Copenhagen
28 June - 2 July 2021

In this Masterclass, we will learn about the high dimensional cohomology of moduli spaces such as the moduli space of curves, graphs, and lattices. These moduli spaces are classifying spaces of groups such as mapping class groups, automorphism groups of free groups, and arithmetic groups. We will learn about duality groups whose high dimensional cohomology of these moduli spaces is related to the low degree homology groups with twisted coefficients. We will also discuss graph homology and tropical curves.

The masterclass is aimed at advanced graduate students and postdocs with an interest in algebraic topology and geometric group theory. Connections with algebraic geometry and number theory will be mentioned but this is not the primary focus.

Graduate students and other early career researchers from US institutes can apply to be considered for financial support.

All graduate students and other early career researchers can apply for financial support to partly cover local expenses. The support should be roughly DKK 500 per day, at most DKK 2500 in total.

If you wish to apply for support, please indicate this on the registration form.

Please note: Due to a match of the UEFA Euro 2020 in Copenhagen on June 28, 2021, the Copenhagen Jazz Festival starting on July 2, 2021, and other events, there will limited accommodation available in Copenhagen. We advise booking accommodation early.

Program

Abstracts for all lectures can be found here: [PDF]

Review package put together by Jennifer Wilson: [PDF]

Recordings of (most of) the lectures can be found on YouTube: [Playlist]

All notes for the lectures can be found by clicking on the title of the lecture in the schedule below.

	Monday	Tuesday	Wednesday	Thursday	Friday
Coffee
9:30-10:30	Patzt Introduction	Galatius High-dimensional cohomology of the moduli space of Riemann surfaces, Part I	Free	Galatius High-dimensional cohomology of the moduli space of Riemann surfaces, Part II	Galatius High-dimensional cohomology of the moduli space of Riemann surfaces, Part III
10:45-11:45	Jansen  Expository: Borel-Serre Duality	Jansen The stratified homotopy type of the reductive Borel–Serre compactification	Free	Sroka On the high-dimensional rational cohomology of symplectic groups	Brück Free factor complexes as boundary structures
Lunch
13:30-14:30	Bux Outer space and its bordification	Brendle The Steinberg module of the mapping class group	Bux Dimension of the Torelli group of Out(F_n), Part I	Brendle Cohomology of congruence subgroups	Bux Dimension of the Torelli group of Out(F_n), Part II
14:45-15:45	Brendle The curve complex and duality for the mapping class group	Exercises	Exercises	Exercises	Exercises
Coffee
16:15-17:15	Wilson The top-degree rational cohomology of the special linear group of a number ring	Wilson A generating set for the Steinberg module of a Euclidean domain	Miller On not the dualizing module of Aut(F_n)	Problem Session
	Pizza and Drinks			Conference dinner