High dimensional cohomology of moduli spaces

 

 

Conference picture

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]

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

 

 

Lecturers (three lectures each)

Tara Brendle (University of Glasgow)
Kai-Uwe Bux (University of Bielefeld)
Søren Galatius (University of Copenhagen)
Jennifer Wilson (University of Michigan)

Speakers (individual talks)

Benjamin Brück (ETH Zürich)
Mikala Ørsnes Jansen (University of Copenhagen)
Robin Sroka (University of Copenhagen)

  

 

 

 

 

 

 

 

 

 

The conference/masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue.

The lectures will be held in Auditorium 4 and on Zoom. All registered participants will receive the information for the Zoom meeting. Breaks will be held in the foyer. And there will be pizza on monday in the lunch room on the fourth floor.

Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation.

A journey planner in English is available.

More information on the "find us" webpage.