CORDIS
EU research results

CORDIS

English EN

Loops and groups: Geodesics, moduli spaces, and infinite discrete groups via string topology and homological stability

Objective

This proposal lies at the intersection of algebra, topology, and geometry, with the scientific goal of answering central questions about homological stability, geodesics on manifolds, and the moduli space of Riemann surfaces. Homological stability is a subject that has seen spectacular progress in recent years, and recent work of the PI has opened up new perspectives on this field, through, among other things, associating a canonical family of spaces to any stability problem. The first two goals of the proposal are to give conditions under which this family of spaces is highly connected, and to use this to prove homological and representation stability theorems, with determination of the stable homology. Particular attention is given to Thompson-like groups, building on a recent breakthrough of the PI with Szymik. The last two goals concern geodesics and moduli spaces via string topology: The third goal seeks a geometric construction of compactified string topology, which we propose to use to address counting problems for geodesics on manifolds. Finally our fourth goal is to use compactified string topology to study the harmonic compactification itself, and give a new approach to finding families of unstable homology classes in the moduli space of Riemann surfaces. The feasibility of the last goals is demonstrated by the PIs earlier algebraic work in this direction; the proposal is to incorporate geometry in a much more fundamental way.
The project combines breakthrough methods from homotopy theory with methods from algebraic, differential and geometric topology. Some of the goals are high risk, but we note that in those cases even partial results will be of significant interest. The PI has a proven track record at the international forefront of research, and as a research leader, e.g., through a previous ERC Starting Grant. The research team will consist of the PI together with 3 PhD students and 3 postdocs in total during the 5 years.

Host institution

KOBENHAVNS UNIVERSITET

Address

Norregade 10
1165 Kobenhavn

Denmark

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 1 864 419

Beneficiaries (1)

Sort alphabetically

Sort by EU Contribution

Expand all

KOBENHAVNS UNIVERSITET

Denmark

EU Contribution

€ 1 864 419

Project information

Grant agreement ID: 772960

Status

Ongoing project

  • Start date

    1 September 2018

  • End date

    31 August 2023

Funded under:

H2020-EU.1.1.

  • Overall budget:

    € 1 864 419

  • EU contribution

    € 1 864 419

Hosted by:

KOBENHAVNS UNIVERSITET

Denmark