Martin David Palmer -- Grant PCE-2020-2798
Grant PCE-2020-2798
Home | Map

(English | Română)

Grant: Moduli spaces of submanifolds and motion groups

Identifier: PN-III-P4-ID-PCE-2020-2798
Duration: 3 years (2021–2023)
Financed by: UEFISCDI
Contract number: PCE 124/2021
Grant director / Principal Investigator: Martin Palmer-Anghel
Team Members:

Abstract

Our domain of research is at the interaction between algebraic topology, quantum topology and algebraic geometry.

The principal objects of study in this project are moduli spaces of submanifolds. These play a central role in algebraic topology, having profound connections with knot theory (predicted by physics) and homotopy theory. In addition, the representation theory of their fundamental groups – motion groups – is very rich.

In dimension 0, these include configuration spaces and braid groups, whose study is a very well-known domain. In higher dimensions, they are more subtle, and their study has developed rapidly recently, leaving nevertheless many open problems.

The aim of our project is to create new interactions between the topology of moduli spaces, TQFTs and motivic and étale cohomology theories, having 4 main directions:
(1) The stable limit of the homology of moduli spaces of disconnected submanifolds. This is an open question for submanifolds of higher dimension.
(2) New kinds of moduli spaces of submanifolds, inspired by physics and number theory. More precisely, the complement of the submanifold is equipped with a 'field' taking values in a bundle.
(3) The definition of new topological representations of motion groups and extensions towards TQFTs. The aim is to create connections with quantum knot invariants.
(4) Algebraic-geometrical analogues of these moduli spaces, and the study of their étale and motivic cohomology.

Project seminarModuli and Friends

Reports

Publications

Preprints

  • Cristina Anghel, Martin Palmer, Lawrence-Bigelow representations, bases and duality
    arXiv:2011.02388
  • Christian Blanchet, Martin Palmer, Awais Shaukat, Heisenberg homology on surface configurations
    arXiv:2109.00515
  • Martin Palmer, Arthur Soulié, Topological representations of motion groups and mapping class groups – a unified functorial construction
    arXiv:1910.13423 (v4: 17.11.2021)
  • Geoffroy Horel, Manuel Krannich, Alexander Kupers, Two remarks on spaces of maps between operads of little cubes
    arXiv:2211.00908
  • Martin Palmer, Arthur Soulié, The pro-nilpotent Lawrence-Krammer-Bigelow representation
    arXiv:2211.01855
  • Geoffroy Horel, Binomial rings and homotopy theory
    arXiv:2211.02349
  • Martin Palmer, Xiaolei Wu, On the homology of big mapping class groups
    arXiv:2211.07470

Talks at conferences

The symbol [*] indicates that participation was financially supported by the grant.

Invited talks at seminars

  • Cristina Palmer-Anghel, "Coloured Jones and Alexander polynomials unified through Lagrangian intersections in configuration spaces", Topology Seminar, Stanford, 16 February 2021.
  • Cristina Palmer-Anghel, "Coloured Jones and Alexander polynomials unified through Lagrangian intersections in configuration spaces", Séminaire d'algèbre et de géométrie, Caen, 11 May 2021.
  • Cristina Palmer-Anghel, "The Witten-Reshetikhin-Turaev invariants for 3-manifolds as state sums of Lagrangian intersections", Knot theory seminar, Warsaw, 28 May 2021.
  • Cristina Palmer-Anghel, "Coloured Jones and Alexander polynomials unified through Lagrangian intersections in configuration spaces", Séminaire AGATA, Montpellier, 3 June 2021.
  • Cristina Palmer-Anghel, "Uq(sl(2))-quantum invariants for links and 3-manifolds from Lagrangian intersections in configuration spaces", Knots and Representation Theory Seminar, Moscow, 19 July 2021.
  • Cristina Palmer-Anghel, "Renormalized Witten-Reshetikhin-Turaev invariants and M-traces associated to the super quantum group Uq(sl(m|n)) at roots of unity", CUNY Representation Theory Seminar, New York, 1 October 2021.
  • Martin Palmer-Anghel, "On homological representations of mapping class groups", Algebra/Topology seminar, Copenhagen, 8 October 2021.
  • Cristina Palmer-Anghel, "Coloured Jones and Alexander polynomials unified through Lagrangian intersections in configuration spaces", Caltech geometry and topology seminar, Pasadena, 22 October 2021.
  • Cristina Palmer-Anghel, "Uq(sl(2))-quantum invariants for links and 3-manifolds from Lagrangian intersections in configuration spaces", Quantum topology seminar, Indiana University Bloomington, 25 October 2021.
  • Geoffroy Horel, "Tour de Goodwillie-Weiss algébrique et invariants de nœuds type fini", Séminaire de topologie algébrique, UCLouvain, 16 November 2021.
  • Cristina Palmer-Anghel, "Coloured Jones and coloured Alexander invariants from two Lagrangians intersected in a symmetric power of a surface", [K-OS] Knot Online Seminar, CNRS/Paris/Regensburg, 2 December 2021.
  • Cristina Palmer-Anghel, "Uq(sl2)-quantum invariants via the intersection of two Lagrangians in a symmetric power of a surface", Séminaire de topologie algébrique, UCLouvain, 7 December 2021.
  • Cristina Palmer-Anghel, "Coloured Jones and coloured Alexander invariants from two Lagrangians intersected in a symmetric power of a surface", Knots and representation theory seminar, Moscow, 24 January 2022.
  • Cristina Palmer-Anghel, "Coloured Jones and coloured Alexander invariants from two Lagrangians intersected in a symmetric power of a surface", Geometry and Topology seminar, Michigan State University, 8 February 2022.
  • Martin Palmer-Anghel, "Mapping class group representations via Heisenberg, Schrödinger and Stone-von Neumann", Fudan Topology Seminar, Shanghai, 10 March 2022.
  • Martin Palmer-Anghel, "Mapping class group representations via Heisenberg, Schrödinger and Stone-von Neumann", Topology seminar, New York University, Abu Dhabi, 30 March 2022.

Scientific visits of team members

Scientific visits (invited guests at IMAR)

Posters at conferences

Participation in conferences and workshops
(other than those listed further above)

Flag Counter