Martin David Palmer -- Grant PCE-2023-2001
Grant PCE-2023-2001
Home | Map

(English | Română)

Grant: The homology and representation theory of moduli spaces

Identifier: PN-IV-P1-PCE-2023-2001
Duration: 3 years (2025–2027)
Financed by: UEFISCDI
Contract number: 58PCE / 03.01.2025
Grant director / Principal Investigator: Martin Palmer-Anghel
Team Members:

Abstract

The domain of this research project lies at the various rich interfaces between algebraic topology, low-dimensional topology, quantum topology, group theory and representation theory. The unifying theme is the study of moduli spaces, their homology and the properties (group-theoretical and representation-theoretical) of their fundamental groups, which include braid groups and mapping class groups.

Moduli spaces are ubiquitous throughout mathematics and have a wide range of applications, from analytic number theory, knot theory and theoretical physics to more applied topics such as robotics and motion planning algorithms. Moreover, the representation theory of their fundamental groups – notably mapping class groups – is extremely rich.

Within this overarching theme, we have 5 directions of study:
(1) The homology of configuration spaces on closed manifolds. Although this is a very classical topic, much is still unknown here.
(2) Representations of mapping class groups of surfaces, inspired by the long-standing open question of whether these groups are linear. We will investigate the kernels of new families of representations.
(3) The homology of mapping class groups of infinite-type surfaces, with connections to dynamical systems.
(4) Non-commutative extensions of quantum representations of knots and links.
(5) Lower central series of arrangement groups (fundamental groups of complements of complex hyperplane arrangements).

Moduli and Friends II

Reports

Publications

  1. Martin Palmer, Arthur Soulié, The pro-nilpotent Lawrence-Krammer-Bigelow representation
    Journal of Pure and Applied Algebra vol. 229 no. 6 (2025) Article no.: 107952 (39 pp.)
  2. Martin Palmer, Xiaolei Wu, Compact and finite-type support in the homology of big mapping class groups
    Journal of the London Mathematical Society vol. 112 no. 3 (2025) Article no.: e70258 (35 pp.)
  3. Christian Blanchet, Martin Palmer, Awais Shaukat, Heisenberg homology on surface configurations
    Mathematische Annalen vol. 393 (2025) pp. 1989-2056

Preprints

  1. Cristina Anghel, Geometric universal Jones invariant from configurations on ovals in the disc
    arXiv:2401.17245
  2. Cristina Anghel, Universal geometrical link invariants
    arXiv:2505.18108
  3. Anca Măcinic, Jean Vallès, Addition-deletion for conic-line arrangements with split Chern polynomial
    arXiv:2510.02771
  4. Martin Palmer, Xiaolei Wu, Embedding groups into acyclic groups
    arXiv:2510.16879
  5. Erik Lindell, Arthur Soulié, Twisted homological stability for handlebody mapping class groups
    arXiv:2510.21383
  6. Cristina Anghel, Christine Ruey Shan Lee, A topological model for the HOMFLY-PT polynomial
    arXiv:2405.03679

Prizes

  1. Cristina Palmer-Anghel: Simion Stoilow prize of the Romanian Academy, December 2025
  2. Cristina Palmer-Anghel: Lucian Bădescu prize, IMAR, December 2025
  3. Martin Palmer-Anghel: Lucian Bădescu prize, IMAR, December 2025

Talks at conferences

  1. Cristina Palmer-Anghel, "A topological model for the HOMFLY-PT polynomial", Journées de topologie algébrique, géométrique et quantique en Picardie II, Amiens, 5–7 March 2025.
  2. Arthur Soulié, "Some stable twisted cohomology computations for handlebody mapping class groups", Algebraic approaches to mapping class groups of surfaces, University of Tokyo, 19–23 May 2025.
  3. Martin Palmer-Anghel, "The homology of Thompson-like groups via algebraic K-theory and étale groupoids", Journée de topologie quantique, Dijon, 26 May 2025.
  4. Cristina Palmer-Anghel, "Universal link invariants via configuration spaces", Conference on Modern Developments in Low-Dimensional Topology, ICTP, Trieste, 9–13 June 2025.
  5. Anca Măcinic, "Curve arrangements. Freeness and geometric constraints", Moduli, Hilbert Schemes and Singularities, Cluj-Napoca, 8–12 September 2025.
  6. Cristina Palmer-Anghel, "Universal link invariants via configuration spaces", AMS Special Session on Quantum Supergroups in Low-Dimensional Topology, 25–26 October 2025.

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

  1. Martin Palmer-Anghel, 36th YaMCATS meeting, Leeds, 24 January 2025.
  2. Martin Palmer-Anghel, Journées de topologie algébrique, géométrique et quantique en Picardie II, Amiens, 5–7 March 2025.
  3. Arthur Soulié, Journées de rencontre des doctorants du RT2171, Amiens, 9–11 April 2025.
  4. Martin Palmer-Anghel, Conference on Modern Developments in Low-Dimensional Topology, Trieste, 9–13 June 2025.
  5. Martin Palmer-Anghel, Workshop: Blooming Beasts: A conference on the geometry, topology, and dynamics of infinite-type surfaces, Casa Matemática Oaxaca, 23–27 June 2025.
  6. Martin Palmer-Anghel, Rencontre 2025 de Topologie algébrique, Marseille, 28–31 October 2025.
  7. Arthur Soulié, Rencontre 2025 de Topologie algébrique, Marseille, 28–31 October 2025.

Invited talks at seminars

  1. Martin Palmer-Anghel, "Homological stability for asymptotic monopole moduli spaces", Geometry and Analysis Seminar, University of Leeds, 19 February 2025.
  2. Martin Palmer-Anghel, "Vanishing results in the homology of big mapping class groups and Thompson-like groups", Geometric Group Theory seminar, University of Cambridge, 21 February 2025.
  3. Martin Palmer-Anghel, "Nullité et indénombrabilité dans l’homologie des groupes de difféotopie des surfaces de type infini", Séminaire GAAO, Clermont-Ferrand, 15 April 2025.
  4. Arthur Soulié, "Some stable twisted cohomology for handlebody mapping class groups", Algebra/Topology seminar, University of Copenhagen, 28 April 2025.
  5. Cristina Palmer-Anghel, "Invariants universels d'entrelacs via des espaces de configurations", Séminaire Géométrie, Algèbre, Dynamique et Topologie, Dijon, 19 June 2025.
  6. Arthur Soulié, "Surface braid and mapping class group homological representations", Northeastern Topology Seminar, Northeastern University, Boston, 16 September 2025.
  7. Cristina Palmer-Anghel, "Universal link invariants via configuration spaces", Brussels-London geometry seminar, University College London, 18 September 2025.

Scientific visits of team members

  1. Martin Palmer-Anghel, Isaac Newton Institute, University of Cambridge (research collaboration with Ulrike Tillmann), 20–28 February 2025.
  2. Arthur Soulié, Université Clermont Auvergne, Clermont-Ferrand (research collaboration with Martin Palmer-Anghel), 23–29 March 2025.
  3. Arthur Soulié, University of Copenhagen (research collaboration with Erik Lindell), 27 April – 3 May 2025.
  4. Arthur Soulié, University of Tokyo (research collaboration with Nariya Kawazumi), 13–28 May 2025.
  5. Martin Palmer-Anghel, Institut de Mathématiques de Bourgogne, Dijon (research collaboration with Lukas Woike), 19–20 June 2025.
  6. Arthur Soulié, Institut de Mathématique de Marseille, Aix-Marseille Université (research collaboration with Christine Vespa), 13–28 July 2025.
  7. Arthur Soulié, Northeastern University, Boston (research collaboration with Anh Trong Nam Hoang), 13–20 September 2025.
  8. Arthur Soulié, University of Chicago (research collaboration with Andreas Stavrou), 20–27 September 2025.

Scientific visits (invited guests at IMAR)

  1. Peter Patzt (University of Oklahoma) from 27 June to 3 July 2025.
  2. Awais Shaukat (Namal University, Mianwali) from 2 July to 31 August 2025.
  3. Xiaolei Wu (Fudan University, Shanghai) from 19 to 27 July 2025.

Flag Counter