Lucien HENNECART

Chargé de recherches, CNRS

LAMFA
Université de Picardie Jules Verne
33 Rue Saint Leu
80000 Amiens
France

Email: Lucien.Hennecart(AT)u-picardie.fr

Office: C102 bis

I am a chargé de recherches within CNRS, hosted by the LAMFA in Amiens (part of the Université de Picardie Jules Verne), since December 2024. I am a member of the team GAT (Groups, Algebra, Topology).

I have been lucky to be a postdoctoral researcher within the School of Mathematics of the University of Edinburgh working with Ben Davison between 2021 and 2024. From 2021 - 2023, I was funded by an ERC Starting Grant. From 2023 - 2024, I was funded by the Royal Society.

In the Spring of 2024, I visited SLMath (=MSRI) for the thematic programme "Noncommutative Algebraic Geometry".

Between September 2018 and September 2021, I was a PhD student at the Laboratoire de Mathématiques d'Orsay (Université Paris-Saclay), in the team Arithmétique et Géométrie Algébrique, supervised by Olivier Schiffmann. During my PhD, I have been interested in the Hall algebra of quivers, curves and their geometric incarnations: Ringel's construction of the positive part of the quantum group, Lusztig perverse sheaves, cohomological Hall algebras, cuspidal polynomials of quivers...

Research

Research themes

My research is in geometric representation theory. It has something to do with representation theory (understanding algebraic structures by making them act on linear spaces), algebraic geometry (involving moduli spaces of sheaves on curves, surfaces, threefolds), topology (cohomology) and may involve a categorical framework (derived categories and stability conditions, dg categories).

Key-words

Moduli spaces, perverse sheaves, coherent sheaves on curves, Higgs sheaves, cohomological Hall algebras, mixed Hodge modules, Calabi-Yau categories, Donaldson-Thomas theory, reductive groups, quivers, quantum groups.

Former Seminars and Workshops

Seminars:

With Ben Davison and Shivang Jindal, we organised the EGRET seminar in Edinburgh between October 2021 and August 2024.
In the Spring of 2024, I organised the Geometric Representation Theory Seminar at SLMath, Berkeley, as part of the thematic semester on Noncommutative Algebraic Geometry.

Workshops:

With Ben Davison, we organised a workshop on the Isle of Skye (17 - 22 April 2023), on "Vertex algebras and Hall algebras in enumerative geometry". Here is a programme. Here is a webpage summarising the workshop.

(Pre)-Publications and other written productions

(Pre)-publications:

Cohomological Mackey formula for quotient stacks, May 2025 (arXiv version)
Cohomological integrality for symmetric quotient stacks, August 2024 (arXiv version)
Cohomological integrality for symmetric representations of reductive groups, June 2024 (arXiv version)
Nonabelian Hodge isomorphisms for stacks and cohomological Hall algebras, July 2023 (arXiv version)
(with Ben Davison and Sebastian Schlegel Mejia) BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories, March 2023 (arXiv version)
(with Ben Davison and Sebastian Schlegel Mejia) BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks, December 2022 (arXiv version)
Geometric realisations of the unipotent enveloping algebra of a quiver, 2024, Adv. Math., arXiv
(with Nikolai Perry) A Quiver Analogue of Higman's Conjecture, August 2022 (arXiv version)
Perverse sheaves with nilpotent singular support on the stack of coherent sheaves on an elliptic curve, July 2022 (online version), Transformation Groups, arXiv
Microlocal characterization of Lusztig sheaves for affine and g-loops quivers, June 2020 (online version), Representation Theory, arXiv
Asymptotic behaviour of Kac polynomials, March 2020 (online version), Experimental Mathematics, arXiv Sage code Update
Isotropic cuspidal functions in the Hall algebra of a quiver, August 2019 (online version), Int. Math. Res. Not., arXiv

Notes:

BPS sheaf for commuting varieties, 7 February 2025

Others

Oberwolfach report: BPS Lie algebra of 2-Calabi-Yau categories and positivity of cuspidal polynomials of quivers, Representation theory of quivers and finite dimensional algebras, 12 - 18 February 2023. The full report is available here.
Abstract for the 14th Ukraine conference, BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories, 3 - 7 July 2023.

PhD thesis

Miscellaneous

here

Communication

Posters

I prepared a poster to present at the conference "Derived Categories, Moduli Spaces, and Counting Invariants" in London, July 3 - 7, 2023. You can find a virtual presentation of the poster here.
I presented a poster at the Introductory Workshop "Noncommutative Algebraic Geometry" at SLMath, Berkeley, February 5 - 9, 2024. The poster is there.
I presented a poster at the workshop "Moduli stacks and enumerative geometry" at the Newton Institute, Cambridge, June 17 - 21, 2024. The poster is there. Abstract

Interview

An interview I gave when I was visiting SLMath in the Spring of 2024. It should eventually appear on this webpage.

Videos

A video explaining the nonabelian Hodge correspondence for stacks and CoHAs.
I gave a series of four lectures at the M-seminar (Kansas State University) on Cohomological Hall algebras of 2-Calabi-Yau categories and applications: Lecture 1, Lecture 2, Lecture 3, Lecture 4.
Here is the video of a talk I gave at SLMath on BPS Lie algebras and quiver varieties.

Talks

here

Teaching

Some pieces of biography

A more detailed CV is available here.

December 2024 - CNRS junior researcher, hosted by the LAMFA in Amiens
January 2024 - May 2024: Uhlenbeck postdoctoral fellow, SLMath, Berkeley, mentored by Yuri Berest
September 2021 - November 2024 : Postdoctoral researcher at The University of Edinburgh working with Ben Davison
September 2018 - August 2021: PhD Thesis supervised by Olivier Schiffmann
2017 - 2018: Master's program M2 AAG à Orsay
2017: Agrégation de Mathématiques. Rank: 5th
2014 - 2018: ENS de Rennes
2012 - 2014: MPSI - MP* au Lycée Claude Fauriel (Saint-Étienne)
2012: Baccalauréat, Lycée Honoré d'Urfé (Saint-Étienne)