Lucien Hennecart Postdoctoral Assistant Researcher Mathematics James Clerk Maxwell Building The University of Edinburgh United Kingdom Email: Lucien.Hennecart(AT)ed.ac.uk Office: 5420

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I am a postdoctoral researcher at the University of Edinburgh working with Ben Davison since September 2021. From 2021 - 2023, I was funded by an ERC Starting Grant. From 2023, I am funded by the Royal Society.

In the Spring of 2024, I am visiting 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... Now, I am working on the connections between constructible and cohomological Hall algebras.

Key-words

Quivers, quantum groups, perverse sheaves, coherent sheaves on curves, Higgs sheaves, cohomological Hall algebra, mixed Hodge modules, Calabi-Yau categories, Donaldson-Thomas theory.

Seminars

With Ben Davison and Shivang Jindal, we organise the EGRET seminar in Edinburgh.
In the Spring 2024, I am organising the Geometric Representation Theory Seminar at SLMath, Berkeley, as part of the thematic semester Noncommutative Algebraic Geometry.

(Pre)-Publications

• 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
• Isotropic cuspidal functions in the Hall algebra of a quiver, August 2019 (online version), Int. Math. Res. Not., arXiv

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.

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.

Workshop

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.

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.

Thesis

My defense took place on July, 13th 2021. A version of my PhD thesis written under the direction of Olivier Schiffmann is available here and the handwritten notes for the presentation are there. At this link, you can find an extended abstract of my doctoral work.

Talks

A list of the talks I gave is here.

Teaching

2023-2024
2022-2023
2021-2022
2020-2021
2019-2020
2018-2019

Miscellaneous

I put here things that I thought were convenient to be written down.

Some pieces of biography

A slightly more detailed CV is available here.
September 2021 - : Postdoctoral researcher at The University of Edinburgh working with Ben Davison
September 2018 - August 2021: PhD Thesis
2017 - 2018: 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)

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School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, United Kingdom