THIBAULT JUILLARD | MATHEMATICIAN

About me

I’m a postdoctoral researcher at the University of Hamburg. My mentor is Sven Möller. My position is funded, through the Emmy Noether Programme, by the Deutsche Forschungsgemeinschaft (project number 460925688).

I did my Ph.D. under the supervision of Professor Anne Moreau, at the Institut de mathématiques d’Orsay (Université Paris-Saclay, France).

My full résumé can be found here.

Representation theory, algebraic geometry and mathematical physics

I use geometric methods to study the structure and representation theory of vertex algebras, which are algebraic structures appearing as symmetries of two-dimensional conformal field theories. The vertex algebras I study (affine W-algebras, quiver vertex algebras) are deformations of the arc spaces of usually well-known Poisson varieties (Slodowy slices, Nakajima varieties).

How to adress me

Languages: French (native), English (fluent), Spanish (intermediary), German (novice, don’t expect me to understand).
Pronunciation of my first name: [ti.bo].
Pronouns: he/him.

Contact

thibault [dot] juillard [at] uni-hamburg [dot] de
tjuillard [dot] math [at] proton [dot] me

Publications

Preprint

Naoki Genra and Thibault Juillard (2025). “Reduction by stages for affine W-algebras”. arXiv: 2501.04501.

Published article

Naoki Genra and Thibault Juillard (2024). “Reduction by stages for finite W-algebras”. In: Mathematische Zeitschrift 308.1, Paper No. 15, 36. issn: 0025-5874,1432-1823. doi: 10.1007/s00209-024-03567-9. arXiv: 2212.06022.

My Ph.D. thesis

Thibault Juillard. “Reduction by stages for W-algebras and applications”. Université Paris-Saclay, 13th of June 2025. English. NNT : 2025UPASM014. tel-05149024v1.

A more recent version (with less typos) can be found here.

Talks

Conferences

Reduction by stages for affine W-algebras (November 2025). “Collaborative Research Center retreat”, Büsum, Germany.
Reduction by stages for affine W-algebras (October 2025). “Collaborations in algebra, representation theory and ethics”, École normale supérieure de Lyon, France.
Reduction by stages for affine W-algebras (July 2025). “Queer and Trans Mathematicians in Algebra and Representation Theory”, University of Bonn, Germany.
Reduction by stages, a geometric approach (June 2025). “Representation theory XIX”, Inter-University Centre, Dubrovnik, Croatia.
Reduction by stages for W-algebras (June 2024). “Vertex algebras, geometric representation theory and quantum groups”, Centre international de rencontres en mathématiques, Luminy, France.
Chiralisation of reduction by stages (June 2024). “Groups and their actions”, Levico Terme, Italy.
Reduction by stages for W-algebras (January 2024). “Winter school in mathematical physics”, Les Diablerets, Switzerland.
Reduction by stages for finite W-algebras (October 2022). “Workshop in quantum symmetries”, Centre de recherche en mathématiques, Montréal, Canada.

Seminars

Reading groups

Symplectic geometry and characteristic varieties (January 2025). “D-modules”, Institut de mathématiques d’Orsay.
Examples of GIT construction: quiver varieties (March 2024). “Good moduli stacks”, Institut de mathématiques d’Orsay.
Equivariant sheaves and linearisations in GIT (February 2024). “Good moduli stacks”, Institut de mathématiques d’Orsay.
Geometric invariant theory (November 2023). “Good moduli stacks”, Institut de mathématiques d’Orsay.
Double poisson vertex algebras (April 2023). “Hall algebras and vertex algebras in enumerative geometry”, Skye Island, Scotland.
Character variety and tautological classes (January 2023). “P=W conjecture”, Institut de mathématiques d’Orsay.

Poster

Reduction by stages for affine W-algebras (January 2025). PDF.

Teaching

Student

Ren Grégoire (2026), Master 1 internship. “Symmetric invariants of the centraliser of a nilpotent element”. Abstract in French.

Supervision of exercise sessions

École polytechnique

Euclidean and Hermitian spaces (2024-2025), Bachelor 2.
Differential geometry (2023-2025), Bachelor 3.
Series of functions, differential equations and Fourier series (2022-2023), Bachelor 2.

École polytechnique fédérale de Lausane

Geometry (2021), Bachelor 2. Course given by Professor Marc Troyanov, see his book.
Linear algebra (2021), Bachelor 1.
Analysis 1 (2021), Bachelor 1.
Group theory (2021), Bachelor 2.

Event organisation

Seminars

Réseau des étudiant-es en geométrie algérique (RéGA) (2023-2025), Institut Henri Poincaré. Algebraic geometry seminar for young researchers.
Popularisation seminar for Ph.D. students (2022-2023), Institut de mathématiques d’Orsay.

Outreach

APEX-Maths (2024), Reșița, Romania. Three-week program to introduce high school students to mathematical research. I was in charge of problem sessions in Number Theory and Topology.
Astromaths camp (2021-2024), Chambon-sur-Lignon, France. Two-week summer camp for high-school students. I was giving lectures about mathematics and Kepler laws.

Miscellaneous

Fighting discriminations

Queer and Trans Mathematicians in Algebra and Representation Theory (July 2025), University of Bonn, Germany. I was a participant to QTMART, which is a workshop on algebra and representation theory, run by and for queer and trans mathematicians.
Journées parité en mathématiques (July 2024), Institut de Mathématiques de Marseille, France. I was part of a public discussion about the inclusion of LGBT+ people in the mathematical community.

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