Papers
- A Kohno-Drinfeld theorem for the monodromy of cyclotomic KZ connections Adrien Brochier Comm. Math. Phys. 2012, 311, 55-96 arXiv:1011.4285
- Cyclotomic associators and finite type invariants for tangles in the solid torus Adrien Brochier Algebraic & Geometric Topology (2013) 13 3365-3409 arXiv:1209.0417
- Fourier transform for quantum D-modules via the punctured torus mapping class group Adrien Brochier, David Jordan Quantum Topology (2017) 8(2):361-379 arXiv:1403.1841
- Integrating quantum groups over surfaces Adrien Brochier, David Ben-Zvi, David Jordan Journal of Topology (2018) 11:874-917 arXiv:1501.04652
- Virtual tangles and fiber functors Adrien Brochier JKTR 20(7):1950044 arXiv:1602.03080
- A Duflo star product for Poisson groups
Adrien Brochier
SIGMA (2016) 12, 088 arXiv:1604.08450
Erratum
The proof of Prop. 3.4 is clearly wrong: the assertion that $(S \otimes S \otimes S)(\Phi)=\Phi^{-1}$ is equivalent to $\Phi$ being even, which gives back Le-Murakami’s original statement. In fact, the statement is just wrong for non even associators, see Rmk 4.2.8 in Ján Pulmann’s thesis. I still believe that Prop. 3.8, which is the statement I really needed, is true in general, but I don’t know how to prove it. Ironically Prop 3.8 was supposed to fix a mistake in Etingof–Kazhdan’s paper on quantization of Lie bialgebras, so at the moment this fix is valid only for even associators. - Quantum character varieties and braided module categories
Adrien Brochier, David Ben-Zvi, David Jordan
Selecta Mathematica (2018) 24, pp 4711–4748 arXiv:1606.04769
Erratum
The definition of a quantum moment map is incomplete. The correct definition can be found in Pavel Safronov’s paper. - On dualizability of braided tensor categories Adrien Brochier, David Jordan, Noah Snyder Compositio Mathematica (2021), 157(3) 435-483 arXiv:1804.07538
- Invertible braided tensor categories
Adrien Brochier, David Jordan, Pavel Safronov, Noah Snyder
Algebraic & Geometric Topology (2021) 21, 2107–2140 arXiv:2003.13812
Erratum
Thm 2.2 is stated as if we proved it for an arbitrary $(\infty,1)$ symmetric monoidal category $S$, though the proof as written assume $S=Pr$ the discrete category of locally presentable category. - Gaudin Algebras, RSK and Calogero-Moser Cells in Type A Adrien Brochier, Iain Gordon, Noah White Proceedings of the London Mathematical Society 126.5 (2023): 1467-1495 arXiv:2012.10177
- A Classification of Modular Functors via Factorization Homology Adrien Brochier, Lukas Woike arXiv:2212.11259
Slides
- TFTs et théorie des représentations In french, short/informal talk I gave to introduce myself and my recent research to my new colleagues in Paris Download
- Quantization of character varieties, topological field theories and the Riemann-Hilbert correspondence Somewhat colloquial-style talk I gave about quantization of character varieties and topological field theories at the conference Geometric representation theory and low-dimensional topology in Edinburgh, in June 2019 Download
- Dualizable and invertible braided tensor categories Algebra seminar, Paris Download
- Virtual knots and quantm groups Mathematical Physics Seminar, University of Nottingham Download
- Higher genus associators and quantum groups Séminaire de topologie algébrique du LAGA, Paris 13 Download
- Une petite présentation de Julia GRAP, Amiens Download
- What is… the Kontsevich integral ZMP seminar, Hamburg Download
- What is… higher algebra ZMP seminar, Hamburg Download
Some notes
- Poisson geometry of character varieties of surfaces (Master 2 course)
- Factorization homology of braided tensor categories (Mini-course at the Hausdorff School TQFTs and their connections to representation theory and mathematical physics)
- The Johnson homomorphisms
Popularization
- Les mathématiques des symétries (in Pourquoi les mathématiques ? , Éditions Ellipses)
- Calendrier mathématique 2023 (PUG)
Thesis
- Un théorème de Kohno-Drinfeld pour les connexions de Knizhnik-Zamolodchikov cyclotomiques (tel-00598766)
Misc
Since it doesn’t seem that they’re available online, here are scanned copies of two of my favourite papers: