## 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 (unfinished) 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)

## 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: