Mathematics

I am a Research Fellow in
Algebraic Topology at the University
of Melbourne, working with Marcy
Robertson. I have been awarded a Andrew
Sisson Early-Career Researcher Award. I am part of the ANR project Higher
Algebra, Geometry and Topology (2021-2024).

I completed my Ph.
D. thesis under the supervision of Eric
Hoffbeck and Bruno
Vallette within the program Cofund
(European Union's Horizon 2020 research and innovation programme, Marie
Skłodowska-Curie grant agreement No 754362) of the Fondation
Sciences Mathématiques de Paris. I also received a Natural
Sciences and Engineering Research Council of Canada Ph. D.
scholarship. My thesis has been awarded the Prix
de thèse Galilée and a Prix
solennel
de thèse 'toutes spécialités' from the Chancellerie
des universités de Paris.

My research involves defining
higher algebraic structures, often with the help of discrete geometry and
the theory of polytopes, and the application of these formulas to obtain
new results in algebraic topology and categorical symplectic geometry. I
am also interested in the associated connections to enumerative and
algebraic combinatorics. A recent and important part of my work is the
study of the Kashiwara–Vergne problem with the help of the theory of
operads.

Keywords: Homotopy, Operads,
Polytopes.

Here is my CV
(May 2024) and a research
statement (Sept. 2021).

Publications
and preprints.

*Framed polytopes and higher categories*, with Arnau Padrol and Anibal M. Medina-Mardones. Poster at FPSAC 2024. Presentation at Oberwolfach. Undergraduate exercise sheet on the topic.

*Term rewriting on nestohedra*, with Pierre-Louis Curien. Submitted. Preprint version: arXiv, HAL.

*Kashiwara-Vergne solutions degree by degree*, with Zsuzsanna Dancso, Iva Halacheva and Marcy Robertson. Submitted. Preprint version: arXiv, HAL. Slides.

*Steenrod operations via higher Bruhat orders*, with Nicholas J. Williams. Submitted. Preprint version: arXiv, HAL. Slides, talk. Poster at FPSAC 2024.

*Cellular diagonals of permutahedra*, with Bérénice Delcroix-Oger, Vincent Pilaud and Kurt Stoeckl. Submitted. Preprint version: arXiv, HAL. Slides, talk.

*Topological proofs of categorical coherence*, with Pierre-Louis Curien. To appear in Cahiers de topologie et géométrie différentielle catégoriques. Preprint version: arXiv, HAL. Slides, talk.

*The diagonal of the multiplihedra and the tensor product of A-infinity morphisms*, with Thibaut Mazuir. Journal de l'École polytechnique - Mathématiques (2023), https://doi.org/10.5802/jep.221. Preprint version: arXiv, HAL. Slides, talk.

*The diagonal of the operahedra*, Advances in Mathematics (2022), https://doi.org/10.1016/j.aim.2022.108494. Preprint version: arXiv, HAL. Slides, talk.

*Framed polytopes and higher categories*, TallCat Seminar, June 20, 2024, 2pm, Tallinn, Estonia.- Title TBA, invited talk at the conference Higher
Structures in Prague II, October 14-18, 2024, Prague, Czech
Republic.

Previous research talks.

*Kashiwara-Vergne operads*, Topology Seminar, May 20th, 2024 at 2:15pm, Melbourne, Australia.*Diagonales cellulaires des permutaèdres*, Séminaire Quantique, January 30, 2024, Strasbourg, France.*Kashiwara-Vergne solutions degree by degree*, Algebra & Topology Seminar, January 25, 2024, Copenhagen, Denmark.*Kashiwara-Vergne solutions degree by degree*, Algebra & Geometry Seminar, January 10, 2024, Stockholm, Sweden. Slides of the talk.*The operadic principle*, Categorical symplectic geometry seminar, December 12, 2023, Berlin, Germany.*Steenrod operations via higher Bruhat orders*, NMSU Geometry & Topology Seminar, December 1st, 2023, at 3:00pm GMT-6, Online. Slides of the talk.

*Convex polytopes and higher categories*, Topology Seminar, September 4th, 2023 at 2:15pm, Melbourne, Australia.*My thesis in 7 minutes*, Galileo Thesis Prize Ceremony, May 26th, 2023 at 2pm, Villetaneuse, France. Slides of the talk (in French).*Higher Yang-Baxter equations via Steenrod squares*, Quantum Mathematics Research Seminar, May 22th, 2023 at 1pm, Odense, Denmark., Copenhagen-Jerusalem Combinatorics Seminar, May 18th, 2023 at 2pm, Copenhagen, Denmark. Slides of the talk.*The combinatorics of the permutahedron diagonals*

*Convex polytopes and higher categories*, Pure Mathematics Seminar, March 24th, 2023 at 14:15, Melbourne, Australia.*The diagonal of the multiplihedra*, invited talk at 56th Spring Topology and Dynamics Conference, March 15th, 2023 at 15:00 US Central Daylight Savings Time, Online. Slides of the talk.*Diagonals of polytopes and higher structures*, Topology Seminar, March 13th, 2023 at 14:15, Melbourne, Australia.*Diagonals of polytopes and higher structures*, invited talk at Higher Geometric Structures along the Lower Rhine XVI, February 17th, 2023 at 10:00, Utrecht, Netherlands.*The diagonal of the multiplihedra*, Seminar on abstract homotopy theory, February 10, 2023 at 10:30, Bonn, Germany.*A simple and connected proof of MacLane's coherence theorem*, Higher Categories, Polygraphs and Homotopy Seminar, February 3, 2023 at 14:00, Paris, France.*Iterated loop spaces*, invited talk at Homotopy theory meets polyhedral combinatorics, January 16, 2023, 14:30, Barcelona, Spain*Topological proofs of categorical coherence*, AustMS annual meeting, December 8, 2022, Sydney, Australia.*Categorical coherence, polytopes, and Koszul duality*, TallCat Seminar, October 20, 2022, 14:00 UTC+3, Tallinn University of Technology, Tallinn, Estonia.*Categorical coherence, polytopes, and Koszul duality*, Categories and Companions Symposium 2022, September 22, 2022, 20:00 UTC+10, Online. Extended slides.

*Categorical coherence, polytopes, and Koszul duality*, invited talk at Higher Structures in Prague, September 13, 2022, 14:00 UTC+2, Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic.*Diagonals of polytopes and higher structures*, September 7th, 2022, 15:15 GMT+2, University of Copenhagen, Denmark.*Ph. D. defense*, Monday June 27th, 2022, Amphi Euler, Institut Galilée, Université Sorbonne Paris Nord, Villetaneuse, France. Slides (in French). Picture!*Diagonals of polytopes and higher structures*, Thursday May 19th, 2022, 14:00 GMT+2, DGeCo Seminar, Sorbonne Université, Paris, France.*Diagonals of polytopes and higher structures*, Thursday May 5th, 2022, 11:00 GMT+2, Topology, Geometry and Algebra Seminar, Nantes Université, Nantes, France.*Diagonals of polytopes and higher structures*, Friday February 25, 2022, 15:10 GMT+2, Higher Algebraic Structures Seminar, Mittag-Leffler Institute, Djursholm, Sweden.

*The diagonal of the operahedra*, Thursday January 13, 2022, 15:00 GMT+2, Algebra, Dynamics and Arithmetic Seminar, Université du Littoral, Calais, France.*The diagonal of the multiplihedra and the tensor product of A-infinity categories*, Wednesday January 5, 2022, 9:30 GMT+1, Opening workshop of the ANR HighAGT, Paris, France.*The diagonal of the operahedra*, Monday December 13, 2021, 14:00 EST, Deformation Theory Seminar, University of Pennsylvania, United States of America. Slides of the talk.*The diagonal of the operahedra*, Monday December 13, 2021, 12:00 GMT+2, Topology Seminar, University of Barcelona, Spain.*The diagonal of the operahedra*, Wednesday December 8, 2021, 10:30 EST, Geometry and Topology Seminar, Toledo University and Bolwing Green State University, United States of America.

*The diagonal of the operahedra*, Friday, December 3, 2021, 14:00 GMT+2, Higher Categories, Polygraphs and Homotopy Seminar, Sorbonne Université, Paris, France.*The diagonal of the operahedra*, Thursday, December 2, 2021, 10:00 MDT, Calgary Peripatetic Seminar, University of Calgary, Canada.*The diagonal of the operahedra*, Thursday October 28th, 2021 at the Annual Meeting of the GDR topologie algébrique et applications, Strasbourg, France.*The diagonal of the operahedra*, Thursday September 16, at 9:45 am, Algebraic Topology seminar, USPN, Paris, France.*Trees, polytopes, and their diagonal*, Friday September 10, 2021, at 11 am, LACIM seminar, UQÀM, Montréal, Québec, Canada.*The diagonal of the operahedra,*Thursday July 15, 2021, online, for the Young Topologists Meeting.

*Operads and polytopes,*Thursday November 5th, 2020, Université Sorbonne Paris Nord. Talk within the Operad Day LAGA-LIPN. Online. Slides of the talk.

Previous expository
talks.

*Cyclic polytopes, orientals and d-Segal spaces*, March 20, 2024, Melbourne, Australia.*Quillen's Small Object Argument*, September 13, 2023, Melbourne, Australia.*Maximal degree subposets of nu-Tamari lattices*, November 11, 2022, Paris, France (Online participation). Talk within the working group*Tamari lattices and related structures*.*The derivatives of the identity*(in French), December 2, 2021, at 10 am, Université Sorbonne Paris Nord, within the Working group on Goodwillie Calculus. Slides of the talk (in French).*Curved pre-Calabi-Yau algebras are curved homotopy double Poisson gebras*, May 28th, 2021, Villaroger, France. Talk within the workshop Double Poisson structures. Slides of the talk (in French).*Twisting the operad of graphs and the formality of the little discs*, May 20th, 2021 at 10 am, Université Sorbonne Paris Nord. Talk within the working group Grothendieck-Teichmüller Groups & Applications. Accessible online. Slides of the talk.*Operads for discrete geometers*(in French), February 18th, 2021, at 5:15 pm, DGeCo Seminar, Paris. Slides of the talk.*Operads and monoidal categories*, Thursday November 12th, 2020 at 2 pm, Université Sorbonne Paris Nord. Talk within the working group Grothendieck-Teichmüller Groups & Applications. Accessible online. Slides of the talk.*A one line proof of MacLane's coherence theorem*, September 30th, 2020 at 10 am, Roberta Seminar, Sorbonne Université, Paris, France.*Opérades et algèbres associatives à homotopie près*, Séminaire de géométrie symplectique de l'Université de Montréal, 4 septembre 2019, Montréal, Québec.*Autour du théorème d'Artin--Rees*, Groupe de lecture en algèbre commutative, 21 janvier 2019, Université Pierre et Marie Curie, Paris, France.

I co-organize the Topology
Seminar of the University of Melbourne, which takes place every
Monday at 2:15 pm, and the Homotopy
Theory Student Seminar, which takes place every Wednesday at 2pm.

Upcoming.

- Higher Structures in Prague II, October 14-18, 2024, Prague, Czech Republic.

Past events.

**Research stays**

**Working groups**

- Homotopy Algebras and Higher Structures, May 22-26, 2023, Paris, France.
- Workshop on Homology of Configuration Spaces and related topics, May 15-17, 2023, Paris, France.
- 56th Spring Topology and Dynamics Conference, March 16-18, 2023, Online.
- Higher Geometric Structures along the Lower Rhine XVI, February 16-17, 2023, Utrecht, Netherlands.
- Homotopy theory meets polyhedral combinatorics, January 16-20, 2023, Barcelona, Spain. Picture!
- AustMS annual meeting, December 6-9, 2022, Sydney, Australia.
- Ib
Fest
*, October 3-4, 2022, Copenhagen, Denmark.* - Categories and Companions Symposium 2022, September 19-23, 2022, Creswick, Australia (Online participation).
- Higher Structures in Prague, September 12-16, 2022, Prague, Czech Republic.
- Young Topologists Meeting, July 18-22, 2022, Copenhagen, Denmark. Picture!
- Twinned conference on Homotopy Theory, June 27-30, 2022, Bonn, Germany.
- Barcelona conference on Higher Structures, June 13-17, 2022, Barcelona, Spain. Picture!
- Higher Algebraic Structures in Algebra, Topology and Geometry, January 10 to April 29, 2022, Mittag-Leffler Institute, Sweden. Visits from February 13 to March 5 and April 15-29.
- Annual meeting of the GDR Topologie algébrique, October 26-29, 2021, Strasbourg, France. Picture!
- Young Topologists Meeting 2021, July 5-16, 2021, Stockholm, Sweden.
- Higher Homotopical Structures Seminar, Winter 2021, online.
- Higher Structures & Operadic Calculus, June 21-25, 2021, Barcelona, Spain. Picture!
- Double Poisson structures, May 24-28, 2021, Villaroger, France.
- Operad Day LAGA-LIPN, November 5, 2021. Online.
- Koszul
duality & operads
*,*October 19-23, 2020, Marseille, France. - Infinity-categories and their applications, August 17-20, 2020, Online.
- Operad Pop-up,
August 11, 2020, Online.

- Higher homotopy algebras in topology 2, March 4-6, 2020, Dublin, Ireland.
- GDR Topologie algébrique et applications, October 28-31, 2019, Arras, France.

- Copenhagen Centre for Geometry and Topology, research in pairs with Nicholas J. Williams, January 22-26, 2024, Copenhagen, Denmark.
- Centre for Quantum Mathematics, visiting Vivek Shende, November 2023, Odense, Denmark.
- Max Planck Institute for Mathematics, February 2023, Bonn, Germany.
- Copenhagen Centre for Geometry and Topology, September--October 2022, Copenhagen, Denmark.
- Max Planck Institute for Mathematics, visiting Anibal M. Medina-Mardones, May 8-11, 2022, Bonn, Germany.
- Mittag-Leffler Institute, February 13--March 5 and April 15-29, 2022, Djursholm, Sweden.
- Centre de Recerca Matemàtica, research in pairs with Vincent Pilaud, December 9-18, 2021, Barcelona, Spain.
- LACIM - Université du Québec à Montréal, visiting Hugh Thomas, July 11--September 11, 2021, Montréal, Québec, Canada.

*Model categories*, The University of Melbourne, Fall 2023. Organizers: Marcy Robertson, Guillaume Laplante-Anfossi.*Higher genus Kashiwara-Vergne groups*, The University of Melbourne, Winter 2023. Organizer: Marcy Robertson.*Tamari lattices and related structures*, Université de Paris, Fall 2022. Organizers: Matthieu Josuat-Vergès and Sylvie Corteel.*Goodwillie calculus*, Fall 2021. Organizer: Geoffroy Horel (Université Sorbonne Paris Nord).*Grothendieck-Teichmüller Groups & Applications*. From October 1st, 2020 to April 30th, 2021. Organizers: Goeffroy Horel (Université Sorbonne Paris Nord) and Bruno Vallette (Université Sorbonne Paris Nord).*Mandell's Theorem*. From September 26th to December 12th, 2019. Organizer: Geoffroy Horel (Université Sorbonne Paris Nord).*Persistent Homology*. From October 11th to December 20th, 2018. Organizers: Grégory Ginot (Université Sorbonne Paris Nord) and Bruno Vallette (Université Sorbonne Paris Nord).

- Approximations cellulaires d'applications diagonales de polytopes opéradiques, Ph. D. thesis. Defended on June 27th, 2022.
- La diagonale de l'associaèdre, Master 2 thesis (in French). July 2nd, 2019.

In the 3rd chapter, I tried to give the
intuition of operads as « treelike » generalization of associative
algebras. Section 2.6 and the beginning of Chapter 4 try to give the
intuition for associative algebras up to homotopy and their tensor
product.

Courses.

- Linear Algebra, Spring 2024, The University of Melbourne.
- Introduction to Chaos Theory, Winter 2019, ESIEE Paris.

Tutorials.

- Linear Algebra (Fall 2023)

- Real Analysis (L1, Fall 2019 & Fall
2020)

- Mathematics for Chemistry & Physics (L2, Fall 2020 & Fall
2021)

- Complex Analysis (L3, Winter 2020 & Winter 2021 & Winter 2022)
- Abstract Algebra (L2, Hiver 2020)
- Introduction to Algebra (L1, Automne 2019)

- Fourier Analysis (Winter 2019)
- Linear Algebra (Fall 2018)
- Set Theory (Fall 2018)