Mathematics

What is an operad? What does it eat in winter?

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).



Research

Publications and preprints.
  
The subdivision of the 3-dimensional permutahedron induced by a cellular approximation of the diagonal. 

Talks

Upcoming.


Utrecht, February 17th, 2023. Picture credit: Marius Crainic.


Previous research talks.

Recording of the talk.


  • 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.

Recording of the talk.





Previous expository talks.

Seminars, Conferences & Workshops

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.
Past events.

Research stays


Working groups


Theses
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.



Teaching

Courses.
Tutorials.

The University of Melbourne
Université Sorbonne Paris Nord
ESIEE Paris


Others


I can be found on Google scholar, ORCiD, MathStack Exchange, Math Genealogy.