Mathematics
My research consists in the
study of higher algebraic structures, often with the help of discrete
geometry and the theory of (fiber) polytopes. A recent and important part
of my work is the study of the Kashiwara–Vergne problem from the operadic
perspective. My past and present work touches to the areas of algebraic
topology, higher category theory, categorical symplectic geometry, quantum
algebra, as well as discrete geometry and algebraic combinatorics.
Keywords: Homotopy, Operads,
Polytopes.
Research
Publications
and preprints.
Framed polytopes and higher
categories , with Arnau
Padrol and Anibal Medina-Mardones.
Poster
and extended abstract
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 . To
appear in
Proceedings
of the London Mathematical Society .
Preprint version: arXiv ,
HAL .
Slides,
talk .
Poster
and extended
abstract 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 . Cahiers
de topologie et géométrie différentielle catégoriques
(2024), Volume
LXV, Issue 4 . 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 .
The
subdivision of the 3-dimensional permutahedron induced by a cellular
approximation of the diagonal.
Talks
Upcoming.
Operadic structures on genus zero Kashiwara-Vergne solutions ,
Algebra
& Geometry Seminar , December 10, 2024, Stockholm, Sweden.
A universal characterization of uncurving ,
Geometry & Topology Seminar , December 12, 2024, Uppsala,
Sweden.
Previous research talks.
A universal characterization of uncurving , Quantum
Mathematics Research Seminar , November 25, 2024, Odense,
Denmark.
Kashiwara-Vergne operads , Grothendieck-Teichmüller,
Kashiwara-Vergne and MZV workshop , August 12, 2024, Geneva,
Switzerland.
Kontsevich's deformation quantization theorem, and the
Kashiwara-Vergne conjecture , Mathematical
Physics Seminar , July 30, 2024, Melbourne, Australia.
Framed polytopes and higher categories , TallCat
Seminar , June 20, 2024, 2pm, Tallinn, Estonia.
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 .
Recording
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.
The
combinatorics of the permutahedron diagonals , Copenhagen-Jerusalem
Combinatorics Seminar , May 18th, 2023 at 2pm, Copenhagen,
Denmark. Slides
of the talk .
VIDEO
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.
VIDEO
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.
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.
VIDEO
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 .
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.
Seminars,
Conferences & Workshops
Upcoming.
Past events.
Uppsala-Odense
Geometry Days , October 24-25, 2024, Uppsala, Sweden.
Topology
of Moduli Spaces , August 19-23, 2024, Copenhagen, Denmark.
Grothendieck-Teichmüller,
Kashiwara-Vergne and MZV workshop , August 12-16, Geneva,
Switzerland.
Kashiwara--Vergne Workshop, August 5-9, 2024, Les Diablerets,
Switzerland.
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.
Research stays
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.
Working groups
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).
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.
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)
Others