Various expository notes from courses, conference proceedings, holiday gatherings, personal reflections, ...
Some are unfinished (like many things including this website), but they may still be useful.
They are organized by type and appear in chronological order.
- Undergraduate research reports and presentations
- Etude statistique des éléments du groupe symmétrique
The research report of my TIPE for applying to the ENS Lyon.
It concerns the distribution of cycle lengths appearing in the factorisation
of random permutations as the order of the symmetric group tends to infinity.
In retrospect, most of the results follow from Polya's counting theorem, the symbolic method for generating functions, and asymptotic analysis.
- Symmetries et invariants en geometrie algébrique
A naïve and short open-ended reflection about Hilbert's invariant theory.
- Modularité des courbes elliptiques
The report of my 1 month research experience in 2016 at IRMAR
with Jean-Pierre Wintenberger.
- Topology and geometry of curves in hyperbolic surfaces
The report of my 3 month research experience in 2017 at Stony Brook
with Moira Chas,
Tony Phillips
and Dennis Sullivan.
- Birational geometry and Jung's theorem after Stéphane Lamy
This presentation of an article by Stéphane Lamy
was written for my class mates of the master program in geometry.
- Personnal notes and accounts of topics
- Dynamics and classical entropies of Z-actions
These lectures notes
of a short master course in 2018 by Mikael de la Salle
were written with, and mostly by, Matthieu Joseph.
- Survival Guide to First Order Logic
These unfinished notes on first order logic
were written with, and mostly by, Tristan Sterin.
- Elementary number theory and quadratic arithmetics
Various notes and thoughts on elementary number theory and arithmetics of quadratic forms,
mostly after
the book Topology of Numbers by Allen Hatcher,
the book
A Classical Invitation to Algebraic Numbers and Class Fields by Harvey Cohn,
the article Sur la théorie de la divisibilité by Jean Dieudonné,
and the Salam lectures on Modular forms by Don Zagier.
- Géométrie des algèbres de quaternions réelles
These personal notes
were written for, and in retrospect of, a mathematical week during the summer 2020
organised with my friends
Felipe Bellio da Nobrega,
Martin Donati,
Colin Jahel,
Matthieu Joseph,
Mickael Nahon,
Quentin Vila.
- Algebras of loops in surface orbifolds and volumes in moduli spaces
Some almost finished notes
about geodesic currents and character varieties of surface groups.
- Conference Symposiums and Surveys
- Introduction au calcul différentiel quantique et aux idées de la géométrie non commutative
I organised the traditional week-end du Goutelas
in 2018 with Nalini Anantharaman, and in 2019 with Alain Connes.
For the latter I coordinated the edition of the notes in a special issue
of the JME journal.
You can access the prepublication
and the JME publication.
