Basile Coron
Current Position
I am currently a postdoctoral research assistant at the School of Mathematical Sciences of Queen Mary University (London).
My supervisor is Alex Fink.
My PhD was supervised by Vladimir Dotsenko in Strasbourg.
Contact informations
E-mail : b.coron@qmul.ac.uk
Research interests
My research area is centered around the study of combinatorial objects such as matroids, via methods of algebraic topology (operadic structures, Koszul duality theory).
Publications
Matroids, Feynman categories, and Koszul duality (arXiv:2211.12370). I introduce a Feynman category over which some combinatorial invariants of matroids form some operads, and I prove a Koszul duality result between those operads. This allows a reinterpretation of the combinatorial Leray models for Orlik-Solomon algebras.
Supersolvability of built lattices and Koszulness of generalized Chow rings (arXiv:2302.13072). I use the operadic structure on geometric lattices introduced in my previous article to prove Koszulness of generalized Chow rings of supersolvable built lattices.
Operadic Kazhdan-Lusztig-Stanley theory (arXiv:2402.09905). I use operadic structures to categorify P-kernels and Kazhdan-Lusztig-Stanley polynomials of geometric lattices.
Communication
Talk at seminar LAGA in Paris (April 2023).
Talk at seminar of homotopy in algebraic geometry in Toulouse (March 2023).
Talk at seminar GATo in Amiens (February 2023).
Talk at Réunion du GDR Topologie Algébrique in Nantes (October 2022, organized by Friedrich Wagemann). Operadic structures on matroids and Koszul duality.
Two talks for a lecture group on Noetherianity and Kemer's proof of the Specht problem (Spring 2022, organized by Vladimir Dotsenko).
Introductory talk on matroids and greedy algorithms for the PhD students seminar (Spring 2022).
Two talks for a lecture group on characteristic classes (Autumn 2022, organized by Adam Chalumeau).
Introductory talk on operads for the PhD students seminar (Spring 2021).
Two talks for a lecture group on K-theory (Spring 2021, organized by Clarence Kineider).
Teachings
Autumn 2020: General maths course for medical students.
Spring 2021: General maths Travaux Dirigés for students in biology.
Autumn 2021: Travaux Dirigés for a course in Topology (third year licence students).
Spring 2022: General maths Travaux Dirigés for medical students.
Autumn 2022: Travaux Dirigés for a course in Topology (third year licence students).
Spring 2023: General maths course for first year maths students.