Research
Publications and preprints
On Kasparov's and Berline-Vergne's approaches to transverse index theory for Lie group actions, in preparation
Algebraic Fredholm modules, in preparation
A transverse Chern character for actions of compact Lie groups on manifolds, preprint Sept 2022
Algebra cochains, the bivariant JLO cocycle and the Mathai-Quillen form, preprint Sept 2022
The Radul cocycle, the Chern–Connes character and manifolds with conical singularities, preprint Sept 2021
Calculation of the JLO cocycle on spin manifolds (in French), preprint Sept 2021
On Kasparov’s proof of the index theorem (with M. Braverman), draft
A KK-theoretic perspective on the quantization commutes with reduction problem, preprint Oct 2020
A KK-theoretic perspective on deformed Dirac operators (with Y. Loizides, Y. Song), Adv. Math 280 (Mar 2021)
An equivariant index theorem for hypoelliptic operators (with D. Perrot), (Nov 2019 version)
Zeta functions, cyclic cohomology and index problems, J. Funct. Anal. 268 (2015), no. 5, 1167‑1204
Work in progress
Algebra cochains and the algebraic index theorem
Bivariant Chern character, the Mathai–Quillen form and the equivariant index formula
History of differential topology and Poincaré's definitions of a manifold (with L. Seaton*)
Galois theory from a historical perspective (Book project inspired from a course taught in Spring 2023)
The influence of Galois theory in Poincaré’s invention of the fundamental group
An asterisk * mentions a student collaborator.