The Poincaré-Hopf theorem, from different noncommutative geometric perspectives, in preparation
Lecture on Index Theory
Draft of an expository article based on a Summer 2026 course taught at Sichuan University, which I intend to turn into something more ambitious... Stay tuned!
Galois theory from a historical perspective
Book project based on a course taught in Spring 2023. The link sends for now to an outline that I used in various outreach talks for undergrads
The influence of Galois theory in Poincaré’s invention of the fundamental group
Expository article project, based on a Topology course taught at Northeastern
On Kasparov's and Berline-Vergne's approaches to transverse index theory for Lie group actions, work in progress
A KK-theoretic perspective on the quantization commutes with reduction problem, preprint (last update: Oct 2026)
A transverse Chern character for actions of compact Lie groups on manifolds, preprint (last update: Oct 2024)
Algebra cochains, the bivariant JLO cocycle and the Mathai-Quillen form, preprint (last update: Sept 2023)
The Radul cocycle, the Chern–Connes character and manifolds with conical singularities, J. Noncommut. Geom. 19 (2025), no. 4, pp. 1323–1342
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 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
Relationship between Connes-Kreimer's and Kontsevich's works
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*)
An asterisk * mentions a student collaborator.