Here are my articles, with a short description of their main results.
Operad and ∞-operad theory:
Operadic right modules via the dendroidal formalism, preprint, 2024.
We show that, for P a closed and Sigma-free simplicial operad, we exhibit an equivalence between the homotopy theory of operadic right modules over P, and the theory of right fibrations in the category of of forest spaces over the dendroidal nerve of P. In particular, this gives an easier setting to compute derived mapping spaces of right P-modules.
We show that the class of dendroidal inner/leaf/root anodynes satisfy the right cancellation property within the the class of normal monomorphisms. As an application, we explain how to associate to a dendroidal ∞-operad X a symmetric monoidal ∞-category Env(X) which resembles the symmetric monoidal envelope of a classical operad.
On the additivity of little cubes operads (with I. Moerdijk), Homology, Homotopy and Applications, 2022.
We give a shorter proof of the classical Dunn additivity result for the little cubes operad. We also explain some mistakes in the literature concerning previous proofs.
Configuration categories:
My Master's thesis on how one can recover the (weak) homotopy type of the space of self-homeomorphisms of a manifold from its natural action on the spaces of (finite) configurations. We show that, for 1-dimensional manifolds and for the real 2-dimensional space, this configuration information is sufficent to recover the space of homeomorphisms, up to homotopy. For a shorter version see the extended abstract. This thesis was done under the supervision of Pedro Boavida de Brito.
Miscellaneous work:
Loops in the fundamental group of Symp(CP^2 # 5\overline{CP^2}) which are not represented by circle actions (with S. Anjos, M. Pinsonnault and A. Reis), Canadian Journal of Mathematics, 2022.
Representations of Thompson groups from Cuntz algebras (with P. R. Pinto), Journal of Mathematical Analysis and Applications, 2019.
Research talks
A straightening-undstraightening equivalence for operadic right modules, TopICS, December 2024.
Seminar Talks
Factorisation homology as a homology theory, Factorisation homology seminar, November 2024.
An introduction to (∞-)operads, Factorisation homology seminar, November 2024.
Segalification of simplicial spaces and some applications, Freudenthal seminar, February 2024.
The Alexander trick for homology spheres, Freudenthal seminar, October 2023.
Applications to power operations, HKR character theory seminar, June 2023.
The Blakers-Massey theory II, Goodwillie calculus seminar, February 2023.
The Taylor tower and first examples, Goodwillie calculus seminar, October 2022.
Telescopic localization vs K(n)-localization, jCHTS, June 2022.
The uniqueness of Morava K-theory, jCHTS, April 2022.
The Atiyah-Bott-Shapiro orientation as a map of spectra, Orientations seminar, March 2022.
Flat modules over the moduli stack of formal groups, jCHTS, January 2022.
On the wavefront set of oscillatory integrals, Friday Fish, December 2021.
The proof of Quillen's theorem, jCHTS, November 2021.
Complex-oriented cohomology theories, jCHTS, October 2021.