I am a postdoc at Charles University, in Prague. Before that, I was an ATER (teaching postdoc) in mathematics at University of Saint-Etienne, France. My work focuses mainly on triangulated categories, group cohomology, 2-dimensional categories and (higher) categorification.
I completed my PhD thesis "Group representations through 2-sheaves" under the supervision of Ivo Dell'Ambrogio, at University of Lille. It focuses on presenting the structure of 2-sheaves that various families of categories relevant to representations exhibit, and how this structure can be exploited.
My mail address is "first name" dot "last name" at gmail dot com. My CV can be found here.
In p-modular representation theory, the Cartan-Eilenberg formula express the cohomology of a group G as a limit of the cohomology its p-subgroups. This article presents an analogous formula, expressing categories associated to the group G - such as the category of modules, or its derived category - as a 2-dimensional limit of the corresponding categories of the p-subgroups of G.
2-final 2-functors are 2-functors along which it is possible to reindex a bicolimit, without changing its value. This articles characterizes 2-final 2-functors using a topological criterion.
Thin article study the full subcategories of dualizable a-torsion and a-complete objects, inside a rigidly-compactly generated tensor-triangulated category T, endowed with an action of graded-commutative Noetherian ring R, for all homogeneous ideal a of R. We show that, on these categories, the action of the ring R extends to an action its completion (with respect to a), and that we can recover entirely these categories of dualizable objects, with their tensor-triangulated structure, from the corresponding categories of compact objects. Moreover, we show that when the compact objects of T have a strong generator, its torsion and completion are strong generators of the corresponding dualizable objects.