Université de Strasbourg

Vladimir Dotsenko

Biography - Vladimir Dotsenko

Institute for Advanced Mathematical Research (IRMA), University of Strasbourg and CNRS, France

Vladimir Dotsenko, USIAS Fellow 2021

Vladimir Dotsenko obtained his PhD from Moscow State University in 2007. Before becoming a professor at the University of Strasbourg in 2019, he was a research fellow at the Dublin Institute for Advanced Studies and at the University of Luxembourg, and an academic staff member of Trinity College Dublin (Ireland). He also spent one year at CINVESTAV (the Center for Research and Advanced Studies of the National Polytechnic Institute in Mexico City) as a Solomon Lefschetz Chair (2016-2017). He is a member of the editorial board of the open-access peer reviewed journal Higher Structures. He has been appointed as a junior member of the Institut universitaire de France (2021-2026).

In 2010, Professor Dotsenko introduced, in joint works with Anton Khoroshkin (HSE, Russia), the concept of a shuffle operad, bringing together the abstract matters of category theory and the concrete methods of symbolic computation; this led to the formalism of Gröbner bases for operads which has since been widely used by researchers in operad theory and related disciplines. A definitive treatment of that theory is contained in his joint work with Murray R. Bremner (University of Saskatchewan, Canada) entitled Algebraic Operads: An Algorithmic Companion. Currently, he is exploring new horizons of operad theory, inspired by operad-like structures arising in algebraic geometry, combinatorics, and representation theory.

Project - Homotopy invariants of wonderful compactifications

01/07/2021 - 30/06/2023

Wonderful compactifications of De Concini and Procesi are remarkable geometric objects that were invented in the context of algebraic geometry for the purposes of regularising otherwise divergent or singular objects.

This project will study these objects from the viewpoint of rational homotopy theory, a domain offering an important source of invariants for geometric shapes considered up to continuous deformations. While such invariants exist for any geometric shape, determining them explicitly is a particularly challenging problem which, for most shapes, is completely open. In this project, all wonderful compactifications will be studied at the same time using a remarkable property of self-similarity that they exhibit. This will bring together several previously disconnected research methods from algebraic geometry, combinatorics, and homotopical algebra.

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Investissements d'Avenir