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CRM - University of Ottawa Distinguished Lecture Series

TITLE:Algebraic relativism: encoding the higher structure of morphisms
SPEAKER:Kathryn Hess (École Polytechnique Fédérale de Lausanne)
DATE:Vendredi, 23 Février 2007
TIME:3:30 pm
ROOM:B005
ABSTRACT:

Operads were developed in the 1970's as a powerful tool for encoding operations and the identities they must satisfy in different types of algebras, such as associative algebras, commutative algebras, Lie algebras, Poisson algebras, etc. Recently, Paul-Eugène Parent, Jonathan Scott and I realized that co-rings over operads play a similar role in the relative case, governing highly structured homomorphisms between different types of algebras.

In this talk I will first define operads and explain how they parametrize algebraic operations. I will then present the relative case, outlining how co-rings over operads characterize higher structure on morphisms between algebras. In particular I will explain how to apply this characterization to proving existence theorems for highly structured morphisms. I will conclude by talking about applications of these existence theorems in homotopy theory.

Présentation de la conférencière Kathryn Hess est professeure au département de Mathématiques de l'École Polytechnique Fédérale de Lausanne depuis 1991. Dans sa thèse de doctorat, obtenue en 1989 au MIT, elle trouva une élégante solution à une importante conjecture de Ganea. Parmi les points saillants de sa carrière, on peut relever qu'elle occupa plusieurs postes de professeur de mathématiques invité dans des universités en Suède, en Belgique, en France et au Canada. Plus récemment, elle reçut en 2005 le prix de meilleur professeur de la faculté des sciences de base de l'EPFL. Elle est aussi éditeur du journal, <q lang="fr"> Algebraic and Geometric Topology </q>.

Professeur Hess travaille principalement en théorie de l'homotopie et en théorie des noeuds. Récemment, elle a apporté d'importantes contributions aux applications de la topologie algébrique à l'informatique théorique.

About the speaker Kathryn Hess has been at the École Polytechnique Fédérale de Lausanne in Switzerland since 1991, holding the position of Titular Professor since 1999. She received her PhD in mathematics from MIT in 1989 in which she solved a long lasting conjecture from Ganea. She has held numerous visiting positions in Sweden, Belgium, France, and Canada. An outstanding expositor, Professor Hess won the prize of best teacher in the Faculty of Basic Sciences at the EPFL in 2005. She is an academic editor of the journal Algebraic and Geometric Topology.

Professor Hess's research interests are in homotopy theory, knot theory, and the applications of algebraic topology to computer science and mathematical physics.