Martin Markl
        Mathematical Institute of the Academy, Prague

            Strongly homotopy bialgebras

Abstract: I will explain how homotopy invariant algebraic structures
(such as A_\infty algebras, L_\infty algebras, etc.) naturally arise
from minimal models of corresponding operads and PROPs. I will then
discuss methods to construct such minimal models and give a couple of
examples of these models.

The remaining part of the talk will be devoted to the theory of
bialgebras (Hopf algebras without an antipode) and to the minimal
model of the corresponding PROP. The study of such objects, which can
be interpreted as certain kinds of graph complexes, was initiated by
Maxim Kontsevich and his deformation quantization program.