George Raptis (Università "Aristotele" di Salonicco)

A central objective of algebraic topology is to construct and study (approximate) models for the homotopy theory of spaces using various types of algebraic structures. This involves the study of useful invariants of spaces as well as a general framework for comparing different homotopy theories. A classical example of a homotopy invariant is given by the simplicial chains of a space (= simplicial set), considered as a  simplicial coalgebra. In this talk, I will review and discuss old and new examples of homotopy theories for simplicial coalgebras and closely related algebraic objects, including connections with Koszul duality, and their comparison with the homotopy theory of spaces. (Based on joint work with M. Rivera.)