GRADUATE STUDENT SEMINAR TALK: (2015 Feb.) Some functors from topological spaces to lie algebras and algebraic varieties

A common theme in algebraic topology is to study functors from the homotopy category of topological spaces to various categories of algebraic objects, such as the classical homology functor, the cohomology functor and the homopoty functor. In this talk, I will introduce some functors from topological spaces to Lie algebras and algebraic varieties, and explore their properties. We can use these functors study the properties of the original topological spaces. We will also use these functors to study the finitely generated groups by studying the corresponding Eilenberg-MaClane spaces. At last, I will state some results from my joint work with Professor Alexander Suciu.