Colloquium: "General homology theory" by Dr. Guilherme Sadovski

Speaker: Dr. Sadovski is a member of this unit (visit his page)

Abstract: In this talk, we will discuss the general idea behind homology theories: a way of associating a sequence of algebraic structures, connected via specific homomorphisms, to other mathematical structures of interest - such as a topological space X.  We will also discuss how such a sequence defines a so-called homology which can carry, for instance, topological information of X. To illustrate the diversity in the implementation of such technique, we will enumerate and briefly discuss some examples such as simplicial homology, singular homology, Khovanov homology, Morse homology and Floer homology.