MTG 7397, Advanced Topics in Topology 2

Course Description

In this course we will introduce some powerful mathematical tools whose origins lie in algebraic topology but which have been useful in many other areas and have become objects of study themselves. Specifically, we will learn about Category Theory, Homological Algebra, and Spectral Sequences. Each of these topics provides a formal framework for organizing mathematical structures and computations, and is an important tool in modern mathematics.

Textbooks

An Introduction to Homological Algebra, Second Edition, by Joseph J. Rotman. Available from the UF library as an eBook download, and there is also reasonably priced paperback edition. Category Theory in Context, by Emily Riehl. Available by download from Riehl’s web page and there is a very inexpensive paperback edition.

Prerequisites

This course will be mostly self-contained. Students should be comfortable with abstract algebra.

Course topics

  • Category Theory: categories, functors, natural transformations, universal properties, limits, colimits, adjoints, Kan extensions, localization, symmetric monoidal categories
  • Homological Algebra: abelian categories, chain complexes, additive functors, derived functors, Hom, Tensor, Ext, Tor, derived categories
  • Spectral Sequences: filtrations, bicomplexes, convergence, Grothendieck spectral sequence

Time

MWF Period 4, 10:40–11:30am Instructor: Peter Bubenik

Please contact me if you have any questions and/or requests!

Signing up for the course

This course is controlled by the math department. You need to provide Stacie Austin or Sandy Gagnon with your name and UF ID to be added to the section before you can enroll in the course.

Course Syllabus