All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
The aim of this course is to cover the classical theory of classical modular forms. The course will begin with basic definitions and examples. In the later of the semester, we will discuss some applications, advanced topics, and open problems, depending on audiences' interests.
In this course, we will develop homological algebra in a modern, algebraic way with a focus on the language of derived categories. We will discuss various applications with a particular emphasis on sheaf cohomology. This course will provide much of the background material needed for the geometric representation theory class Math 7250 that will be offered in the spring.
The course will be mainly based on Hatcher's book Algebraic topology, and additional material that we will hand out.
In this course, we will begin with the necessary prerequisites about Riemannian manifolds and Lie groups, and then spend a large part of the semester getting comfortable with symmetric spaces of noncompact type (which are the simply-connected models for manifolds of non-positive curvature). We will end with the Mostow Rigidity Theorem and (hopefully) generalizations by Gromov, Ballman and Burns--Spatzier. A good reference for this material is the book Geometry of Nonpositively Curved Manifolds by Patrick Eberlein.