Topics Courses | RTG@LSU
Skip to main content
[←]

Topics Courses

Each year, the Mathematics Department offers a wide range of topics courses which cover topics in Geometry, Topology, Representation Theory, and Mathematical Physics. Here is a list of current and recently offered courses:

Current Courses (Spring 2026)

This course will cover the basics of sheaf theory, including abelian and derived categories of sheaves, (derived) sheaf functors, and major theorems about them, such as the proper base change theorem and the projection formula. Topics for later in the semester may include Poincare-Verdier duality, Borel-Moore homology, and Artin's vanishing theorem. If time permits, I may introduce perverse sheaves and discuss applications in representation theory.

Manifolds, vector fields, vector bundles, transversality, deRham cohomology, metrics, other topics.

The course will start with some basics of homotopy theory, fibrations, Postnikov towers, and de Rham cohomology. The goal is then to study the rational homotopy type of a simply-connected space X, which is the homotopy type of its localization (or rationalization). The homotopy and homology groups of the rationalization are rationalizations of those for X, killing all torsion. The rational homotopy type of X has the advantage of being more computable than the (ordinary) homotopy type of X, thanks to the algebraic models (using differential graded algebras or Lie algebras) from Sullivan and Quillen. The story is more complicated when X is not simply connected, when one needs to make sense of how to "rationalize" the (possibly non-abelian) fundamental group.

The goal of this class is to give a fairly complete proof of a recent theorem of Kielak connecting algebraic fibering of groups to the vanishing of L^2-homology. We will go through the basics of group cohomology, classical constructions of embedding group rings into division rings, and the connection of Bieri-Neumann-Strebel invariants to Novikov homology. Given time, we will see some other recent applications of this theory to the study of 3-manifolds and free-by-cyclic groups.

Past Courses

  • Fall 2025

    • Ng: Representation Theory [7250]
    • Hoffman: Homological Algebra [7260]
    • Cohen: Algebraic Topology [7510]

  • Spring 2025

    • Baldridge: Differential Geometry [7550]
    • Schreve: L^2 Homology [7590-1]
    • Baldridge: J-Holomorphic Curves and Gromov-Witten Invariants [7590-2]

  • Fall 2024

    • Vela-Vick: Riemannian Geometry [7560]
    • Bibby: Combinatorial Algebraic Topology [7590]

  • Spring 2024

    • Ólafsson: Lie Groups and Representation Theory [7370]
    • He: Harmonic Analysis in Phase Space [7380]
    • Zeitlin: Differential Geometry [7550]
    • Dani: Topological Groups [7590-1]
    • Vela-Vick: Contact Geometry [7590-2]

  • Fall 2023

    • Hoffman: Homological Algebra [7260]
    • Singh: Geometric Methods in Representation Theory [7290]
    • Cohen: Algebraic Topology [7520]
    • Baldridge: Gague Theory and Seiberg-Witten Invariants [7590]

  • Spring 2023

    • Achar: Infinity Categories [7290]
    • Cohen: Differential Geometry [7550]
    • Schreve: Coxeter Groups [7590-1]
    • Baldridge: Moduli Spaces of Curves [7590-2]

  • Fall 2022

    • Hoffman: Algebraic Geometry [7240]
    • Sage: Representation Theory [7250]
    • Dani: Riemannian Geometry [7560]
    • Zeitlin: Complex Geometry [7590]