**Course:**Math 595, Differential Geometry II, Section DM2

**Time:** 1/14--1/25: MWF 2:00--2:50. 1/28--4/30: MW 2:00--3:15pm.

**Location:** 447 Atlgeld Hall

**Instructor:** Chris Leininger

**Phone:** 265-6763

**Email:** clein (at) math.uiuc.edu

**Office:** 265 Altgeld Hall

**Office hours:** TBA

**Text:** *Lecture Notes by Chris Wendl*, Available first day of class.

*A Comprehensive Introduction to Differential Geometry, Volume II*, Michael Spivak

*Lecture Notes by Victor Guillemin*, Available from MIT's open courseware here

*Foundations of Differentiable Manifolds and Lie Groups*, Frank Warner.

The books will be put on reserve in the library.

**Homework:** This will be assigned periodically and collected on Fridays. Everyone should turn in their own solutions, but I also expect you to work together as well as independently.

An optimal strategy is to: (1) try each problem yourself first; (2) get together with others to discuss your solutions and questions; (3) write up the solutions yourself. There is a balance which must be achieved to optimize the benefits of homework: Struggling with a problem leads to a much deeper understanding of the concepts. On the other hand, if you are really stuck, talking to other can help you get ``unstuck'', and can help you move on.

I may give more problems than you can reasonably do, and some may be difficult. Please be sure you can do the more routine problems before tackling the harder ones. Turn in only polished solutions---don't hand in your scratch work!

**Grading:** Grades are based entirely on homework. You may resubmit homework solutions until you recieve the grade you like.

**Syllabus:** Lie groups (a little), vector bundles, principal bundles, connections, curvature, DeRham and Cech cohomology, Laplace operator, harmonic forms, and spectral theory.

Problem Set
1

Problem Set 2

Problem Sets... for a while, these will consist of the exercises set
during the lecture.

Back to Prof. Leininger's homepage