Fall 2017 MATH 214 214 LEC

Differentiable Manifolds
214 LECTuTh 12:30PM - 01:59PMEvans 6Mariusz Wodzicki45429
UnitsEnrollment Status
Additional Information: 

Prerequisites: familiarity with basic notions of Algebra (rings, modules) is helpful but not required

Description: A thoroughly modern introduction to “Differential Calculus” on general “spaces” (classical and quantum alike).

The topics to be covered:

(I) Theory of derivations: definitions, examples, the universal derivation, Bar and Hochschild complex, graded and super-derivations

(II) Infinitesimal deformations ; description of derivations from 3 fundamental algebras — tensor, symmetric, and exterior

(III) Theory of differential forms: the de Rham super-algebra, the de Rham cohomology

(IV) Connections and the curvature, characteristic classes, Chern character, K-theory

(V) Integration of differential forms, de Rham’s theorem

Office: 995 Evans Hall

Office Hours: after my lectures or by appointment

Required Text: my own notes distributed in class

Recommended Reading: announced throughout the semester

Grading: weekly homework and the final project

Homework: assigned once a week, due a week later

Course Webpage: TBA