MATH-F310: Differential Geometry I

2021

Room: P.OF.2068-2070;     Time: Mondays, 10:00-12:30.

Course content: This course is the first part of the Differential Geometry course. In particular, basic notions and methods of differential geometry such as smooth manifolds, vector fields, vector bundles etc. appearing both in various branches of mathematics and physics will be introduced and developed.

Lecture notes (Last updated: 15 SEP 2021)

Literature

D.Barden, C.Thomas. An introduction to differential manifolds, Imperiall College Press.
J.Lee. Introduction to smooth manifolds, Springer Verlag.
L.Tu. An introduction to manifolds, Springer Verlag.
A.Shastri. Elements of differential topology, CRC Press.

Excercises

Room: P.2NO 707.
Time: Tuesdays, 16:00-18:00.

Excercise sheet 1 (Deadline: 05.10)

MATH-F419: Algebraic topology

2021

Room and Time: Wednesdays 10:00-11:00 in P.OF.2078 and Fridays 14:00-15:00 in P.1C3.203.

Course content: The idea is to associate to topological spaces algebraic objects (groups, rings etc). If this is done judiciously, one can hope for example to distinguish non-homeomorphic spaces or essentially different continuous maps (in a suitable sense). This in turn allows one to prove interesting results, for example that any continuous map from a closed ball in a finite-dimensional Euclidean space into itself has a fixed point (Brouwer’s theorem).

Lecture notes (Last updated: 22 SEP 2021)

Literature

J. Vick. Homology theory. An introduction to algebraic topology.
A. Hatcher. Algebraic Topology ( Chapters 1 and 2), available online: http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Course "Introduction to Gauge Theory"

PCMI Summer School "Quantum Field Theory and Manifold Invariants", July 2019

Lecture notes (Last updated: 22 OCT 2019)