MATH 669--TOPICS IN GEOMETRIC ANALYSIS--SPRING 2025--A. FREIRE

Syllabus (includes references)


Course log and notes:

Tu 1/21  Ricci-de Turck flow, Part I
Ref: [TOP] Ch 2, 4, 5

Th 1/23 Decomposition of Einstein equations/Initial data sets, constraint equations
Ref: Constraint equations notes

Tu 1/28 Ricci-de Turck flow, Part 2
Ref: [TOP], Ch. 5, [BRE], 2.2

Th 1/30 Intro to causality in Lorentzian manifolds.
Ref:[ON], Ch. 14

Tu 2/4 Evolution of curvature under RF, blowup criterion
Ref:[TOP], Ch. 3, 5

Th 2/6 The Hawking and Penrose incompleteness theorems
Ref: [ON] Ch. 14, [LEE] Ch.7