MAT1318H S LEC0101 20231:Seminar in Geometry and Topology

Faculty: Vitali Kapovitch
email: vitali.kapovitch@utoronto.ca

office hours: F 12-2, https://utoronto.zoom.us/j/83272248586 Passcode: 142567

• Lectures will take place via Zoom: Tu 10:10-11:30am F  9:10-10:30am https://utoronto.zoom.us/j/87352812967  Passcode:  231588
• Course Description:
  This course would be a direct continuation of the MAT1342/MAT464 Differential geometry course.  It would cover various comparison theorems (Rauch and Toponogov comparison) and their applications such as Bishop-Gromov volume comparison,  critical point theory of distance functions, diameter sphere theorem, negative and nonnegative curvature, Gromoll-Meyer splitting theorem and Cheeger-Gromoll soul theorem.
• Text: 

  The Text for this course: We will use a variety of sources including (but not exclusive) the following

  • Lecture Notes on Comparison geometry by Jost Eschenburg

  • Comparison Theory for Riccati equations by Eschenburg and Heintze,

  • A section on the proof of Toponogov triangle comparison from the book on Alexandrov geometry  by Stephanie Alexander, Anton Petrunin and myself

  • Wolfgang Meyer's notes on comparison geometry. 

  • Lecture notes by Karsten Grove on Critical Point Theory for distance functions.

  • Cheeger Gromoll On the Structure of Complete Manifolds of Nonnegative Curvature

  • Paper "Proof of the soul conjecture of Cheeger and Gromoll" by G. Perelman.

• There will be no tests or homework assignments in the course. The final mark will be based on a presentation near the end of the course.
• Lecture recordings will be available in the Modules sections.