MAT 569: Tuesday and Thursday 11:30am-12:50pm, Harriman Hall 115

MAT 569: Differential Geometry II

Course Instructor: Mark McLean

Tuesday and Thursday 11:30am-12:50pm. From March 30th onwards, this course will be taught online through Zoom. The Zoom meeting code will be on blackboard. You can also email me for the code.

Syllabus

We will hopefully cover the following topics:

The Bochner Technique.
Symmetric Spaces and Holonomy Groups.
Ricci Curvature and distance and volume bounds and the Cheeger-Gromoll splitting theorem.
Convergence (Gromov-Hausdorff and smooth convergence).

There will be homework for this course. However there will be no final exam.

Textbook

Peter Petersen, Riemannian Geometry, Graduate Texts in Mathematics, 2006, ISBN 978-0-387-29403-2.

Prerequisites

You should be familiar with the contents of the differential geometry I course MAT 568. This course covered the first six chapters of Petersons book. In particular, metrics, geodesics, covariant derivatives (connections) and curvature, leading to the Cartan-Hadamard theorem on the universal cover of manifolds with negative sectional curvature and Myers' theorem on the diameter of manifolds of positive sectional curvature.

Office Hours via Zoom: Fri 1pm-2pm, Tuesday 1pm-2pm and Wednesday 10:30am-11:30am.
The Zoom meeting code will be on blackboard. You can also email me for the meeting code.

Old Syllabus before March 30

Student Accessibility Support Center (SASC) Statement:
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center (SASC), ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the staff at the Student Accessibility Support Center (SASC). For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities.

Academic Integrity Statement:
Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website, http://www.stonybrook.edu/commcms/academic_integrity/index.html.

Critical Incident Management Statement:
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.