| Instructor/TA | Office | Office hour | |
| Dr. Chi Li | Wednesday 10am-12pm | chi.li@rutgers.edu |
| Reference Books | Canvas | Policies | Services |
|
Week |
Sections |
Notes |
|
Week 1: 1/15-1/19 |
Riemann metrics and geodesics |
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Week 2: 1/22-1/26 |
Jacobi fields Conjugate points Hopf-Rinow Theorem |
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Week 3: 1/29-2/2 |
Hopf-Rinow Theorem Hadamard Theorem |
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Week 4: 2/5-2/9 |
Variations of Energy Bonnet-Myers, Synge-Weinstein |
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Week 5: 2/12-2/16 |
Synge-Weinstein Theorem Index Lemma |
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Week 6: 2/19-2/23 |
Rauch comparison Theorem Hessian of distance function |
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Week 7: 2/26-3/1 |
Law of Cosine in space forms Toponogov Theorem Morse Index Theorem |
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Week 8: 3/4-3/8 |
Estimates of injectivity radius Sphere Theorem |
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Week 9: 3/11-3/15 |
Spring Recess | |
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Week 10: 3/18-3/22 |
Hodge Theory, harmonic forms Bochner Technique |
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Week 11: 3/25-3/29 |
Clifford multiplication Positive curvature operators |
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Week 12: 4/1-4/5 |
Symmetric spaces Holonomy |
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Week 13: 4/8-4/12 |
Curvature and holonomy |
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Week 14: 4/15-4/19 |
Einstein manifolds |
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Week 15: 4/22-4/26 |
Presentations |
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Week 16: 4/29-5/3 |
Presentations Classes end on 4/29 Reading Days (4/30-5/1) |
All students in the course are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously.
Rutgers is fully commited to compliance with the American with Disabilities Act; policies and procedures are indicated at http://ods.rutgers.edu/
Students who wish to request special accommodations must present a Letter of Accommodations to the instructor as early in the term as possible (see https://ods.rutgers.edu/letter-accommodation )
Counseling, ADAP & Psychiatric Services (CAPS) http://health.rutgers.edu/medicalcounseling- services/counseling/ , (848) 932-7884 / 17 Senior Street, New Brunswick, NJ 08901. CAPS is a university mental health support service that includes counseling, alcohol and other drug assistance, and psychiatric services staffed by a team of professional within Rutgers Health services to support students efforts to succeed at Rutgers University. CAPS offers a variety of services that include: individual therapy, group therapy and workshops, crisis intervention, referral to specialists in the community and consultation and collaboration with campus partners.
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Disability Services https://ods.rutgers.edu , (848) 445-6800/ Lucy Stone Hall, Suite A145, Livingston Campus, 54 Joyce Kilmer Avenue, Piscataway, NJ 08854. Rutgers University welcomes students with disabilities into all of the University’s educational programs. In order to receive consideration for reasonable accommodations, a student with a disability must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation: https://ods.rutgers.edu/students/documentation-guidelines . If the documentation supports your request for reasonable accommodations, your campus’s disability services office will provide you with a Letter of Accommodations. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. To begin this process, please compete the Registration form on the ODS web site at: https://ods.rutgers.edu/students/registration-form .
Scarlet Listeners https://rutgers.campuslabs.com/engage/organization/scarletlisteners (732) 214 9069. Free and confidential peer counseling and referral hotline, providing a comforting and supportive safe space.