AIS - AIS Riemannian Geometry (2019)
Speakers and Syllabus
|
Name of the speaker |
No of lectures: |
Detailed syllabus |
|
Harish Seshadri (IISc) |
6 lectures |
Riemannian manifolds, metrics, connection, curvature, basics of elliptic PDE, Ricci flow for surfaces |
|
Gautam Bharali (IISc) |
6 lectures |
Basics of complex manifolds, Hermitian and Kähler geometry |
|
Dheeraj Kulkarni (IISER Bhopal) |
3 lectures |
Basics of foliations and surface laminations, Beltrami equation, Candel’s uniformization for surface laminations |
|
Soma Maity (IISER Mohali) |
3 lectures |
Hamilton’s proof of uniformization for higher genus surfaces |
|
Sugata Mondal (TIFR) |
6 lectures |
Laplace operator: definition and its spectrum, Laplace spectrum of domains in the plane, Some structural properties of eigenfunctions of the Laplacian (*). |
|
Vamsi Pingali (IISc) and Ved Datar (IISc) |
6 lectures each |
Topics in complex geometry towards Yau’s proof of the Calabi conjecture for Kahler-Einstein metrics for negative first Chern class. |
References:
- S-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampere equation I, Comm. Pure Appl. Math, 31, 1978.
- R.Hamilton, The Ricci Flow on surfaces, Contemp. Math, 71, Amer. Math. Soc., 1988.
- P. Buser, Geometry and Spectra of Compact Riemann Surfaces,Birkhauser Basel, Springer-Verlag, 2010, reprint of 1992 edition. (*)
- I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984.
Time Table
Tentative Timetable:
- Lec. 1: 9:30 – 11 AM
- Tea: 11 – 11:30 AM
- Lec. 2: 11:30 – 1 PM
- Lunch: 1 – 2:30 PM
- Lec. 3: 1: 2:30 – 4:00 PM
- Tea: 4:00 – 4:15 PM
- Tutorial : 4:15 – 5:15 PM
- Dinner: 7:00 – 8:30 PM
|
Day |
Date |
Lec. 1 |
Tea |
Lec. 2 |
Lunch |
Lec. 3 |
Tea |
Tut. |
Dinner |
|
Mon |
8/7 |
HS |
|
GB |
|
GB |
|
GB |
|
|
Tue |
9/7 |
HS |
|
GB |
|
DK |
|
HS |
|
|
Wed |
10/7 |
HS |
|
GB |
|
DK |
|
PS |
|
|
Thu |
11/7 |
HS |
|
VP |
|
DK |
|
DK |
|
|
Fri |
12/7 |
HS |
|
VP |
|
VD |
|
PS |
|
|
Sat |
13/7 |
HS |
|
VP |
|
VP |
|
PS |
|
|
Sun |
14/7 |
Sunday Recess |
|||||||
|
Mon |
15/7 |
VP |
|
VP |
|
SU |
|
PS |
|
|
Tue |
16/7 |
VP |
|
VD |
|
SU |
|
VP |
|
|
Wed |
17/7 |
VD |
|
VD |
|
SU |
|
VD |
|
|
Thu |
18/7 |
SU |
|
VD |
|
SO |
|
SU |
|
|
Fri |
19/7 |
SU |
|
VD |
|
SO |
|
SO |
|
|
Sat |
20/7 |
SU |
|
VD |
|
SO |
|
PS |
|
Key:
- HS: Harish Seshadri
- VP: Vamsi Pingali
- VD: Ved Datar
- SU: Sugata Mondal
- GB: Gautam Bharali
- DK: Dheeraj Kulkarni
- SO: Soma Maity
- PS: Problem Session (organizers)