AIS - AIS Riemannian Geometry (2019)

Speakers and Syllabus


Name of the speaker

No of lectures:
Each lecture is of duration 1.5hours

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)

 

 

 

 

 

 

 

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