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 and hyperbolic surfaces, Some structural properties of eigenfunctions of the Laplacian  (possible reference: Buser’s book)

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.

 

 

 

 

 


Time Table

Day Date 09:30 AM
to
11:00 AM
11:00 AM
to
11:30 AM
11:30 AM
to
01:00 PM
01:00 PM
to
02:30 PM
02:30 PM
to
04:00 PM
04:00 PM
to
04:15 PM
04:15 PM
to
05:15 PM
05:15 PM
to
05:30 PM
Lec. 1
Tea
Lec. 2
Lunch
Lec OR Tut
Tea Tut Tea
Mon 8/7 HS        GB        SU        GB       
Tue 9/7 HS GB SU HS
Wed 10/7 HS GB VP PS
Thu 11/7 HS GB VP SU
Fri 12/7 HS HS SU VP
Sat 13/7 GB GB SU PS
Sun 14/7 Sunday Recess
Mon 15/7 VP        VD        SO        PS       
Tue 16/7 VP VD SO VD
Wed 17/7 SU VD SO SO
Thu 18/7 SU VD DK PS
Fri 19/7 VP VD DK DK
Sat 23/6 VP VD DK PS

Key:

  • VD: Ved Datar
  • VP: Vamsi Pingali
  • SU: Sugata Mondal
  • SO: Soma Maity
  • HS: Harish Seshadri
  • GB: Gautam Bharali
  • DK: Dheeraj Kulkarni
  • PS: Problem Session (organizers)

 

 

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