AIS Riemannian Geometry (2019)

  Convener(s)
Name:

Subhojoy Gupta

Mahan Mj
Mailing Address:

Dept. of Mathematics,
Indian Institute of Science, Bangalore 560012

School of Mathematics, Tata Institute of Fundamental Research,
Mumbai 400005
Email:

subhojoy at gmail.com

mahan.mj  at gmail.com

This school is to provide PhD students working in geometry and topology to have an exposure to certain key results and techniques in the study of Riemannian manifolds and complex geometry. Apart from the fundamental theory, topics that the mini-courses aim to cover include the Ricci flow on surfaces, spectral geometry of hyperbolic surfaces, surface laminations, and Yau’s work on the Calabi conjecture.

Please Note:  Participants have to arrange for their own travel.

Dates: 

Monday, July 8, 2019 - 09:30 to Saturday, July 20, 2019 - 17:30

Venue: 

Venue Address: 

Dept. of Mathematics, Indian Institute of Science,
Bangalore 560012

 

 

Venue State: 

Venue City: 

PIN: 

560012

Chrono Order: 

324

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)

 

 

 

 

 

 

 

Selected Applicants: 

 

Sr. SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Details of Ph.D if applicable Ph.D. Deg Date
1 24556 Mr Arijit Nath Male IIT Madras Ph.D student Ramakrishna Mission Vivekananda University 2013    
2 24643 Mr Soumik Ghosh Male Indian Statistical Institute M Math Student Indian Statistical Institute Appeared    
3 24653 Mr Pritthijit Biswas Male Chennai Mathematical Institute PhD Ramakrishna Mission Vivekananda University 2017    
4 24713 Mr. Umar Mohammad Khan Male Aligarh Muslim University PhD Student Aligarh Muslim University 2015    
5 25529 Mr. Reebhu Bhattacharyya Male Indian Institute of Technology Bombay Integrated Masters Student(Final Year) Indian Institute of Technology Bombay Appeared    
6 25558 Mr Anantadulal Paul Male NISER BHUBANESWAR PhD UNIVERSITY OF PUNE MAHARASTRA 2015    
7 26039 Mr. Sourav Holme Choudhury Male Institute of Mathematical Sciences PhD Indian Statistical Institute, Kolkata 2018    
8 26174 Mrs. Arifa Naz Female Department of Mathematics, Aligarh Muslim University PhD Aligarh Muslim University 2016    
9 26824 Mr. Sachchidanand Prasad Male IISER Kolkata PhD NIT Rourkela 2017    
10 26968 Mr Sriram Raghunath Male (IISER) Pune 4th Year BS MS Student Indian Institute of Science Education and Research, Pune Appeared    
11 27050 Mr. George Shaji Male IISER Mohali Integrated MS-Ph.D Student IISER Mohali Appeared    
12 27301 Mr. Ritwik Chakraborty Male Indian Institute of Technology BS (Double Major) Student        
13 27480 Mr M V Ajay Kumar Nair Male IISER Bhopal Project Student IISER B 2018    
14 27561 Mr. Anant Singh Male Chennai Mathematical Institute MSc Student Chennai Mathematical Institute      
15 27579 Mr. Debjit Basu Male Indian Institute Of Science Education And Research, Mohali Int PhD Student Indian Institute Of Science Education And Research, Mohali Appeared    
16 27650 Mr. Neeraj Kumar Dhanwani Male IISER Bhopal PhD Devi Ahilya University 2015 ongoing 4th year, I have submitted a paper in some peer reviewed journal.  
17 27652 Ms. Jigyasa Gaurav Female IIT, Bombay PhD Indian Institute of Science, Bangalore 2017    
18 27700 Mr. Sourav Ghosh Male Chennai Mathematical Institute MSc Student Chennai Mathematical Institute      
19 27731 Mr. Kumar Sannidhya Shukla Male National Institute of Science Education and Research (NISER), Bhubaneswar Integrated MSc. Student NISER, Bhubaneswar Appeared    
20 27745 Mr. Kushlam Srivastava Male IIT Kanpur B.S. Student None      
21 27792 Ms. Monika Yadav Female IISER Bhopal PhD IIT Kanpur 2017    
22 27800 Ms. Ramya Nair Female IISER Pune PhD student Mumbai 2015    
23 27833 Mr. Adithyan P Male IISER, Pune Fourth year BS-MS Student Indian Institute of Science Education and Research Pune Appeared    
24 27846 Mr. Paramjit Singh Male Chennai Mathematical Institute MSc II year Chennai Mathematical Institute Appeared    
25 27899 Mr. Sannidhi Alape Male Indian Institute of Science Education and Research Bhopal PhD Chennai Mathematical Institute 2016    
26 27007 Mr. Partha Sarathi Ghosh Male Indian Statistical Institute M.Math Student Indian Statistical Institute, Kolkata      
27 27284 Mr.Pradeep Singh Male Indian Institute of Technology, Delhi PhD Indian Institute of Technology, Delhi 2017    
28 27969

Devendra Tiwari

 Male Bhaskaracharya Pratishthana          
  Local participants *     
1 25125 Mr. Kartick Ghosh Male IISc Bangalore Int. PhD Student IISc Bangalore      
2 26163 Mr. Sumit Kumar Singh Male Indian Statistical Institute Student   Appeared    
3 26288 Ms Annapurna Banik Female IISC Bangalore PhD Student University Of Calcutta 2018    
4 27065 Mr. Gobinda Sau Male Indian Institute of Science PhD Chennai Mathematical Institute 2015    
5 27104 Mr. Akshay Sateesh Hegde Male Indian Statistical Institute BMath Student        
6 27191 Mr. Rithwik Susheel Vidyarthi Male Indian Institute of Science Education and Research- Pune BS-MS student Indian Institute of Science Education and Research- Pune Appeared    
7 27254 Mr. Chinmaya Kausik Male Indian Institute of Science Undergraduate Student -Still an undergraduate student-      
8 27318 Mr. Karthik Vasu Male Indian Statistical Institute M.Math Student Indian Statistical Institute Appeared    
9 27390 Mr Deepak Badarinath Male Indian Statistical Institute BMath(Hons) 3rd Year student        
10 27517 Mr. Pabitra Barman Male Indian Institute of Science PhD Student Indian Institute of Science 2018    
11 27534 Mr Manish Kumar Male Indian Statistical Institute , Bengaluru Undergraduate ( Final Year)        
12 27584 Mr. Indrayudh Roy Male Indian Statistical Institute, Bangalore Centre M.Math Student Indian Statistical Institute, Bangalore Centre      
13 27947 Mr Ramesh Mete Male Indian Institute of Science Int. PhD 2nd year student Indian Institute of science Appeared    
14 28024 Mr. Pranab Sarkar Male Indian Institute of Science, Bangalore PhD Indian Institute of Science, Bangalore 2018    
 
*  Local participant will not be eligible for accommodation, breakfast or dinner.

 

How to Reach: 

Click here

School Short Name: 

rg

List of Conveners: 

  • Subhojoy Gupta
  • Mahan Mj

School Type: 

AIS