NCMW Differential Geometry (2017)

Venue: IISER Pune,  Pune, Maharashtra
Date:  24th, Jul 2017 to 29th, Jul 2017



School Convener(s)

Name Prof. Indranil Biswas Prof. Mahan Mj Prof. Tejas Kalelkar
Mailing Address School of Mathematics
TIFR Mumbai
School of Mathematics
TIFR Mumbai
Department of Mathematics



Speakers and Syllabus

Courses and instructors

There were five courses with particulars as follows:

  1. Complex differential geometry, dealing with connections and curvature  on vector bundles culminating in the Kodaira embedding theorem. Vamsi Pingali (IISc Bangalore) was the instructor. The course was of 9 hour du ration (6 X 1.5 hrs).
  2. Riemann surfaces, dealing with complex analytic techniques and Fenchel Nielsen co-ordinates on Riemann surfaces, culminating in the Riemann Roch theorem. Subhojoy Gupta (IISc Bangalore) was the instructor. The course was of 9 hour duration (6 X 1.5 hrs).
  3. Gauge theory and Yang Mills, dealing with connections and curvature on principal bundles culminating in the Yang-Mills functionsl and ADS connections. Sushmita Venugopalan (IMSc Chennai) was the instructor.The course was of 6 hour duration (4 X 1.5 hrs).
  4.  Geodesic flow, dealing with hyperbolic dynamics and geodesic flow. Kingshook Biswas (ISI Kolkata) was the instructor. The course was of 6 hour duration (4 X 1.5 hrs).
  5. h-principle, dealing with the techniques evolved by Gromov and Eliashberg to solve the Smale-Hirsch immersion theorem. Dishant Pancholi (IMSc Chennai) was the instructor. The course was of 6 hour duration (4 X 1.5 hrs).
  6. All courses were pitched at a beginning 2nd year PhD level at standard Indian research institutes. Students had been selected so that they have the background to absorb such advanced material. As a consequence students systematically attended all lectures and were able to participate meaningfully. We feel that the program fulfilled what we had aimed at, viz. providing beginning PhD students in geometry a broad sampler of advanced topics in which they can do further study.



4 classes of 1.5 hr duration from 9:30-11, 11:30-1; 2-3:30; 4-5:30 were held every day from Monday-Saturday as per the following particulars:

(1) V. Pingali – M, Tu, W: 9:30-11, 11:30-1
(2) S. Gupta – Th, F: 9:30-11, 11:30-1; Sa: 9:30-11, 4-5:30
(3) D. Pancholi – M 4-5:30, Tu 2-3:30 W–2-3:30, Th– 2-3:30
(4) S. Venugopalan – M 2-3:30, W 4-5:30, F, Sa - 2-3:30
(5) K. Biswas–Tu 4-5:30, Th, F- 4-5:30, Sa 11:30-1


Actual Participants 


Full Name Affiliation
Ms. Gargi Ghosh IISER Kolkata
Mr. Balarka Sen Sodepur High School 
Mr Anantadulal Paul NISER.
Mr. Sambit Senapati Chennai Mathematical  Institute
Mr. Neeraj Kumar IISER Kolkata
Mr. Nidhish Unnikrishnan University of Hyderabad
Mr. Abhrojyoti Sen National Institute of Science Eductaion and Research
Mr. Akashdeep Dey Chennai Mathematical Institute
Ms Swathi Krishna IISER Mohali
Mr. Aritra Bhowmick Indian Statistical Institute, Kolkata
Mr. Abhishek Khetan Tata Institute of  Fundamental Research
Mr. Mohan Swaminathan Chennai Mathematical Institute
Mr. Sagar Balasaheb Kalane IISER MOHALI
Mr. Sridhar Venkatesh Chennai mathematical Institute
Mr Yash Uday Deshmukh Chennai Mathematical Institute
Mr. Sumit Roy Tata Institute of Fundamental Research
Mr. Harshit Yadav IIT Kanpur
Mr. Abhijeet Atmaram Ghanwat Chennai Mathematical Institute,Chennai
Mr. Tanuj Gupta IISER Kolkata Indian Institute of
Mr Selvakumar A Technology, Madras
Mr. Sujoy Chakraborty Tata Institute of Fundamental Research, Mumbai
Master Neetal Neel Chennai Mathematical Institute
Mr. Nihar Prakash Gargava Indian Institute of Technology, Kanpur
Mr. Joji Benny Indian Institute of Technology Madras
Mr. Mayuresh Mahadeo Londhe Indian Institute of Science,Bangalore. Indian Institute of
Mr. Saikat Panja Science Education and Research
Ms. Mita Banik Institute of Mathematical Sciences, Chennai
Mr Mohit Upmanyu Tata Institute of Fundamental Research
Mr Sahil Gehlawat Indian Institute of Science
Mr. Soumyadip Sahu Chennai Mathematical  Institute
Ms. Umme Zainab Soumyajit Maity Aligarh Muslim University Chennai Mathematical Institute


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