AIS Invariant Theory (2011)

Venue: Chennai Mathematical Institute, Chennai
Dates: 12 Dec - 30 Dec, 2011


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name V. Balaji
A. J. Parameswaran
Mailing Address Chennai Mathematical Institute     Chennai Mathematical Institute 


Speakers and Syllabus 



  • V. Balaji
  • Pramath Sastry
  • D. S. Nagaraj
  • K. N. Raghavan
  • A. J. Parameswaran
  • Jugal Verma



  • Revision of algebraic geometric methods, affine algebraic groups and elementary representation theory local algebra, Lie algebras and their representation theory, essential for the rest of the course.
  •  Hilbert's fourteenth problem, Reynold's operator, Mumford's theorem on existence of quotients for linearly reductive groups, Weitzenbock's theorem, Fischer's theorem, classical invariant theory (first and second fundamental theorems), geometric reductivity, Mumford's conjecture (various proofs), quotients by reductive algebraic groups, basic GIT, Hilbert- Mumford criterion, and examples of moduli problems as applications of GIT such as endomorphisms of vector spaces, ordered points on the line, elliptic curves. Geometry of quotients, Cohen-Macaulay properties, Hochster-Roberts theorem, Boutot's theorem on rational singularites of good quotients in char 0, Kempf- Rousseau theory of instability, Luna's etale slice theorem, theorems of Luna- Richardson.


Suggested Texts:
1. Invariant Theory, by J. Fogarty.
2. Introduction to moduli problems and orbits spaces, by P. Newstead.
3. Geometric Invariant Theory, by Mumford, Fogarty and Kirwan,
4. Invariant Theory, by Springer.

Selected Applicants

 List of selected candidates

Name Gender
State Affilation
     Position in College /University
University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg.Date
1  88 Dr. Yashonidhi Pandey Male Tamil Nadu Chennai Mathematical Institute Post-Doc     4 Dec 2008
2  92 Mr. Susobhan Mazumdar Male Tamilnadu Indian Institute of Technology Madras Junior Research Scholar Indian Institute of Technology Madras 2010  
3  98 Mr. Swapnil Ashok Lokhande Male Maharashtra Indian Institute of Technology-Bombay. Senior Research Fellow IIT-Guwahati 2008  
4 100 Mr Vivek Sadhu Male Maharastra IIT Bombay Junior Research Fellow Jadavpur University 2007  
5 101 Mr Rakesh tippireedy reddy Male Maharastra IIT Bombay research scholar IIT Madras 2008  
6 102 Mr Husney Parvez Sarwar Male Maharastra IIT Bombay Junior Research Fellow IIT Guwahati 2010  
7 107 Mr. kamalakshya mahatab Male Tamil Nadu THE INSTITUTE OF MATHEMATICAL SCIENCES Junior Research Fellow      
8 128 Prof manoj keshari Male maharashtra IIT Bombay Asst Prof      
9 136 Mr. Siddharth Mathur Male Haryana Central European University Masters Student Central European University 2012  
10 210 Mr. Ramakrishna Nanduri Male Tamil Nadu The Institute of Mathematical Sciences (IMSc) Post Doctoral Fellow Hyderabad Central University 2005  
11 257 Mr Narasimha Chary B Male Tamilnadu Chennai Mathematical Institute,H-1, SIPCOT IT Part,Siruseri, Chennai. Research scholar University of Hyderabad 2009  
12 277 Ms. Sonica Anand Female Punjab IISER Mohali Junior Research Fellow M.Sc., IIT, Delhi 2010  
13 296 Mr. Ajay Kumar Male Punjab IISER Mohali. Research Scholar Panjab University, Chandigarh. 2008  
    Dr. Wong     TIFR        
15 298 Mr. shiv Parsad Male Punjab IISER Mohali Research Scholar Punjabi University, Patiala. 2007  
16 307 Mr Sanjay Kumar Singh Male Maharasra TIFR,Mumbai research Scholar University of Allahabad 2005  
17 319 Mr. SESHADRI CHINTAPALLI Male Tamil Nadu Institute of Mathematical Sciences Research Scholar Andra University 2009  
18 328 Mr. Gaurab Tripathi Male West Bengal Jadavpur University. Junior Research Fellow Padova University 2008  
19 329 Mr. Krishanu Dan Male Tamil Nadu The Institute of Mathematical Sciences. Senior Reserch Fellow. The University of Burdwan 2008  
20 330 Mr. Joydip Saha Male West Bengal Rama Krishna Mission Vivekananda University. Junior Research Fellow RKMVU 2010  
21 347 Mr. Sagar Kolte Male Maharashtra Tata Institute of Fundamental Research Research Scholar      
22 348 Mr. Pabitra Barik Male Tamilnadu CMI Research Scholar      
23 365 Mr Abhishek Hemantkumar Dang Male Tamil Nadu Chennai Mathematical Institute Junior Research Fellow      

How to reach

The Chennai Math Institute is situated in the south of Chennai towards Mahabalipuram. It is on the newly formed ``Old Mahabalipuram Road"(OMR) or Rajiv Gandhi Salai. The easiest way to reach CMI is to come to the start of the OMR at Madhya Kailash and take the bus 19-B which comes to the entrance of the SIPCOT IT Park. The Institute is a 1 KM walk. The better way would be to come to the Institute of Mathematical Sciences, Taramani and take the regular shuttle service from IMSc to CMI. This shuttle also passes through Madhya Kailash. Please call the CMI Security to ask the shuttle to stop and pick people up at Madhya Kailash.The CMI Security Telephone Number is: 32983442, 32983441.