AIS Lie Groups (2014)

Venue: IIT, Bombay
Dates: 7th to 26th July

 

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

 

School Convener(s)
Name S.G. Dani S.M. Garge
Mailing Address Department of Mathematics
Indian Institute of Technology Bombay
I.I.T. P.O., Powai
Mumbai – 400 076		 Department of Mathematics
Indian Institute of Technology Bombay
I.I.T. P.O., Powai
Mumbai – 400 076

 

Speakers and Syllabus 

Speakers:

  1. Siddhartha Bhattacharya, TIFR Mumbai
  2. S.G. Dani, IIT Mumbai
  3. Shripad Garge, IIT Mumbai
  4. Anish Ghosh, TIFR Mumbai
  5. C.S. Rajan, TIFR Mumbai
  6. T.N. Venkataramana, TIFR Mumbai

Schedule outline:
Each of the speakers will give a course of 6 lectures of 90 minutes each. There will be two lectures per day (Monday through Saturday each week). These will be supplemented with tutorials (10 hours per week). There will also be 6 Guest lectures on suitable related topics, during the workshop.

Tentative plan of the courses:
1 st week:

  • Matrix Lie groups: Examples of matrix groups, topology, compact groups, connectedness, homomorphisms , one-parameter subgroups, products, semidirect products, group actions, adjoint action, homogeneous spaces, more advanced examples (e.g. symplectic groups, unitary groups)
  • Lie algebras: Abstract Lie algebras, examples of matrix Lie algebras, associating Lie algebras to matrix groups, basic structure theory of Lie algebras, Engel’s and Lie’s theorem, radicals.

2 nd week:

  • Structure of Lie groups: Exponential map, Jordan canonical form, linear first order differential equations in matrices, Campbell-Hausdorff formula, nilpotent and solvable Lie groups.
  • Semisimple Lie algebras: Structure of semisimple Lie algebras over complex numbers, Cartan subalgebras, root systems and root spaces etc, Dynkin diagrams, classification.

3 rd week:

  • Structure of Lie groups II: Structure of compact groups, maximal tori, representation theory, Peter-Weyl theorem. Levi decomposition, Iwasawa and Cartan decompositions, E.Cartan’s theorem for closed subgroups.
  • Representation theory of semisimple Lie algebras: Representation theory of Lie algebras, weight spaces, introduction to infinite - dimensional theory.
Selected Applicants

 

Note:

  • Outstation candidates will be provided accommodation (shared).
  • The candidates are requested to confirm their participation as early as possible, latest by May 12, 2014 by sending an e-mail to the liegroups2014@gmail.com
Serial SID Full Name Gender Affiliation City, State Position University/Institute M.Sc./M.A. Year of Passing M.Sc./M.A
1 5446 Ms Purnima Satapathy Female IIT, KHARAGPUR Kharagpur, West Bengal PhD NIT, Rourkela 2012
2 5481 Mr Sumit Kumar Male Institute of Mathematical Sciences Chennai, PHD Student   2013
3 5505 Mr Sushil Bhunia Male IISER Pune Pune, Maharashtra PhD Jadavpur University 2010
4 5520 Mr Muna Naik Male Indian Statistical Institute, Kolkata Kolkata, West Bengal PhD National Institute of Science Education and Research 2013
5 5595 Ms. Neha Prabhu Female IISER, Pune Pune, Maharashtra PhD Student IIT, Bombay 2012
6 5634 Mr Makarand Sanjay Sarnobat Male Indian Institute of Science Education and Research Pune, Maharashtra Research Scholar Sir Parshurambhau College, Pune 2012
7 5655 Mr. Amit Kumar Singh Male The Institute of Mathematical Sciences Chennai, Tamil Nadu Ph.D University of Allahabad 2011
8 5672 Mr. Bhooshan Uday Gadre Male IUCAA, Pune Pune, Maharashtra PhD Student Department of Physics, University of Pune 2012
9 5925 Ms Gunja Sachdeva Female IISER Pune Pune, Maharashtra PhD Student Dayalbagh Educational Institute, Dayalbagh, Agra 2011
10 5968 Ms Rekha Biswal Female Institute of Mathematical Sciences Chennai, Tamil Nadu INTEGRATED Ph.D, SRF INDIAN INSTITUTE OF TECHNOLOGY,BOMBAY 2011
11 5995 Mr. Rohit Suhas Joshi Male IISER PUNE Pune, Maharashtra PhD Student IIT kanpur 2009
12 6027 Mr Anirban Bose Male ISI, Delhi Centre New Delhi, Delhi Ph. D. Calcutta University 2008
13 6034 Ms Saudamini Nayak Female National Institute of Technology, Rourkela. Sundergarh, Orissa Ph.D. scholar Sambalpur University, Odisha 2008
14 6060 Mr. Arun Kumar Male Indian Institute Of Science Education And Research Mohali, Punjab Int. Phd Indian Institute Of Science Education And Research Appeared/Awaiting Result
15 6165 Mr Partha Sarathi Patra Male IIT, Hyderabad Hyderabad, Andhra Pradesh PhD STUDENT Guru Ghasidas Viswavidyalaya 2012
16 6187 Mr. Alok Kumar Yadav Male JNU New Delhi, Delhi Ph.D. D.D.U Gorakhpur University 2011
17 6253 Mr. Ripan Saha Male IISER Mohali Mohali, Punjab PhD IIT Kanpur 2013
18 5638 Mr. Advait Sudhir Phanse Male S.P.Collge, Pune. Pune, Maharashtra MSc Student S.P.College , Pune. Appeared/Awaiting Result
19 5977 Mr. Neeraj Ravindra Deshmukh Male Indian Institute of Science Education and Research, Mohali Mohali, Punjab 4th year Integ. MS student Indian Institute of Science Education and Research, Mohali Appeared/Awaiting Result
20 5992 Mr. Koushik Ghosh Male Indian Statistical Institute,Bangalore Bangalore, Karnataka Master's Student Indian Statistical Institute,Bangalore Appeared/Awaiting Result
21 6015 Mr Priyankur Chaudhuri Male Indian Statistical Institute Bangalore, Karnataka Msc student Indian Statistical Institute Appeared/Awaiting Result
22 6114 Mr. Priyadip Mondal Male Indian Statistical Institute Bangalore, Karnataka MSc Student Indian Statistical Institute Appeared/Awaiting Result
23 6147 Mr. Vishal Gupta Male National Institute of Science Education and Research, Bhubaneswar Bhubaneswar, Orissa MsC Student National Institute of Science Education and Research Appeared/Awaiting Result
Local Candidates
24 5866 Mr. Ashish Mishra Male IIT Bombay Mumbai, Maharashtra Phd Student Delhi University 2008
25 6096 Mr Plawan Das Male UM-DAE Centre For Excellence in Basic Sciences, Mumbai Mumbai, Maharashtra Int MSc Student (2nd yr) UM DAE Centre For Excellence in Basic Sciences Appeared/Awaiting Result
26 6195 Mr Arunava Mandal Male IIT Bombay Mumbai, Maharashtra Research Scholar Ramakrishna Mission, Vivekanand University 2010
27 6237 Mr. Manoj Choudhuri Male TIFR Centre for Applicable Mathematics Bangalore, Karnataka Research Scholar University of Calcutta 2008
28 6241 Mr. Lovy Singhal Male TIFR Mumbai Mumbai, Maharashtra Research Scholar Indian Institute of Technology Kanpur 2011
29 6242 Ms Komal Pravin Wategaonkar Female Royal college of Arts, Science and Commerce Thane, Maharashtra Assistant Professor I.I.T. Bombay 2000
30 -- Mr. Provanjan Mallick            
31 -- Mr. Mahendra Verma            
32 --   Mr. Mrinmoy Datta            

 

How to reach

http://www1.iitb.ac.in/campus/howto/howtoget.html