ATMW Probabability and Representation Theory (2016)


The Institute of Mathematical Sciences, Chennai


7th to 12th March 2016


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


School Convener(s)

Name Prof. Arvind Ayyer Prof. K N Raghavan
Mailing Address Assistant Professor
Department of Mathematics
Indian Institute of Science
Bangalore 560 012
Professor H
Mathematics Group
The Institute of Mathematical Sciences,
CIT Campus, Taramani
Chennai 600 113


Speakers and Syllabus 

 There were five lecture courses in all. Listed below in separate subsections are the synopses of the courses in the words of the respective speakers.

2.1. Vershik-Okounkov theory for representations of the symmetric group: 4 lectures by Murali Srinivasan of IIT Mumbai. The first two lectures covered basic (ordinary) representation theory of finite groups. The third and fourth lectures covered the Vershik- Okounkov approach to the representation theory of the symmetric group. These results
were used to determine eigenvalues of the transitions matrices involved in the transpose- top-to-random and the random-transposition models of card shuffling.

2.2. Markov chains: 2 lectures by Antar Bandyopadhyay of ISI Delhi. Topics covered:Discrete Markov chains with countable state space, Examples including two state chain,Simple Symmetric Random Walk, random walk on d-dimensional integer lattice, Ehren-fest chain, and card shufflings. Classification of states, recurrence and transience; irre-ducibility, decomposition of state space into irreducible classes, examples. Stationary distributions, limit theorems, positive and null recurrence. Definition of periodicity, ape-riodic chains. Limit theorems for aperiodic irreducible chains, proof for positive recurrent case using coupling. Total variation distance and definition of mixing time.

2.3. Computer algebra: 2 lectures by Amritanshu Prasad of IMSc. Topics covered: In-troduction to Sage, basics of python programming, construction of some transition ma-trices using Sage. Irreducible representations of symmetric groups in Sage. Use of Sage’s
symmetrica interface to compute character values of symmetric groups.

2.4. Semigroup theory: 2 lectures by Pooja Singla of IISc. Topics covered: Interplay between representation theory of semigroup algebras and Markov chains on semigroups.Semilattice and Left regular band semigroups. Eigenvalues of Tsetlin library.

2.5. Card shuffling models: 4 lectures by Arvind Ayyer of IISc. The following random walk models on the symmetric group were discussed, with emphasis on the stationary distribution, eigenvalues of transition matrices, and mixing times:

(1) Random transpositions
(2) Transpose-top-to-random model
(3) Tsetlin library
(4) Top-to-random insertions
(5) Random-to-random insertions

There were four half-hour research talks as follows:

• Amritanshu Prasad (IMSc): Representations of the symmetric group with non-trivial determinant
• Sushil Bhunia (IISER, Pune): z-classes in unitary groups
• Ashish Mishra (CMI): Vershik-Okounkov approach to representations of the wreath product
• Hassain M (IISc): Representations of SL2 (Z/16Z) and SL2 (F2 [t]/t4 )


Speakers and Schedule

Timings Monday Tuesday Wednesday Thursday Friday Saturday
09:00 – 09:30 Breakfast
09.30 – 11:00 Representation
Theory 1
Theory 2
Theory 1
Theory 2
Model 3:
Tsetlin Library
Model 4:
Random-to-random shuffle
11:00 – 11:30 Coffee/Tea break
11.30 – 13:00 Markov Chain
Theory 1
Markov Chain
Theory 2
Theory 1
Theory 2
Research talks
1 and 2
13:00 – 14:30 Lunch break
14:30 – 16:00 Computer
Algebra 1
Model 1:
Random Transpositions
Algebra 2
Model 2:
Top-to-random shuffle
Research talks
3 and 4
16:00 – 16:30 Coffee/Tea break
16.30 – 17:30 Discussion Discussion Discussion Discussion Discussion


Local organisers

Arvind Ayyer (IISc Bangalore)
Amritanshu Prasad (IMSc Chennai)
K N Raghavan (IMSc Chennai)


Actual Participants 
Sr. SID Full Name Gender Affiliation City Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg
1 5593 Mr. Tulasi Ram Reddy Annapareddy Male Indian Insitute of science Bengaluru Junior Research Associate Indian Statistical Institute 2010  
2 5664 Mr. Prashant Vasantrao Uswadkar Male Shiv Nadar University Gautam Buddha Nagar PhD student University of Pune 2010  
3 5679 Mr. Debashish Bose Male Shiv Nadar University Gautam Buddha Nagar Asst. Prof. IIT Kanpur 2001 12/1/2010
4 5681 Mr. Subhajit Ghosh Male Indian Institute of Science Bangalore Int. PhD Indian Institute of Science, Bangalore 2015  
5 5752 Mr. Dipankar Roy Male Indian Institute of Science Bangalore PhD IIT Kharagpur 2015  
6 5753 Mr. Pradeep Kumar Male Central University Of South Bihar Patna MPhil-PhD Student Central University of South Bihar 2014  
7 5870 Ms. Rashmi Jain Female IISER , Mohali Mohali MSc Student IISER , Mohali Appeared / Awaiting Result  
8 5934 Ms. Priyanga Ganesan Female National Institute of Science Education and Research Khurda Integrated M.Sc - fourth year student National Institute of Science Education and Research Appeared / Awaiting Result  
9 5935 Mr. Sanjoy Kumar Jhawar Male Indian Institute of Science Bangalore Bangalore PhD IIT Delhi 2014  
10 5994 Ms. Yasmeen Shameem Akhtar Female Indian Institute of Science Education and Research Pune PhD Student S.P. Pune University 2010  
11 6002 Mr. Soumitra Das Male North-Eastern Hill University Shillong Phd Student North-Eastern Hill University 2012  
12 6036 Mr. Pritam Majumder Male Tata Institute of Fundamental Research Mumbai PhD IIT Kanpur 2014  
13 6199 Mr. Jyotirmoy Ganguly Male IISER, Pune Pune Ph.D University of Hyderabad 2013  
14 6200 Mr. Harshit Yadav Male IIT, Kanpur Kanpur B.S. student N/A Appeared / Awaiting Result  
15 6214 Mr. Nihar Prakash Gargava Male IIT, Kanpur Kanpur Student None Appeared / Awaiting Result  
16 5630 Mr Uday Bhaskar Sharma Male The Institute of Mathematical Sciences Chennai Senior Research Fellow University of Hyderabad M.Sc. 2011  
17 5637 Mr Sridhar Poojyam Narayanan Male Institute of Mathematical Science Chennai PhD BITS Pilani 2012  
18 5887 Dr. Kumarapandiyan G Male Indian Statistical Institute, Chennai Center Chennai Post Doctoral Fellow Pondicherry University 2011 1/21/2015
19 6230 Mr. Krishanu Roy Male Institute of Mathematical Sciences Chennai JRF Institute of Mathematical Sciences 2015  
20 6311 Ms. Ananya Lahiri Female Chennai Mathematical Institute Chennai DST INSPIRE fellow   2005  

Prof. Anupam Singh




Mr. Pritam Majumdar


TIFR, Mumbai.


Prof. Suresh Govindarajan


IIT Madras


Prof. S. Krishnan


IIT Bombay


Mr. Muthuvel Murugan


CMI, Chennai


Mr. Anish Mukherji


CMI, Chennai


Ms. N. Karimilla Bi


IMSc, Chennai

28   Mr. Debajyoti   Chennai Mathematical Institute          



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Telephone Numbers

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The Institute of Mathematical Sciences is located in a campus-like area variously known as the ``CIT Campus'' or the ``CPT Campus''. Many people in Madras may not have heard of the Institute, but almost everyone would have heard of the M.G.R. Film City and Tidel Park which are further down in the same campus area. IMSc has two complexes. One houses the main Institute building, the library building and the new building. The other has the students' hostel and Guest House. These two complexes are across the road from each other.