AIS Algebra (2012)

Venue: Indian Institute of Science Education and Reseach (IISER Mohali)
Sector 81, Knowledge City, P.O. Manauli
S.A.S. Nagar, Mohali (Punjab) 140306
Dates: 3rd -21st July, 2012.


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


School Convener(s)

Name Prof. Sudesh Kaur Khanduja Dr. Gurmeet K. Bakshi
Mailing Address

Indian Institute of Science Education and Reseach
Sector 81, Knowledge City, P.O. Manauli
S.A.S. Nagar, Mohali (Punjab) 140306

Centre for Advanced Study in Mathematics,
Panjab University,

Algebra is a branch of mathematics which is a subject of fundamental importance to numerous areas ofmathematics besides its applications to many other subjects including Physics and Chemistry. The aim of this school will be to discuss basic notions in non- commutative rings, algebraic number theory representation theory of finite groups and then focus on the algebraic structure of group rings, representations of symmetric groups and finite groups of Lie type. Applications to Fermat’s last theorem and to coding theory will also be discussed.

Speakers and Syllabus 


Speaker Hrs
Dipendra Prasad 3 UM Lectures
R.J.Hans Gill 3 UM Lectures
A.K.Bhandari 9 Non-commutative rings, Jacobson radical, semi-simple modules, semisimple rings, Wedderburn- Artin theorem, tensor Product of modules and algebras, central simple algebras, Skolem-Noether theorem,
Sudesh Kaur
9 A study of rings of integers of algebraic number fields and their discriminants, ideals in the ring of algebraic integers and their norm,explicit determination of imaginary quadratic fields whose rings of integers are Euclidean domains, factorization of ideals into prime ideals and connections with Fermat’s last theorem.
Ravi Kulkarni 9 Representation theory of finite groups, F-conjugacy, including the formula for F-idempotents and formula for Q-idempotents, inductive construction of irred F-reps of solvable group.
Kapil Paranjapee 9 General Linear Group. Orthogonal, Unitary and Symplectic groups;groups of similitudes. Projective groups.Tori and Unipotent subgroups.Jordan decomposition. Parabolic groups and Levi subgroups. ( Only a few indicative proofs will be given.)Principal Series Representations. Representations of Tori. Induced representations. Induction from Parabolics. (The lectures will largely be centred around GL_n. However, some indication will be given for other groups as well.)
Murli Srinivasan 6 Representations of symmetric groups
Gurmeet K. Bakshi 9

Induced representations, representations induced from normal subgroups, character of induced representation, Frobenius Reciprocity
Theorem, Mackey's irreducibility criterion, , Representations of metacyclic, metabelian and generalized metabelian groups. Algebraic
structure of some group algebras

Time Table

DATE  Lecture Tea Lecture 2 Lunch Tutorial Tea
  9.30-11.00   11.30-1.00   2.00-4.00  
3.07.12 AKB   SKK   AKB, SM  
4.07.12 AKB   SKK   SKK, SK  
5.07.12 AKB   SKK   AKB, SM  
6.07.12 AKB   SKK   SKK, SK  
7.07.12 AKB   SKK   AKB, SM  
9.07.12 AKB   RK   SKK, SK  
10.07.12 SKK   RK   RK, Ra ,__  
11.07.12 Special lecture   RK   RK, Ra,__  
12.07.12 MS   RK   MS, Ra,__  
13.07.12 MS   RK   RK, Ra,__ DP (UM lecture) after tea
14.07.12 MS   RK   MS, Ra,__ DP(UM lecture after tea)
16.07.12 MS   KP   KP, ___ RJHG (UM lecture) after tea
17.07.12 GKB   KP   GKB, SM RJHG (UM lecture) after tea
18.07.12 GKB   KP   KP, ___  
19.07.12 GKB   KP   GKB, SM  
20.07.12 GKB   KP   KP, ___  
21.07.12 GKB   KP   GKB(lecture) GKB, SM(tutorial)



KP- Kapil Paranjapee IISER Mohali DP-Dipendra Prasad, TIFR Mumbai RK-Ravi Kulkarni, IIT Bombay
AKB-Ashwani Kumar Bhandari, Panjab University, Chandigarh SKK-Sudesh Kaur Khanduja, IISER Mohali GKB-Gurmeet Kaur BakshiPanjab University, Chandigarh
MS-Murli Srinivasan, IIT Bombay RJHG-R.J.Hans Gill, Panjab University, Chandigarh  


Associates for the tutorials

SM-Sugandha Maheshwary,Panjab University, Chandigarh SK- Sanjeev Kumar, Panjab University, Chandigarh Ra-Rahul, \Bhaskaracharya Parashthana, Pune.


Selected Applicants
  • Following applicants are shortlisted to participate in the school.
  • The selected participants are requested to confirm their participation by 1st May 2012 by sending an e-mail to Prof. Sudesh Kaur Khanduja at skhanduja at  and Dr. Gurmeet K. Bakshi at gkbakshi at
Sr. SID Full Name Gender Affiliation State Position Univ./ Institute M.Sc./M.A. Year of Passing M.Sc./ M.A
1 1288 Mr. Ashish Mishra M IIT Bombay Maharashtra Research Scholar Univ. of Delhi 2008
2 1295 Mr. Rahu Dattatraya Kitture M Bhaskaracharya Pratishthana Maharashtra Ph.D. Shivaji Univ., Kolhapur 2008
3 1297 Ms. Sangita Vinod Choudhary F Pune Univ. Maharashtra student Univ. of Pune Appeared/ Awaiting Result
4 1302 Ms. Dilpreet Kaur F IISER Mohali Punjab Ph.D SCD Govt. College, Ludhiana 2009
5 1308 Mr Dillip Kumar Pradhan M Sambalpur Univ. Orissa MPhil Sambalpur Univ. 2011
6 1309 Mr Biswajit Mallick M Sambalpur Univ. Orissa MPhil Utkal Univ. 2011
7 1312 Mr Sanjay Kumar Singh M TIFR Maharashtra Research scholar Univ. of Allahabad 2007
8 1321 Ms. Tarannum Bano F Aligarh Muslim Univ. Uttar Pradesh Research Scholar Aligarh Muslim Univ. 2009
9 1323 Ms. Neha Makhijani F IIT Delhi Delhi PhD Student IIT Delhi 2008
10 1326 Mr. Anurag Singh M IIT-Guwahati Assam Student IIT-Guwahati Appeared/ Awaiting Result
11 1328 Ms. Sugandha Maheshwary F Panjab Univ. Chandigarh Ph.D. (JRF) Panjab Univ.,Chandigarh 2011
12 1329 Mr Vikas Sopan Jadhav M Bhaskaracharya Pratishthana Maharashtra Ph.D Student Pune Univ. 2004
13 1332 Ms. Swati Sidana F IIT Delhi Delhi PhD Student Panjab Univ., Chandigarh 2010
14 1342 Mr. Sanjeev Kumar M Dept. of Mathematics, Panjab Univ. Chandigarh pursuing PhD Dept. of Mathematics, Panjab Univ., Chandigarh 2009
15 1344 Ms Dishari Chaudhuri F IIT-Guwahati Assam Research Scholar IIT, Kharagpur 2010
16 1346 Ms. Kuldeep Kaur F IIT-Ropar Punjab PhD Student Punjabi Univ. Patiala 2008
17 1348 Mr. Sumit Kumar Debnath M IIT Kharagpur West Bengal 2nd IIT Kharagpur 2012
18 1355 Mr. Abdul Nadim Khan M Aligarh Muslim Univ. Uttar Pradesh PhD Bareilly College, Bareilly 2009
19 1356 Mr. Soham Swadhin Pradhan M IIT BOMBAY Maharashtra Ph.D Calcutta Univ. 2006
20 1367 Mr. Sachin Pandurang Basude M S R T M Univ.,Nanded. Maharashtra PhD student S R T M Univ., Nanded. 2011
21 1377 Mr. Nitin Shridhar Darkunde M School Of Mathematical Sciences,
S.R.T.M. Univ., Nanded
Maharashtra Asst. Prof. Dept. OF Mathematics, Univ. OF Pune, Pune. 2008
22 1399 Ms. Nazia Parveen F Aligarh Muslim Univ. Uttar Pradesh M.PHIL Aligarh Muslim Univ. 2009
23 1402 Mr. Sunil Kumar Prajapati M IIT Delhi Delhi PhD Student Banaras Hindu Univ., M.Sc, 2005
24 1429 Mr Tushar Kanta Naik M Chennai Mathematical Institute Tamil Nadu M.Sc (1st year )   Appeared/ Awaiting Result
25 1438 Dr. Harpreet Kaur F Guru Nanak Dev Univ., Amritsar   Asst. Prof. Panjab Univ., Chandigarh 2005
26 1444 Mr. Shailesh Kumar Tiwari M IIT Delhi Delhi Ph.D Purvanchal Univ. Jaunpur U.P. 2007
27 1450 Ms Kumari Saloni F IIT Guwahati Assam Research Scholar IIT Guwahati 2010
28 1459 Mr. Vinit Kumar Sinha M Madurai Kamraj Univ. Tamil Nadu Research Scholar Madurai Kamraj Univ. 2008
29 1470 Mr Praphulla Kumar Kowshik M Univ. Of Hyderabad Andhra Pradesh Student Univ. Of Hyderabad Appeared/ Awaiting Result
30 1471 Mr. Sahil Gupta M Guru Nanak Dev Univ.,Amritsar Punjab Asst. Prof. Guru Nanak Dev Univ. 2011
31 1386 Ms Snehal Suryakant Mitragotri F Shiavji Univ., Kolhapur Maharashtra Asst. Prof. IIT, Roorkee 2009


How to reach

How to reach the venue: IISER MOHALI

By Air: Arrive at Chandigarh airport. There are lots of connecting flights from Delhi/Mumbai to to Chandigarh.

By Train: Nearest railway stations are
Chandigarh (Station Code: CDG, 14 Km from IISER)
Ambala (Station Code: UMB, 50 Km from IISER)
Mohali (Station Code: SASN, 1 Km from IISER): There are very few connections to Mohali. One useful connection from Delhi is Una Jan-Shatabdi (Train No. 12057)

From Airport/Chandigarh Railway station to IISER: Take a Radio taxi (phone numbers: 0172-4141414, 0172-4646464) to Phase-IX, Mohali. Ask the driver to locate the Philips factory . On reaching Philips, keep moving in the same direction till you hit a dead end near a nala. From there you take a right turn. After 100 meters IISER is at your left. Distance between Philips and IISER is about 1 Km, between Airport and IISER is about 9 Kms and between Chandigarh Railway station and IISER is about 15 Kms. Mohali Railway station (called Sahibzada Ajit Singh Nagar station or SAS Nagar station) is just 1 km from IISER.