# 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: |
3^{rd} -21^{st} July, 2012. |

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

Name |
Prof. Sudesh Kaur Khanduja | Dr. Gurmeet K. Bakshi |

Mailing Address |
Indian Institute of Science Education and Reseach |
Centre for Advanced Study in Mathematics, |

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.

Speaker |
Hrs |
Syllabus |

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 Khanduja |
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 |

**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) |

**Speakers**

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 iisermohali.ac.in*and Dr. Gurmeet K. Bakshi at*gkbakshi at pu.ac.in*

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.