AIS Quadratic Forms (2014)

 Venue: Indian Institute of Science Education and Research (IISER), Mohali Dates: 2nd - 21st June,  2014

 School Convener(s) Name Amit Kulshrestha Shripad M. Garge Mailing Address Department of Mathematical Sciences,IISER Mohali, Knowledge city, Sector 81,  Mohali, 140 306. Department of Mathematics, IIT Mumbai,Powai, Mumbai. 400 076.

 Speakers and Syllabus

Brief Description of School :
A quadratic form has an innocuous definition, a homogeneous polynomial in degree 2, but has far-reaching connections to many parts of mathematics; linear algebraic groups, division algebras, modular forms and class field theory, to name a few. Quadratic form may also be used to assess how complicated a field is. The main focus of the workshop is the study of various cohomological invariants associated to quadratic forms so as to classify quadratic forms in some cases. This will provide a background to study numerical invariants such as level, Pythagorean number and the recent progress on u-invariant. In this AIS, we intend to learn basics of quadratic forms so as to be able to learn more about these invariants in a follow-up workshop a year later.

We will follow the well-known book Introduction to quadratic forms over fields by T. Y. Lam. We are interested in the algebraic theory of quadratic forms. So we expect a prospective participant to be familiar with linear algebra over arbitrary fields and abstract algebra including Galois theory.

Syllabus and Lecturer
Prerequisites: Linear algebra over arbitrary fields and Galois theory. This material can be fin many books, for instance, in:

1. Artin: Algebra
2. Dummit, Foote: Abstract Algebra.
3. Jacobson: Basic Algebra.
4. Lang: Algebra.

Syllabus: T. Y. Lam: Introduction to quadratic forms over fields

References:

1.  Larry J. Gerstein: Basic quadratic forms.
2.  O'Meara: Introduction to quadratic forms.
3.  Serre: A course in arithmetic.

Speakers/Tutors :

1. A. Chandrakant Sharma, IISER Mohali (Ch. 1. Foundations)
2. Anuradha Garge, University of Mumbai (Ch. 2. Introduction to Witt rings)
3. Shripad Garge, IIT Mumbai (Ch. 3, 4. Quaternion algebras and the Brauer-Wall group)
4. Maneesh Thakur, ISI Delhi (Ch. 5. Clifford algebras)
5. Ch. V. G. Narasimha Kumar, IIT Hyderabad (Ch. 6. Local fields and global fields)
6. Amit Kulshrestha, IISER Mohali (Ch. 11. Field invariants)

There  will  also be guest lectures by senior  mathematicians

1. Anupam Singh, IISER Pune (T)
2. Anuradha Nebhani, IIT Mumbai (T)
3. Anand Sawant, TIFR Mumbai (T)
4. Anirban Bose, ISI Bangalore (T)
5. Preena Samuel, University of Hyderabad (T)
6. Pratyusha Chattopadhyay, ISI Bangalore (T)

Typical daily schedule:

 FN1 9:30 – 11:00 Tea 11:00 – 11:30 FN2 11:30 – 13:00 Lunch 13:00 – 14:30 AN1 14:30 – 15:30 Tea 15:30 – 15:45 An2 15:45 – 16:45 Extra slot (if needed) 17:00 – 18:00
 Monday Tuesday Wednesday Thursday Friday Saturday 06/02/14 06/03/14 06/04/14 06/05/14 06/06/14 06/07/14 FN1 Preview ofthe school Speaker 1 Speaker 1 Speaker 1 Speaker 2 Speaker 3 FN2 Speaker 1 Speaker 2 Speaker 2 Speaker 2 Speaker 3 Review of Week 1 AN1 Tut.0 Tut.1 Tut.1 Tut.1 Free AN2 Tut.1 Tut.2 Tut.2 Tut.2 Tut.3 Free 06/09/14 06/10/14 06/11/14 06/12/14 06/13/14 06/14/14 FN1 Speaker 4 Speaker 4 Speaker 4 Speaker 4 Speaker 4 Speaker 6 FN2 Speaker 3 Speaker 3 Speaker 3 Speaker 3 Speaker 5 Review of week 2 AN1 Tut.4 Tut.4 Tut.4 Tut.4 Tut.4 Free AN2 Tut.3 Tut.3 Tut.3 Tut.3 Tut.5 Fee 06/16/14 06/17/14 06/18/14 06/19/14 06/20/14 06/21/14 FN1 Speaker 5 Speaker 5 Speaker 5 Speaker 5 Speaker 5 FN2 Speaker 6 Speaker 6 Speaker 6 Speaker 6 Speaker 6 AN1 Tut.5 Tut.5 Tut.5 Tut.5 Tut.6 AN2 Tut.6 Tut.6 Tut.6 Feedback Review of the School

Young researchers.
1. Dilpreet Kaur, IISER Mohali (Quadratic forms over fields of characteristic 2)

 Selected Applicants

 Serial SID Full Name Gender Affiliation State Position University/Institute M.Sc./M.A. Year of Passing M.Sc./M.A Ph.D. Degree Date 1 5162 Mr Soutrik Roy Chowdhury Male IISER Mohali Punjab Integrated P.hD student Appeared/ Awaiting Result 2 5318 Mr. Amit Kumar Singh Male The Institute Of Mathematical Sciences Tamil Nadu Ph.D University of Allahabad 2011 3 5367 Ms. Dilpreet Kaur Female IISER Mohali Punjab PhD student Panjab University Chandigarh 2009 4 5380 Mr. Subramani Muthukrishnan Male Chennai Mathematical Institute Tamil Nadu PhD Madras University 2009 5 5504 Mr Sushil Bhunia Male IISER Pune Maharashtra PhD Jadavpur University 2010 6 5585 Mr Abhishek Kumar Shukla Male IISER,Pune 3rd year BS-MS Appeared/ Awaiting Result 7 5615 Mr. Neeraj Sangwan Male IISER Mohali Punjab Integrated MS student Appeared/ Awaiting Result 8 5623 Mr. Anuj Jakhar Male IISER, Mohali Punjab MS Student IISER Mohali Appeared/ Awaiting Result 9 5709 Ms Neha Hooda Female Indian Statistical Institute, Delhi Centre Delhi PhD IIT Delhi 2010 10 5714 Mr. Anirban Bose Male Indian statistical institute, delhi centre Delhi PhD CALCUTTA UNIVERSITY 2008 11 5726 Mr. Sampat Kumar Sharma Male IISER, Mohali Punjab MS student IISER Mohali Appeared/ Awaiting Result 12 5733 Mr Lachit Bora Male Jawaharlal Nehru University Delhi PhD student IIT Madras 2013 13 5734 Mr Sumanth Bharadwaj H S Male Bangalore University Karnataka Ph. D Bangalore University 2008 14 5735 Mr Hemanthkumar B Male Bangalore University Karnataka Ph.D. Bangalore University 2008 15 5748 Mr. Ripan Saha Male IISER, Mohali Punjab PhD IIT KANPUR 2013 16 5762 Mr. Arun Kumar Male Indian Institute Of Science Education And Research Punjab Int. Phd Indian Institute of Science Education And Research Appeared/ Awaiting Result 17 5773 Mr. Satyabrata Jana Male IIT Bhubaneswar Orissa JOINT MSC-PHD STUDENT IIT Bhubaneswar Appeared/ Awaiting Result 18 5780 Mr. Sudip Mazumder Male Bengal College of Engg. & Tech., Durgapur West Bengal Assistant Professor The University of Burdwan 2006 19 5789 Mr. Soumya Dey Male IISER Mohali Punjab PhD 1st Year Student RKM Vivekananda University 2013 20 5797 Ms. Monika Kaushal Female IISER, Mohali Punjab BS-MS Student IISER Mohali Appeared/ Awaiting Result 21 5798 Ms. Leena Jindal Female IISER, Mohali Punjab Integrated PhD IISER Mohali Appeared/ Awaiting Result 22 5799 Mr Nitesh Bhardwaj Male IISER, Mohali Punjab BS-MS student IISER, Mohali Appeared/ Awaiting Result 23 5802 Mr. Rahul Kumar Choudhary Male IISER, Mohali Punjab MS student IISER Mohali Appeared/ Awaiting Result 24 5803 Mr. Amit Ranjan Male IISER, Mohali Punjab M.S. student IISER Mohali Appeared/ Awaiting Result 25 Mohd. Ali Zinna 26 Dr. Manoj Verma 27 Ms. Chetana Sharma

How to reach

• By Air: Arrive at Chandigarh airport. There are many of connecting flights from Delhi/Mumbai to Chandigarh.
• By Train: Nearest railway stations are
1. Chandigarh (Station Code: CDG, 14 Km from IISER)
2. Ambala (Station Code: UMB, 50 Km from IISER)
3. Mohali (Station Code: SASN, 2 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/auto (phone numbers: 0172-4141414, 0172-4242424, 0172-4646464) to IISER Mohali. Almost all the drivers know the location and way to IISER. Neighbouring locations are Indian School of Business (ISB) Mohali and National Institute of Pharmaceutical Education and Research (NIPER) Mohali.  The distance between airport and IISER is about 10 kms and between Chandigarh Railway station and IISER is about 14 Kms. Mohali Railway station (called Sahibzada Ajit Singh Nagar station or SAS Nagar station) is just 2 km from IISER.