AIS Quadratic Forms (2014)
|Venue:||Indian Institute of Science Education and Research (IISER), Mohali|
|Dates:||2nd - 21st June, 2014|
|Convener(s)||Speakers, Syllabus and Time table||Applicants/Participants|
|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.
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:
- Artin: Algebra
- Dummit, Foote: Abstract Algebra.
- Jacobson: Basic Algebra.
- Lang: Algebra.
Syllabus: T. Y. Lam: Introduction to quadratic forms over fields
- Larry J. Gerstein: Basic quadratic forms.
- O'Meara: Introduction to quadratic forms.
- Serre: A course in arithmetic.
- A. Chandrakant Sharma, IISER Mohali (Ch. 1. Foundations)
- Anuradha Garge, University of Mumbai (Ch. 2. Introduction to Witt rings)
- Shripad Garge, IIT Mumbai (Ch. 3, 4. Quaternion algebras and the Brauer-Wall group)
- Maneesh Thakur, ISI Delhi (Ch. 5. Clifford algebras)
- Ch. V. G. Narasimha Kumar, IIT Hyderabad (Ch. 6. Local fields and global fields)
- Amit Kulshrestha, IISER Mohali (Ch. 11. Field invariants)
There will also be guest lectures by senior mathematicians
- Anupam Singh, IISER Pune (T)
- Anuradha Nebhani, IIT Mumbai (T)
- Anand Sawant, TIFR Mumbai (T)
- Anirban Bose, ISI Bangalore (T)
- Preena Samuel, University of Hyderabad (T)
- 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|
|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|
|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|
|FN1||Speaker 5||Speaker 5||Speaker 5||Speaker 5||Speaker 5|
|FN2||Speaker 6||Speaker 6||Speaker 6||Speaker 6||Speaker 6|
|AN2||Tut.6||Tut.6||Tut.6||Feedback||Review of the School|
1. Dilpreet Kaur, IISER Mohali (Quadratic forms over fields of characteristic 2)
|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
- Chandigarh (Station Code: CDG, 14 Km from IISER)
- Ambala (Station Code: UMB, 50 Km from IISER)
- 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.