Math 520/620/702, Fall 2011

Quadratic forms

Faculty: David Harbater
E-mail: harbater AT math.upenn.edu
Telephone: (215) 898-9594; Department office: (215) 898-8178
Office: DRL 4E2A; Department office: DRL 4W1-6.
Office hours: After class, by appointment, and as scheduled.

Quadratic forms: This course will study quadratic forms from an algebraic and arithmetic point of view. It is intended for a wide range of students, ranging from advanced undergraduates who have had Math 502/503 or the equivalent, to grad students who might already have taken the more usual version of Math 620 (class field theory). Topics will include quadratic spaces, Witt groups and rings, quaternion algebras, Brauer group, quadratic forms over local and global fields, Hasse-Minkowski, and field invariants.

Class schedule: Mon and Wed, 1:30-3pm in DRL 4C8.

Textbook: T.Y. Lam, Introduction to Quadratic forms over Fields, Graduate Studies in Mathematics, vol. 67, AMS, 2005.
Course structure: The class will meet twice weekly. There will be regular homework assignments to be handed in. Those students who are registered in 620 or 702 will also make oral presentations, either individually or in groups. Those who are registered in 520 can also choose to make such a presentation for extra credit.

Homework assignments for Math 502

Student presentations: Presentations can be made individually, or in groups of two or three, depending on the scope of the presentation. Individual presentations should be for 20-30 minutes; group presentations should be about twice that length. Presentations can be made on suggested topics or on other approved topics. Presentations will be made at the beginning of class, beginning November 21, until the last day of class. Topics and dates need to be reserved and approved in advance. To request or reserve a topic, as well as to reserve a time, email Prof. Harbater.

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