Course Outline:
These are all natural, tantalizing questions discussed in cafes, on walks, at parties, and on soccer breaks. They are connected with ideas in K-theory.
Amazingly, some of these questions have been solved, and in some of the other questions, spectacular progress has been made. We are living in awesome mathematical times, and I would like to share them with you.
In this course only a basic, solid background in linear algebra is assumed, so that the members of this class will not fall from their chairs, surprised that vector spaces can be considered over all fields; not necessarily just real or complex numbers. Stress will be given to K0 and K2, as well as to basic Milnor K-theory. Connections with Witt rings of quadratic forms, representation rings, Brauer groups, and cohomology and Galois groups, will be explored. The Bloch-Kato conjecture and its various applications will be discussed.
| Instructor: | Ján Mináč |
| E-mail: | minac@uwo.ca |
| Office: | Middlesex College, room 131 |
| Office Phone: | 519 661-2111 x86519. |
| Office Hours: | Will be discussed in class. |
| Class times and | |
| location: | To be decided in Department of Mathematics meeting, September 8, 2011. |
| Prerequisites: | Good knowledge of undergraduate algebra. |
| Evaluation: | Will be discussed in class. |
Text:
An Algebraic Introduction to K-Theory, by Bruce A. Magurn, Cambridge University Press, 2009. This book will be available at the campus bookstore.
Scholastic offences: Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/univsec/handbook/appeals/scholastic_discipline_grad.pdf