The K-group at Reed

See the poster!

The K-group is a small summer research team at Reed College focused on Milnor-style K-theories and their applications in number theory, algebraic geometry, and motivic homotopy theory. Under the supervision of Kyle Ormsby, paricipants will undertake a two-week mini-course in K-theory and then pursue various research projects related to Milnor and Milnor-Witt K-theory.

Dates: July 6 - August 28, 2015

Support: Stipends available to qualified applicants.

Requirements: Participants must be students at Reed College who have completed Math 332 or the equivalent by the end of spring term.


July 6: Milnor K-theory, symbols, and Hilbert reciprocity. Notes [pdf].

July 7: Quadratic forms and Witt rings (selections from Chapters I and II of Lam, Introduction to quadratic forms over fields).

July 8: The discriminant, presentation of the Grothendieck-Witt ring, Pfister forms, and the Milnor conjecture (Lam II.2, II.4, and X.6).

July 10: Milnor-Witt K-theory: basic properties. Notes [pdf].

July 13: Stiefel-Whitney invariants (Nico).


Kyle M. Ormsby