Professor Detlev Hoffmann (TU Dortmund)

will speak on

Sums of squares invariants of rings

Time: 2:00PM
Date: Fri 16th March 2012
Location: Mathematical Sciences Seminar Room (Ag 1.01) [map]

Abstract: Let R be a ring with identity. The level (resp. sublevel) of R is the smallest positive integer n such that -1 (resp. 0) can be written as a sum of n squares (resp. n+1 squares in a "unimodular" way), or infinity if such an n doesn't exist. The Pythagoras number of R is the smallest n such that each sum of squares in R can be represented as a sum
of n squares or infinity if such an n doesn't exist. We present some old and some more recent results on these invariants with particular emphasis on noncommutative division rings and arbitrary commutative rings.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)

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