Mathematical Sciences - Colloquium

An Introduction to Noncommutative Geometry Professor Adam Nyman Algebra Candidate Pomona College Given a system of polynomial equations (in n unknowns) with real coefficients, can we find all real solutions, i.e. can we find all n-tuples of real matrices such that When , solutions are elements of . The set of all solutions is a geometric object called a variety. Algebraic geometry is the study of the interplay between the geometry of the variety and the nature of the polynomials When d >1, it is often true that for matrices M and N, so in this case, our equations are "noncommutative". Is there still a bridge between the worlds of algebra and geometry? We describe recent efforts to make sense of the notion "noncommutative variety". We shall see that, while some important noncommutative varieties don't have any points, they can be embedded in slightly larger spaces which have enough points so that they can be understood geometrically. Friday, 8 March 2002 4:10 p.m. in Math 109 Coffee/treats at 3:30 p.m. Math 104 (Lounge)

Spring 2002 Colloquium Schedule | Mathematical Sciences | The University of Montana