Colloquium

Duality in Noncommutative Algebra and Geometry

Amnon Yekutieli Ben Gurion University - Be'er Sheva, Israel on sabbatical at the University of Washington

Duality is one of the fundamental concepts in mathematics. From the basic duality for finite dimensional vector spaces it extends in many directions: Banach spaces and topological groups in analysis, Poincare duality in topology, Serre duality in algebraic geometry, and so on. Grothendieck showed us that working with complexes in the derived category we get even more dualities. Grothendieck's theory of dualizing complexes adapts well to noncommutative rings. It provides a powerful tool to study rings and their representations. It also makes sense on noncommutative algebraic spaces. In the lecture I will sketch the basics of duality theory (with illuminating examples) and explain some applications in noncommutative ring theory. I will mention recent developments in noncommutative algebraic geometry, and some relations to (commutative) algebraic geometry and theoretical physics.

Friday, 14 November 2003 4:10 p.m. in Skaggs 117 Coffee/treats at 3:30 p.m. in Math 104

Fall 2003 Colloquium Schedule          Mathematical Sciences | The University of Montana