The University of Michigan Geometry Seminar
Fall 2004: Tuesdays 3:10-4:00, 3096 East Hall

Seminar for September 14, 2004

Dan Burns (University of Michigan)

``RATIONALITY OF RENORMALIZED CHERN CLASSES"

Abstract: Renormalized Chern forms are invariants of a complex manifold X with strongly pseudoconvex boundary M. They give rise to numerical invariants because though X may have infinite (invariant) volume, the characteristic numbers are given by convergent integrals. Prompted by numerous examples in two complex dimensions, JS Ryu and the speaker have shown that if the boundary M is locally spherical (CR equivalent to the sphere), then these forms give rational cohomology classes. The methods of proof are analytic continuation and showing that monodromy eigenvalues are roots of unity, and a residue calculation. Speculations on the real analogue, and analytic applications will also be discussed.




Information for speakers
East Hall, the home of the Department of Mathematics, stands at the corner of Church St. and South University Ave. in Ann Arbor. Check out maps and directions,dining advice, the calendar of local events, the weather forecast, and the lowest fares to/from Detroit (DTW). Lodging options include the university-operated Michigan League and Oxford Conference Center (both within walking distance of East Hall), as well as a number of hotels.
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UM Math seminars