Geometry
Seminar
November
20, 2007 (Tuesday)
517 Meng Wah
Complex, HKU
Dr. Kiyonori Gomi
University of Texas,
Austin, USA & IMR Junior Fellow, HKU
Twisted K-theory and finite-dimensional
approximation
2:00 – 3:00pm
Abstract
I
will talk about an answer to a problem in twisted K-theory, that is, to realize
twisted K-groups generally by means of finite-dimensional geometric objects,
like vector bundles. One key to my answer is a twisted version of Furuta's
generalized vector bundle, and the other is a notion of a finite-dimensional
approximation of Fredholm operators.
3:00
– 3:10 Tea
Break
Professor Nessim Sibony
Université de Paris-Sud,
Equidistribution properties for endomorphisms
of
Pk
3:10 – 4:10pm
Abstract
We will discuss the following
conjecture. Let f be a holomorphic endomorphism of Pk
of algebraic degree d ³ 2 and T its Green current. Then d-pn (f n)* [H] converge to sTp for every
analytic subset H of Pk of pure codimension p and of degree s which is generic. Here, H
is generic if either H Ç E = ø or codim H Ç E = p + codim E for any
irreducible component E of a totally
invariant proper analytic subset of Pk. The conjecture is proved
for p = 1 and p = k. In this last case
it means that there is an analytic set E,
totally invariant such that for a not
in E, if we put equal Dirac masses at
the preimages of order n of a, then the
corresponding measures converge independently of a to a measure m, which is
the measure of maximal entropy. To study the case of arbitrary codimension we introduce the theory of super potentials for
positive closed currents on Pk and prove the conjecture for a Zariski dense set of maps. This is joint work with T.C. Dinh.
All are
welcome