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



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, Orsay, France

Equidistribution properties for endomorphisms of Pk

3:10 – 4:10pm



        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