The Student Complex Analysis and Dynamical
Systems Seminar, Meets Friday, 10:30am – 12:30pm, Room: 4419, coordinated by
Yunping Jiang, Linda Keen, and Fred Gardiner
If you have any suggestion and question, please email to Professor
Jiang at
In the fall semester of 2009, we are interested in complex manifold structures of Teichmuller
spaces T(E) of closed sets E and quasiconformal
mapping theory and applications to complex dynamical systems like combinatorial
characterization of rational maps and entire functions. The seminar will start on Sept 11th. Prof. Jiang
will give the first few lectures and distribute a list of general references in
the Sept 11th seminar. Students in the seminar will read these papers and
report in the seminar either in this semester or in the next semester.
List of papers to be read
1.
Douady
and J. H. Hubbard, A proof of Thurston's topological characterization of
rational functions, Acta Math., Vol. 171 (1993),
263-297.
2.
G.
Cui, Y. Jiang, and D. Sullivan, Geometrically finite and semi-rational branched
coverings of the two-sphere (a new version which I just wrote).
3.
G.
Zhang and Y. Jiang, Combinatorial characterization of sub-hyperbolic rational
maps. Advances in Mathematics, Vol. 221 (2009), 1990-2018.
4.
J. H.
Hubbard, D. Schleicher, and M. Shishikura,
Exponential Thurston maps and limits of quadratic differentials, Journal of
Amer. Math. Soc. 22 (2009), 77-117.
5.
F.Gardiner
and N.Lakic, Quasiconformal
Teichmuller Theory, AMS Mathematical Surveys and
Monographs, 76, American Mathematical Society, Providence, RI, 2000.
6.
G. Lieb, Thesis 1990 (also Earle and Mitra,
Variation of moduli under holomorphic
motions, Contemporary Mathematics, Vol. 256 (2000) 39—67).
Schedule:
September 11: Yunping Jiang, On combinatorial characterization of rational maps I
September 18: No class
September 25: Yunping Jiang, On combinatorial characterization of rational maps II
Octoter 2: Fred
Gardiner, Moving points on Riemann surfaces
October 9: Oleg Muzician,
On barycenter extensions of quasisymmetric homeomorphisms I
October 16: Oleg Muzician,
On barycenter extensions of quasisymmetric homeomorphisms II
October 23: Tao Chen, On
canonical Thurston obstructures for branched covers
of two sphere I
October 30: Tao Chen, On
canonical Thurston obstructures for branched covers
of two sphere II
November 6: Hengyu
Zhou, On combinatorial characterization of \lambda e^{z}
November 20: Zhe
Wang, On complex structures on the Techmuller space T(E) I
November 13: Zhe
Wang, On complex structures on the Techmuller space T(E) II
December 4: Michael Beck, Null homotopy for holomorphic motions
December
11: Yunchun Hu, Martingale for
quasisymmetric homeomorphisms of the circle