Complex Analysis and Dynamical Systems Student Seminar
Department of Mathematics, CUNY Graduate Center
Schedule: (Friday 10:30am-12noon,Room: 4419)
If you are interested in this seminar and if you have suggestions,
please contact with Professor Yunping Jiang at yunping.jiang@qc.cuny.edu
Please also check our research seminar at http://qcpages.qc.cuny.edu/~zakeri/seminar.html
Spring of 2012 Schedule (Friday, 10:30am-12noon, Room 4419)
1. February 10, organizing and Yunping Jiang,
Title: Geometrization of
sub-hyperbolic semi-rational branched coverings I.
Abstract: Given a sub-hyperbolic semi-rational branched covering
which is not CHL-equivalent a rational map, it must have the non-empty
canonical Thurston
obstruction (as proved in a joint work with Tao Chen). By using this
canonical Thurston obstruction,
we decompose this dynamical system into several sub-dynamical systems.
Each of these sub-dynamical systems is either a post-critically finite
type branched covering or a sub-hyperbolic semi-rational
type branched covering. If a sub-dynamical system is a post-critically
finite type branched covering with a hyperbolic orbifold,
then it has no Thurston obstruction and is combinatorially equivalent to
a unique post-critically finite rational map
(up to conjugations by automorphisms of the Riemann sphere) and, more
importantly, if a sub-dynamical system
is a sub-hyperbolic semi-rational type branched covering, it has no
Thurston obstruction and is CHL-equivalent
to a unique geometrically finite rational map (up to conjugations by
automorphisms of the Riemann sphere).
This is a joint work with Tao Cheng.
2.
February
17, Fred Gardiner, Title: Univalent functions, extremal
length, the minimum Dirichlet principle for measured foliations.
3.
February
24, Hengyu Zhou, Title: Harmonic Map and Heat Flow I.
4.
March
2, Hengyu Zhou, Title: Harmonic Map and Heat Flow II.
5. March 9, Yoshihiko Shinomiya (Tokyo Institute of Technology)
Title: Veech holomorphic families of Riemann
surfaces and Diophantine problem
Abstract: Veech holomorphicfamilies of Riemann surfaces are holomorphic
families constructed from Veech groups.
In this talk, we characterize their holomorphic sections by points of
corresponding flat surfaces.
By applying this characterization, we solve certain Diophantine equations over
function fields.
6. March 16, ShenglanYuan
Title: Complex
dynamics and the related 3x+1 problem
Abstract. The 3x + 1 problem, also known as the Collatz Conjecture, has
attracted much attention over the years.
The problem considers the following iterative
procedure applied to any positive integer: When the given integer is
even,
it is divided by two; when it is odd, it is multiplied by three and one
is added.
The conjecture states that the procedure will eventually reach the
unique
periodical circle 1 ->4 ->2 -> 1. In this talk we'll look at
the 3x + 1 problem
through a complex dynamics point of view and examine the dynamical
implications
on
the problem and generalized problems.
7.
March
23, Ozgur Evren
Title: Kinjo's Results on the Length Spectrum Metric
Abstract: In his 2003 paper, Hiroshige Shiga showed that on the
Teichmuller space of a Riemann surface
with an infinitely generated fundamental group which admits a pants
decomposition where
all the boundary components are either punctures or geodesics with
lengths bounded from
above and below; the topologies defined by the Length Spectrum Metric
and the Teichmuller metric
are the same. The converse to this statement, after remaining open for
some time, was proven to be false
by Erina Kinjo in 2011. We will talk about this result, namely, we will
construct a Riemann surface with
an infinitely generated fundamental group which admits no pants
decomposition where the lengths of
the boundary components are bounded from above, but the Length Spectrum
Metric and the Teichmuller Metric
defines the same topology on the Teichmuller space of the surface.
8.
March
30, Yunping Jiang,
Title:Teichmuller spaces T(E) and
characterization of holomorphic maps.
Abstract: We will review known results in
this direction and mention some interesting problems to work on.
(The following talk, Yunchun Hu, Title: Estimates for Hausdorff dimensions for
non-conformal dynamics, will be rescheduled to next semester).
9. April 6 (Spring Break),
10. April 13 (Spring Break)
11.
April
20 Gerardo Jimenez, Title: Comparison
between the length spectrum metric and the Teichmuller metric under partial
twists.
12.
April
27 No event. Time slot and room are contributed to the
afternoon seminar. (Original Scehdule, Zhe Wang, Title: Quasiconformal
Isotopies from Earle and McMullen.
13.
May
4, Tao Chen, Title: Limiting Thurston maps III.
14.
May
11, Tao Cheng, Title: Geometrization of sub-hyperbolic semi-rational branched coverings
II.
15. May 18, Final Examination Period
Past Student Seminar: