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 firstname.lastname@example.org
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: