**Dynamics and Complex Analysis Research Seminar**

Organized by Yunping Jiang (yunping.jiang@qc.cuny.edu)
with Linda Keen and Fred Gardiner

Department of Mathematics, CUNY Graduate Center

Fall of 2015 Schedule

Wednesday, 1:30pm-3:00pm (Math Thesis Room, Rm. 4214-03):

September 16, Jinhua Fan (Nanjing
University of Science and Technology), Universal Teichmuller
space and BMO Teichmuller spaces

September 23, (No Classes, Yom Kippur)

September 30, Jinhua Fan (Nanjing
University of Science and Technology), Complex analytic property of the VMOA Teichmuller spaces

October 7, Tao Chen (Queens Borough Community College),
Characterization of exponential maps

October 14, Linda Keen (Kehman
College and the Graduate Center), Shell components of transcendental meromorphic functions

October 21, Enrique Pujals
(IMPA and The Graduate Cneter), On a conjecture
of Charles Tresser about

surfaces diffeomorphisms in
the boundary of chaos

Abstract:
Inspired by his initial studies about the boundary of chaos for

one-dimensional interval endomorphisms,
C. Tresser conjectured that

in the space of C^k
orientation preserving embedding of the two disk

which are area contracting, maps which belongs to the
boundary of positive

topological
entropy exhibit a period doubling cascade. In a joint work with

S. Crovisier and C. Tresser
we prove such conjecture assuming also

that the embedding are in the boundary of
zero-entropy systems

and are ``strongly dissipative". We will relate our
results with the problem

of (topological) renormalization for two-dimensional diffeormorphisms and

Sharkovskiiś type results.

October 28, Mike Shub (The
Graduate Center), TBA

November 4, Umberto L. Hryniewicz (Universidade Federal do Rio de Janeiro), Title: Systolic
inequalities in symplectic geometry

Abstract:
Given a Reeb flow on a closed
3-manifold,

how small is the smallest period among closed
trajectories?

A
conjecture of Viterbo would imply that for convex
energy levels

in symplectic 4-space the smallest period is not larger than
square

root of contact volume. This question contains as a special
case the

following one: Given a closed riemannian surface, how short is the

shortest non-constant closed geodesic? A conjecture of Babenko-Balacheff

states that for metrics on the 2-sphere near
the round one, the length of the shortest

closed geodesic is not larger than square root of pi times
total area.

In this talk I will discuss recent results concerning both conjectures:

we confirm the Babenko-Balacheff
conjecture (even for metrics not so

close to the round one), and obtain sharp systolic
inequalities for

convex energy levels near the standard
3-sphere. This is joint work

with Abbondandolo, Bramham and Salomão.

November 11, Yingqing Xiao (Hunan Normal University),
TBA

November 18, Junyang Gao (China University of
Mining and Technology (Beijing)), TBA

November 25, Before Thanksgivings, no event

December 2 (2pm-3:20pm), Sudeb Mitra (Queens College and
the Graduate Center), Some metric properties of Teichmueller
space of a closed set in the sphere.

December
9, Enrique Pujals (IMPA and the
Graduate Center), TBA

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