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 9, Organization and Yunping Jiang (Queens College and the Graduate Center), Sarnak’s Conjecture and Ergodic Theory

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



Spring of 2015 Schedule

Fall of 2014 Schedule

Spring of 2014 Schedule

Fall of 2013 Schedule

Spring of 2013 Schedule