Extremal Length Geometry Seminar

 

Organized by Fred Gardiner (frederick.gardiner@gmail.com) with Yunping Jiang and Linda Keen

Department of Mathematics

CUNY Graduate Center

Fall of 2013 Schedule 

Wednesday, 3:30pm-4:55pm (Math Thesis Room, Rm. 4214-03):

 

January 29, No Event (First Week of the Semester)

February 5, Fred Gardiner (GC), The quasidisc cocycle and on the uniqueness problem of symmetric invariant measures I.

February 12, No Event (Lincolnís Birthday)

February 19, Fred Gardiner (GC), The quasidisc cocycle and on the uniqueness problem of symmetric invariant measures II

February 26, Fred Gardiner (GC), The quasidisc cocycle and on the uniqueness problem of symmetric invariant measures III

March 5, TBA or Fred Gardiner (GC), The quasidisc cocycle and on the uniqueness problem of symmetric invariant measures IV

March 12, No Event (YPJ will be UMA)

March 19, Zhe Wang (BCC), Teichmuller theory and quadratic differentials I

March 26, Kealey Dias (BCC), Title: Landing Separatrices are Stable.

††††††††††††††††††††††††††††††††††††††††††††††††† Abstract: The main objects of study in this talk are the (single-variable)

††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† complex polynomial (autonomous) ODEs.

††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† We are interested in these objects from a qualitative dynamics perspective.  

††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† This elementary talk will first outline the basic properties of these ODEs.

††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Then the main proof, joint result with Tan Lei, will show that the topological

††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††structure of the maximal trajectories exhibits a kind of stability under certain bifurcations.

April 2, Maxime Fortier Bourque (GC), A generalization of Teichmuller's theorem for embeddings

April 9, Maxime Fortier Bourque (GC), Moving one Riemann surface inside another

April 16, No Event (Spring Break)

April 23, Diogo Pinheiro (BC), Title: Non-integrability of the motion of a charged particle

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† in a lattice of fixed charges and under the effect of

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† a uniform magnetic field

†††††††††††††††††††††††††††††††††††††††††††† Abstract: We study the dynamical properties of the motion of a charged particle

†††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††in a lattice of fixed charges and under the effect of

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† a uniform magnetic field. This dynamical system is Hamiltonian with two degrees of freedom.

†††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††The main result states that there exists a subset on the space of parameters

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† and energy level sets for which there is an invariant subset where the Hamiltonian system

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† under consideration contains a suspension of a subshift of finite type with positive entropy.

April 30, Fred Gardiner (GC), Teichmuller theory and quadratic differentials III (representation of the derivatives of length invariants by quadratic differentials)

May 7, Fred Gardiner (GC), Teichmuller theory and quadratic differentials IV (representation of the derivatives of length invariants by quadratic differentials)

May 14, TBA