Complex Analysis and Dynamics Seminar

Department of Mathematics
Graduate Center of CUNY

Fridays 2:00 - 3:00 pm
Room 5417
Organizers: Ara Basmajian, Patrick Hooper, Jun Hu, Yun Yang, and Saeed Zakeri

Past seminars:

Fall 2006, Spring 2007
Fall 2007, Spring 2008
Fall 2008, Spring 2009
Fall 2009, Spring 2010
Fall 2010, Spring 2011
Fall 2011, Spring 2012
Fall 2012, Spring 2013
Fall 2013, Spring 2014
Fall 2014, Spring 2015
Fall 2015, Spring 2016
Fall 2016, Spring 2017
Fall 2017

Spring 2018:

Feb 9: Daniele Alessandrini (University of Heidelberg)
Geometric Structures with Quasi-Hitchin Holonomy

Higher Teichmuller Theory is a way to generalize Teichmüller Theory to higher rank Lie groups. I will describe some manifolds admitting real and complex projective structures whose holonomy is a Hitchin or a Quasi-Hitchin representation. This generalizes the Thurston’s theories of Fuchsian and Quasi-Fuchsian representations to higher rank Lie groups. The results come from a joint work with Qiongling Li and a joint work with Sara Maloni and Anna Wienhard.

Feb 16: Joseph Maher (College of Staten Island, CUNY)
Random Mapping Classes Have Generic Foliations

A pseudo-Anosov element of the mapping class group determines a quadratic differential, which lies in the principal stratum if all zeroes are simple, equivalently, if the corresponding foliations have trivalent singularities. We show that this occurs with asymptotic probability one for random walks on the mapping class group, and furthermore, the hitting measure on the boundary gives weight zero to foliations with saddle connections. This is joint work with Vaibhav Gadre.

Feb 23: David Aulicino (Brooklyn College of CUNY)
Trajectories on the Platonic Solids

Given any of the five Platonic solids, can we find a straight-line trajectory on the surface of the solid that starts and ends at the same vertex without passing through any other vertex? It was proven for the tetrahedron, octahedron, cube, and icosahedron that there is no trajectory from a vertex to itself that does not pass through another vertex. We will give a simple proof of this for the tetrahedron and outline the proof for the other solids. Finally, we will show that there does indeed exist such a trajectory on the dodecahedron, and using translation surfaces, we give a complete classification of such trajectories. All of the necessary theory of translation surfaces will be developed and the connection to $k$-differentials will be mentioned. This is joint with Jayadev S. Athreya and Pat Hooper.

March 2: Tao Chen (Laguardia Community College of CUNY)
Shell Components of Extended Family of the Tangent Map

Each hyperbolic component of the Mandelbrot set consists of quadratic maps with an attracting periodic cycle. Similarly, we consider the family of maps $f_\lambda=\lambda \tan^p z^q$. Each component of the set of $\lambda$ such that $f_\lambda$ has an attracting cycle is called a shell component. In this talk, we mainly give a topological and combinatorial description of shell components. This is joint work with Linda Keen.

March 9: Enrique Pujals (Graduate Center of CUNY)

March 16:

March 23: Tarik Aougab (Brown University)

April 13: Christian Wolf (City College of CUNY)

April 20: Huiping Pan (Fudan University)

April 27:

May 4:

May 11:

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