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, 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:

Sep 4: Diogo Pinheiro (Brooklyn College)
Optimal Control of Dynamical Systems with Multiple Sources of Uncertainty

Title: I will discuss optimal control problems associated with dynamical systems containing different sources of randomness. I will focus on the derivation of generalized dynamic programming principles, as well as on the corresponding Hamilton-Jacobi-Bellman equations. Joint work with N. Azevedo (University of Lisbon, Portugal).

Sep 11: Rodrigo Trevino (NYU)
Quasicrystals, Ergodic Theory and Cohomology

I will talk about some recent results on deviation of ergodic averages for systems coming from aperiodic tilings and aperiodic point sets which are self affine (the Penrose tiling is an example of these). These rely on fun interactions between ergodic theory and some cohomology theories associated with aperiodic point sets. Time permiting I will discuss applications to problems of diffraction, counting problems, and futue directions. This is joint work with S. Schmieding (Maryland).

Sep 18: Enrique Pujols (IMPA, Brazil and Graduate Center of CUNY)
The Prisoner’s Dilemma: The Emergence of Cooperation

Note: This is part of the seminar "Dynamical Systems: Ideas in Applications" and will be held in Room 9204.

Sep 25: No seminar

Oct 2 : No seminar

Oct 9: Athanase Papadopoulus (Université de Strasbourg)
On the Arc Metric for Surfaces with Boundary

Oct 16: Konstantin Mischaikow (Rutgers University)
Regulatory Networks

Note: This is part of the seminar "Dynamical Systems: Ideas in Applications" and will be held in Room 4102.

Oct 23: Richard Schwartz (Brown University)
The Projective Heat Map

One of the simplest polygon iterations works by taking a polygon and replacing it by the new polygon whose vertices are the midpoints of the sides of the original one. This construction is related to heat flow and is well understood. In this talk I will explain a projectively natural version of the midpoint map, and I'll explain how you analyze what it does to pentagons. The analysis involves a computer-assisted analysis of a fairly high degree rational map in 2 real variables.

Oct 30: Ethan Akin (City College of New York)
The Prisoner's Dilemma

For the iterated Prisoner's Dilemma, there exist Markov strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally any other strategy, i.e. these are Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent's payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these "good strategies" effectively stabilize cooperative behavior. We characterize the good strategies and relate them to the recent exciting work of Press and Dyson. The talk should be accessible to advanced undergraduates.

Nov 6: Jeremy Kahn (CUNY)
Surface Subgroups, the Ehrenpreis Conjecture, and the Construction of Semi-Arithmetic Fuchsian Groups

Nov 13:

Nov 20: Lai-Sang Young (Courant Institute, NYU)
Dynamics of the Visual Cortex

Note: This is part of the seminar "Dynamical Systems: Ideas in Applications" and will be held in Room 9204.

Nov 27: No seminar

Dec 4: Grace Work (University of Illinois)

Dec 11: Tarik Aougab (Brown University)

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