Abstract: 

In real dynamics it is easy to find mappings whose topological entropy is any given real number. For example, a tent map with slope of absolute value equal to s has topological entropy equal to log(s).  In holomorphic dynamics, the situation is more complicated, with all previously known examples having topological entropy equal to log of an algebraic number.   I will explain why this is so and then present a family of "toric" rational self-mappings of the complex projective plane that includes mappings whose topological entropy is log of a transcendental number.   This is joint work with Jeffrey Diller and it builds on previous work of Bell-Diller-Jonsson.  

Bio-Sketch:

 Roland Roeder is a professor at Indiana University Indianapolis who focuses on dynamics in several complex variables and also its connections with problems from mathematical physics.   He has previous research also in hyperbolic geometry.  Prior to arriving at Indiana University Indianapolis, Roeder had positions as a postdoctoral fellow at SUNY Stony Brook, University of Toronto, and the Fields Institute.   He received a PhD in 2005 from Cornell University for work in holomorphic dynamics and a French Doctorate in 2004 from Universite de Provence in Marseille for work in hyperbolic geometry.