Event Detail

Event Type: 
Number Theory Seminar
Date/Time: 
Tuesday, May 31, 2022 - 10:00 to 10:50
Location: 
Zoom only, contact Clayton Petsche for details

Speaker Info

Institution: 
Boston College
Abstract: 

The exponential of the topological entropy of any dynamical system that admits a Markov partition is a special kind of number -- a weak Perron number. These are positive, real, algebraic integers that are at least as big as the modulus of all of their Galois conjugates. A question that remains mysterious is: which weak Perron numbers are realized as exp(entropy) by which families of dynamical systems? For families of unicritical polynomials, this question leads to the definition of Thurston sets and Master Teapots -- 2-D and 3-D (respectively) sets with rich geometric structures that encode information about this question. I will discuss this circle of ideas and some recent results (joint with C. Wu and G. Tiozzo) about the structure of Thurston sets and Master Teapots.