## Seminar:

Fall 2015, Thursdays, Blocker 506A, 4:00-4:50 PM
__ Date:__ ** September 17 **

**" Mini-Talks "**

* Prof. Volodymyr Nekrashevych

* Prof. Gregory Berkolaiko

* Prof. Volodymyr Nekrashevych

* Prof. Gregory Berkolaiko

__Abstract__ * V. Nekrashevych*: **"Dynamical systems and groups" Abstract**: I will talk about connections between group theory and dynamical systems. One can use groups to study topology of Julia sets of complex dynamical systems, and structure of their parameter spaces (e.g., the Mandelbrot set). There are also interesting connections in the opposite direction: using dynamical systems to construct groups with interesting properties.

*G. Berkolaiko*:

**"Fold me a drum: an origami proof of isospectrality"**

Abstract: In 1966 Kac asked the question "Can one hear the shape of a drum?", i.e. do the frequencies of a drum's vibration fully determine its shape? For plane domains with fixed boundary (which are the closest to the physical drums), this question was asnwered in the negative by Gordon, Webb and Wolpert (GWW) in 1992. Their construction based on the so-called Sunada method (1984) that uses representation theory. Various proofs, generalizations and applications of this construction exist; in particular one recent application is in the study of Dirac points in the spectrum of graphene, by A.Comech and the speaker. In this talk, however, we will go back to the basics and present a proof (due to Chapman) of the GWW example using foldable paper models.

Abstract