Connections Between Complex Dynamics, Statistical Physics, and Limiting Spectra of Self-similar Group Actions

Indiana University Purdue University Indianapolis from August 15 to 19, 2016.

Funded by the National Science Foundation, the IUPUI School of Science, and the IUPUI Office for Academic Affairs.

Material for the learning talks.

The objective of these talks is for everyone to learn how certain problems from the Ising Model and self-similar group theories are related to iteration of rational maps (often in two variables).

For the most part, the learning talks will present sections of the following three papers (and of earlier works leading up to them):

[GZ] The Lamplighter Group as a Group Generated by a 2-state Automaton, and its Spectrum (by Grigorchuk and Zuk)

[FJ] Brolin's Theorem for Curves in Two Complex Dimensions (by Favre and Jonsson)

[BLR] Lee-Yang Zeros for the DHL and 2D Rational Dynamics, I. Foliation of the Physical Cylinder. (by Bleher, Lyubich, and Roeder).

Mathematical Physics:
A good general reference is Baxter's Book (free online). Self-Similar Groups Good general references: Nekrashevich survey, Zuk survey.
Several Complex Variables Dynamics (and connections):
Good general references are Paper by Hubbard and Papadopol, Sibony's survey and Dinh and Sibony's later survey.
Further Instructions For the Speakers:
We would like very much for these initial learning talks to do the following: Preparing a good talk on your assigned topic may require some discussions with us by email or skype--we're all very friendly and open to discussion. Please contact us about whatever you need.

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