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.

Logistics

All of the talks and refreshments will take place in the IUPUI Science Building, room LD 026. Campus Map

Abstracts

Schedule of talks

Learning talks BY AND FOR grad students, postdocs, and young faculty:

• Dianne Holcomb (U. Arizona): The Ising Model
• Hongming Nei (Indiana University): Self-similar groups and Iterated Monodromy Groups.

• Stefano Silvestri (IUPUI): Compactness Theorem for Subharmonic Functions.
• Joanna Furno (IUPUI): Application of the Compactness Theorem for Subharmonic Functions to Brolin's Theorem.
• Sara Lapan (Northwestern and UC Riverside): What is a closed positive (1,1) current and explanation of introduction to ``Brolin's Theorem in Dimension 2'' by Favre and Jonsson.

• Mikel de Viana (Georgia Tech): Fisher Zeros on the Diamond Heirarchical Lattice.
• Olivier Remy (École Polytechnique): Lee-Yang zeros for DHL.
• Ivan Chio (IUPUI): Lee-Yang-Fisher zeros for the DHL

• Yuki Takahashi (UC Irvine): Calculation of the spectrum for the action of the Lamplighter group.
• Scott Kaschner (Butler U): Rational map in two variables arising when trying to compute the spectrum of the action of the IMG for z^2-1.
• Danielle Larcomb (U. Denver): Exponential Random Graph Models.

Mini-course talks

• 9:00 - 9:30 Refreshments.
• 9:30 - 10:00 Roland Roeder (IUPUI), Brief explanation of why these three topics are related.
• 10:00 - 11:00 Jeffrey Diller (Notre Dame University), Title: Two-variable rational maps: dynamics by example.
• 11:00 - 11:30 BREAK
• 11:30 - 12:30 Eric Bedford (SUNY Stony Brook), Title: Dynamics of rational maps in dimension two.
• 12:30 - 2:30 LUNCH
• 2:30 - 3:30 Pavel Bleher (IUPUI), Title: Renormalization Group in Statistical Mechanics.
• 4:00 - 5:00 Robert Shrock (SUNY Stony Brook), Title: The Potts Model and Tutte Polynomial, and Associated Connections between Statistical Mechanics and Graph Theory.

• 8:30 - 9:00 Refreshments.
• 9:00 - 10:00 Volodymyr Nekrashevich (Texas A&M University), Title: Self-similar groups, dynamical systems, and spectra.
• 10:10 - 11:10 Andrzej Zuk (Université Paris 7), Title: Automata groups.

Research talks

• 11:30 - 12:30 Sandrine Daurat (University of Michigan), Title: Hyperbolic saddle measures and laminarity for holomorphic endomorphisms of CP^2.
• 12:30 - 2:30 LUNCH
• 2:30 - 3:30 Tanya Firsova (Kansas State University), Title: Hedgehogs in C^2.
• 4:00 - 5:00 Mei Yin (University of Denver), Title: Phase transitions in (generalized) exponential random graphs.

Thursday 8/18, 6:30PM: Conference Dinner at The Ram restaurant and brewery.
Dinner is followed by a special evening lecture titled "Deformation space of rational maps and the topology of moduli space" by John Hubbard (Cornell University and Universite de Provence)

• 8:30 - 9:00 Refreshments.
• 9:00 - 10:00 Robert Shrock (SUNY Stony Brook), Title: Zeros of Chromatic and Tutte (Potts) Polynomials and their Accumulation Sets for Families of Graphs.
• 10:10 - 11:10 Tzu-Chieh Wei (SUNY Stony Brook), Title: Density of Yang-Lee zeros from tensor network methods.
• 11:10 - 11:30 BREAK
• 11:30 - 12:30 Dmytro Savchuk (University of South Florida), Title: Lamplighter groups from affine automorphisms of rooted trees .
• 12:30 - 2:15 LUNCH (ends earlier!)
• 2:15 - 3:15 Andrzej Zuk (Université Paris 7), Title: Spectra of automata.
• 3:30 - 4:30. Open Problem Session

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