[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).

A good general reference is Baxter's Book (free online).

- Dianne Holcomb (U. Arizona): The Ising Model.

Section 1.1 and 2.1-2.4 of BLR and possibly Appendix E.1. Also, Onsager's solution for zero external magnetic field. - Mikel de Viana (Georgia Tech): Fisher Zeros on the Diamond Heirarchical Lattice.

Paper by Derrida, DeSeze, and Itzkson. Possibly also p. 1-4 and Figure 1.3 from Lee-Yang-Fisher zeros for DHL and 2D rational dynamics, II. Global Pluripotential Interpretation. - Danielle Larcomb (U. Denver): Exponential Random Graph Models.

Summary of the key definition and ideas from the paper by Chatterjee and Diaconis.

- Hongming Nei (Indiana University): Self-similar groups and Iterated Monodromy Groups.

Material through Section 3.1, skipping Example 2.5.4, of Nekrashevich survey. - Yuki Takahashi (UC Irvine): Calculation of the spectrum for the action of the Lamplighter group.

Sections 6 and maybe 7 of [GZ]. - 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.

This talk will be based on some calculations Scott, Rodrigo, and Roland did a few years ago. (No notes are available to post.)

Good general references are Paper by Hubbard and Papadopol, Sibony's survey and Dinh and Sibony's later survey.

- Stefano Silvestri (IUPUI): Compactness Theorem for Subharmonic Functions.

Definition of subharmonic functions and proof of Theorem 4.1.9 from The analysis of Linear partial differential operators I by Hormander. (See also Theorem 1.18 from my informal notes.) - Joanna Furno (IUPUI): Application of the Compactness Theorem for Subharmonic Functions to Brolin's Theorem.

Hartogs' Lemma and Application to Complex Dynamics slides by Ivan Chio. - Sara Lapan (Northwestern and UC Riverside): What is a closed positive (1,1) current and explanation of the introduction of [FJ]. Slides from Sara's talk.

For definitions involving currents, see Section 3 of Paper by Hubbard and Papadopol or the appendices from Sibony's survey and Dinh and Sibony's later survey. - Olivier Remy (École Polytechnique): Lee-Yang zeros for the DHL.

Summary of [BLR]. - Ivan Chio (IUPUI): Lee-Yang-Fisher zeros for the DHL

Summary of Lee-Yang-Fisher zeros for DHL and 2D rational dynamics, II. Global Pluripotential Interpretation.

We would like very much for these initial learning talks to do the following:

- provide a background for each of the topics generally
- provide background for specific connections between the topics
- have a colloquium-style atmosphere
- welcome questions and comments from the audience
- be accessible to a first-year graduate student
- be approximately forty minutes in length (and no more than fifty).