Speaker: Michael Yampolsky (U. Toronto)

Title: Renormalization of rotation domains

Abstract: Renormalization has emerged as a key theme in low-dimensional dynamics. I will start with a review of renormalization of maps of the circle, and will then discuss applications of renormalization theory to the study of Siegel disks in one and two complex variables.

Speaker: Robin Deeley (U Colorado)

Title: Minimal dynamical systems

Abstract: A self-homeomorphism of a compact Hausdorff space is called minimal if each of its orbits is dense. I will discuss the following question: given a compact Hausdorff space does there exist a minimal homeomorphism on it? Although the answer is no, a similar question has a positive answer for any finite CW-complex. I will also discuss a number of explicit examples of minimal dynamical systems. All of our constructions are motivated by questions in C*-algebra theory. Nevertheless no knowledge of C*-algebras is required for the talk. This is joint work with Ian Putnam and Karen Strung.

Speaker: Rohit Nagpal (U. Wisconsin)

Title: S_{infty}-equivariant modules over polynomial rings in infinitely many variables

Abstract: Let R be the polynomial ring k[x_1, x_2, ldots] in countably many variables. Cohen proved that S_{infty}-stable ideals in R satisfy the ascending chain condition. This makes the category of smooth equivariant R-modules a noetherian category. Smooth modules over R appear naturally in algebraic statistics and chemistry, and so it makes sense to study this category in detail. The first step in this direction is to understand its spectrum. In this talk, we describe this spectrum. In particular, we show that the S_{infty}-stable ideal I_n generated by n-variable discriminants is in this spectrum. We show that every nonzero S_{infty}-stable ideal must contain I_n for some large n, and so these ideals are of primary interest. We also mention some new algebraic properties of discriminants. This is a part of an ongoing project with Andrew Snowden.

Speaker: Yash Lodha (Ecole Polytechnique Federale de Lausanne)

Title: Group actions on 1-manifolds: A plethora of treasures.

Abstract: The study of group actions on 1-manifolds has seen some striking developments in recent years. In this talk I will describe some concrete examples that illustrate the richness of the theory. These groups are relatives of the famous groups F and T discovered by Richard Thompson in the 1970s.

Speaker: Yago Antolin (U. Autonoma de Madrid)

Title: Growth in graphs with symmetry

Abstract: In the early 1980′s Jim Cannon showed that the Cayley graph of a

group acting properly co-compactly and by isometries on a hyperbolic

space had a growth function (i.e. counting how many vertices at distance

n from a base point) satisfied a linear recursion. This property is now

known as rational growth of the graph. Cannon’s ideas were fundamental

for the development of the theory of automatic groups. In this talk I

will review Cannon’s ideas and I will explain how they can be used to

show the rationality of other growth functions. Part of the talk will

be based on joint works with L. Ciobanu.