|Monday 28||Tuesday 29||Wednesday 30||Thursday 1||Friday 2|
|9:00-10:15||Course 1||Course 1||Course 1||Course 3||Course 3|
|10:45-12:00||Course 2||Course 2||Course 2||Course 4||Course 4|
|12:00-12:45||Talk 1||Talk 4||Talk 7||Talk 10||Talk 15|
|14:30-16:00||Course 3||Course 4||Talk 8 & Talk 9||Talk 11 & Talk 12|
|16:30-17:15||Talk 2||Talk 5||Talk 13|
|17:15-18:00||Talk 3||Talk 6||Talk 14|
Speaker: Bryna Kra
Title: Infinite patterns in large sets of integers
Summary: Resolving a conjecture of Erdos and Turan from the 1930’s, Szemeredi showed that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Soon thereafter, Furstenberg used Ergodic Theory to gave a new proof of this result, leading to the development of combinatorial ergodic theory. These tools have led to uncovering new patterns that must occur in sufficiently large sets of integers and an understanding of what types of structures control these behaviors. Only recently have we been able to extend these methods to infinite patterns, resolving conjectures of Erdos from the 1970s. This series of lectures will cover these new developments, leading to numerous open problems as to what other infinite configurations occur in sufficiently large sets of integers. This is joint work with Joel Moreira, Florian Richter, and Donald Robertson.
Speaker: Scott Schmieding
Title: Automorphism groups of symbolic systems
Summary: The automorphism group of a topological dynamical system consists of all homeomorphisms of the underlying space which commute the base dynamics. In the context of symbolic systems, these groups form a rich collection of countable groups whose structure can vary dramatically depending on the complexity of the underlying dynamics. The automorphism groups of shifts of finite type in particular have been heavily studied, beginning with Hedlund and others in the late 60’s, yet remain highly mysterious. More recent work has focused on these groups in the context of low complexity systems, where their structure is much more constrained. These lectures will give an introduction to these areas, as well as the recently introduced stabilized automorphism groups, along with some newer results on these in the context of shifts of finite type.