Program

Mini-courses

Mini-Course Schedule

Time Monday Tuesday Wednesday Thursday Friday
9:30-10:30 Adam Clay Adam Clay Problem Session Andrés Navas Andrés Navas
10:30-11:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
11:00-12:00 Tyrone Ghaswala Tyrone Ghaswala Problem Session Thomas Koberda Thomas Koberda
12:00-13:30 lunch lunch lunch lunch lunch
13:30-14:30 Adam Clay Adam Clay Andrés Navas Andrés Navas Problem Session
14:30-15:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
15:00-16:00 Tyrone Ghaswala Tyrone Ghaswala Thomas Koberda Thomas Koberda Problem Session

Conference Schedule

Time Monday Tuesday Wednesday Thursday Friday
9:30-10:30 Cameron Gordon Cristóbal Rivas Andrés Navas Zoran Sunic Dale Rolfsen
10:30-11:00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
11:00-12:00 Tao Li Harry Baik Nathan Dunfield Filippo Calderoni Idrissa Ba
12:00-13:30 lunch lunch break lunch lunch
13:30-14:30 Jonathan Johnson Thomas Koberda Sebastian Hurtado Tetsuya Ito
14:30-15:00 Coffee Break Coffee Break Coffee Break Coffee Break
15:00-16:00 Tyrone Ghaswala Michele Triestino Yago Antolin

Abstracts

Introduction to order structures in groups

This course will serve as an introduction to the various kinds of total orders on groups, and their behaviour with respect to other standard algebraic structures and constructions, such as quotients, free products, and amalgams. I will presume no prior knowledge of group orderings and will develop many of the essential tools and structures from scratch, such as the dynamical realisation of an ordering, the Burns-Hale theorem, Hölder’s theorem and its relationship with local indicability, and so forth. Many of the topics, even at a basic level, lead naturally to open problems in the field, and so there will be plenty of connections with open, active areas of research for the more experienced students as well.

Introduction to circular orderings

This course will be a purely algebraic and combinatorial introduction to circularly-orderable groups. We will begin with the definitions and investigate how circular orderability behaves under basic group operations (subgroups, extensions, products, quotients). Then the second cohomology of the group (both bounded and unbounded) will enter the picture, bringing with it the left-ordered central extension of a circularly-ordered group. This will lead to investigating the relationship between properties of the cohomology class of a circular ordering and properties of the circular ordering, and of the group, itself. The course will conclude with a discussion of the obstruction spectrum of a circularly-orderable group and direct products of circularly-orderable groups.

Plenty of fun (for some definition of fun) exercises will be given, some of which are open problems. There will be a small amount of interplay with Adam Clay’s minicourse on left-orderability, but the vast majority of the course will be self-contained.

Countable subgroups of homeomorphism groups: dimension one and beyond

I will discuss some problems concerning finitely generated (and more generally countable) subgroups of homeomorphism groups with specified properties. In dimension one, I will concentrate on regularity, and discuss some aspects of joint work with S. Kim on critical regularity. I will then discuss the outline of a program to generalize results known in dimension one to higher dimension. Along the way, I will discuss a recent result joint with S. Kim and J. de la Nuez Gonzalez about the model theory of homeomorphism groups of compact manifolds, and indicate how those ideas may be generalized in the future.

Spaces of orderings and applications

For an orderable group G, the space of all orders on G carries a natural topology which makes it compact (independently of the cardinality of G). This minicourse will be devoted to study the most general properties of these spaces and their relation with the algebraic properties of the underlying group. Several open questions will be discussed.