Foliations on 3-manifolds

Organizers: Siddhi Krishna, Chi Cheuk Tsang, Jonathan Zung

Scientific Committee: Ken Bromberg, Jing Tao, Kathryn Mann

Sponsor: National Science Foundation

This workshop, inspired by the GEAR log cabin workshops, will be a week-long retreat themed around foliations on 3-manifolds. It will take place in St. George, Utah. 

Description: The study of foliations on 3-manifolds has been a fruitful ground of interaction between many ideas in low-dimensional topology. Seminal work of Thurston shows that foliations carry information about representations into 1-dimensional homeomorphism groups, minimal genus of surfaces, the hyperbolic geometry of 3-manifolds, and its symplectic fillings by 4-manifolds. These directions have been explored and expanded in the decades since then, and recent interests in the L-space conjecture and in pseudo-Anosov flows have brought these ideas back together. This workshop aims to provide a beginner-friendly environment for graduate students and postdocs to learn about some perspectives of this theory, and to meet with peers that share similar research interests. We are not expecting prior background in foliations -- simply enthusiasm to learn more about them! For more on participant eligibility, please click here. 

Format: Participants will be divided into small groups that are tasked to develop a minicourse on one subtopic. Each participant will be asked to give a talk as part of the minicourse. 

Potential subtopics include but are not limited to:

• Constructions and existence of foliations (e.g sutured manifolds, laminar branched surfaces, classifications of foliations on Seifert manifolds)

• Foliations and 1-dimensional dynamics (e.g. leaf spaces and actions on \R-trees, universal circles and circular orders)

• Foliations and flows (e.g. transverse pseudo-Anosov flows)

• Foliations and contact structures (e.g. bicontact structures, the Eliashberg-Thurston theorem, sutured Floer homology)