Jan 13 (Tue) 2 pm - 3 pm
KIAS (Room 1423) & Zoom https://kimsh.kr/vz
Javier de la Nuez-González (KIAS)
Title: Sharply k-homogeneous actions on relational structures
Abstract: We say that an action by isomorphisms of a group G on a relational structure M is sharply k-homogeneous if for any two tuples of distinct elements of M, a and a', which are in the same orbit under the diagonal action of Aut(M) there is exactly one element g in G mapping a to a'. I will discuss recent work joint with Rob Sullivan in which we establish sufficient conditions for the existence of sharply k-homogeneous actions of finitely generated virtually free groups on relational Fräissé limits.
Jan 20 (Tue) 10 am - 11:30 am
KIAS (Room 1423) & Zoom https://kimsh.kr/vz
Insung Park (Stony Brook)
Title: Pressure Metrics on Geometric Structures of Manifolds and Dynamical Systems
Abstract: The study of the pressure metric began with the extension of the Weil–Petersson metric from Teichmüller space to quasi-Fuchsian space (Bridgeman–Taylor) and its connection to thermodynamic formalism (McMullen). This talk will review foundational results and recent developments on pressure metrics, followed by open questions and partial results concerning the pressure metric on the space of Blaschke products. The talk is based on joint work with Yan Mary He and Homin Lee.
Jan 23 (Fri) 10 - 11:30 am
Zoom only https://kimsh.kr/vz
Nic Brody (UC Santa Barbara)
Title: Surface Groups and Products of Trees
Abstract: Can a surface group act properly on a product of trees? We examine three distinct approaches to constructing such actions, and ultimately decide that none of them hold much promise. We provide a large amount of computational evidence against these approaches, and instead suggest a strong negation. Central to this analysis is a novel variation on a classical machine learning algorithm which is particularly well-suited for group theory. We describe how this resolves some long-standing computational questions about groups. Finally, we’ll gesture at how this points towards a much larger research program.