• Ser Peow Tan

Title : Identities on hyperbolic surfaces old and new 

Abstract : We will survey some older results on identities on hyperbolic surfaces due to Basmajian, McShane, Bridgeman and Luo-Tan, and talk about some newer results on generalizations of the Basmajian and Bridgeman identities to surfaces with only cusps and/or cone points, and the main ideas behind the proofs. The newer results are based on joint work with Ara Basmajian, Hugo Parlier and Nhat Minh Doan.

• Ara Basmajian

Title : TBA

Abstract : TBA

• Federica Fanoni

Title : Brouwer classes: tempered, well tempered and flows

Abstract : An orientation-preserving homeomorphism of the plane is a Brouwer homeomorphism if it has no fixed points. By looking at the mapping class of such a homeomorphism relative to finitely many orbits, one obtains a mapping class of an infinite-type surface. For these surfaces an interesting family of mapping classes are the tempered ones: loosely speaking, those without any pseudo-Anosov behavior. I will discuss work with Juliette Bavard, Frédéric Le Roux and Nelson Schuback where we relate the fact that a Brouwer class is tempered to a dynamical property of the underlying homeomorphism.

• Sanghoon Kwak 

Title : Thurston's theorem: entropy in dimension one 

Abstract : In his paper named "Entropy in dimension one," Thurston showed that a positive real number h occurs as the topological entropy for an ergodic train track representative of an outer automorphism of a free group if and only if its expansion constant exp(h) is a weak Perron number. This is a powerful result, answering a question analogous to one regarding surfaces and stretch factors of pseudo-Anosov homeomorphisms. In this talk, I will present a streamlined account of Thurston's proof, following joint expository work with Ryan Dickmann, George Domat, Thomas Hill, Carlos Ospina, Priyam Patel, and Rebecca Rechkin. 

• Youngju Kim

Title : TBA

Abstract : TBA

• Jan Kim

Title : Maximal free abelian subgroups of generalized cactus groups

Abstract :  Cactus groups are finitely presented groups acting properly and cocompactly on median graphs, and therefore can be viewed as nonpositively curved groups. This naturally leads to the question of whether they are hyperbolic. For cactus groups, their hyperbolicity can be characterized by the absence of subgroups isomorphic to \mathbb{Z}^2. Regarding this, Genevois studied the algebraic dimension of cactus groups and proposed a conjecture on the maximal ranks of their free abelian subgroups. Motivated by Genevois's work, we study free abelian subgroups of generalized cactus groups, which form a natural generalization of cactus groups. In this talk, we discuss upper bounds on the ranks of free abelian subgroups of generalized cactus groups, and construct explicit free abelian subgroups realizing these bounds in several cases. This is joint work with Junseok Kim.

• Bram Petri

Title : TBA

Abstract : TBA

• Hyeran Cho

Title : TBA

Abstract : TBA

• Inhyeok Choi

Title : Counting closed curves for convex cocompact subgroups 

Abstract : Let X be a closed negatively curved surface and let C be a closed curve on X. How many closed curves on X are there with the same topological type as C and with length less than L? This is a counting problem for the mapping class group orbit. Mirzakhani’s celebrated theorems assert that the count grows polynomially, with precise asymptotics. In this talk, I will report an ongoing project with Dongryul M. Kim and Marie Trin regarding analogous counting problem for the orbits of convex cocompact subgroups. 

• Sebastian Hensel

Title : TBA

Abstract : TBA