KAIX Summer School 2018

KAIST Advanced Institute for Science-X (KAIX) will host its first thematic program this summer. As a part of the program, there will be a summer school on mathematics in June. This year's theme is "Introduction to the recent developments in PDE and Topology, and their intersection." Topology session will be organized by me, and PDE session will be organized by Prof. Soonsik Kwon.

Topology session's title is "Topics in Geometric Group Theory".
PDE session's title is "Dynamics of Partial Differential Equations". 

Now here are more information about the topology session of the summer school. 
One can also take this officially as a course in summer semester of 2018; 
MAS481(25.481): Topics in Mathematics I<Topics in Geometric Group Theory>. 


All talks will be at the building E6-1, Room 2413. 
The schedule is as in the table below. 

  June 25June 26 June 27 June 28 June 29 July 2 
9:00-10:30 Bestvina Bestvina FujiwaraFujiwaraBestvina
10:30-12:00 Bestvina Bestvina FujiwaraFujiwaraBestvina
14:00-15:30BestvinaKoberda Ohshika OhshikaKoberda
15:30-17:00 BestvinaKoberda Ohshika OhshikaKoberda
       

Mladen Bestvina (University of Utah) 
Title: Introduction to Out(F_n)
Abstract: The following topics will be covered. 
1. Stallings folds and applications. 
2. Culler-Vogtmann's Outer space, contractibility, and consequences for Out(F_n) 
3. Lipschitz metric on Outer space, train track maps and growth of automorphisms.

Koji Fujiwara (Kyoto University) 
Title: Group actions on quasi-trees and application.
Abstract: A quasi-tree is a geodesic metric space that is quasi-isometric to a tree. 
With Bestvina-Bromberg, I introduced an axiomatic way to construct a quasi-tree and group actions on it. 
I explain the basic of it, then discuss some applications including some recent ones.

Kenichi Ohshika (Osaka University) 
Title: Kleinian groups and their deformation spaces
Abstract: Historically, deformation spaces of Kleinian groups appeared as generalisations of Teichmuller spaces. Thurston’s work in the 1980s gave a quite novel viewpoint coming from his study of hyperbolic 3-manifolds. In this talk, I shall describe the theory of deformations of Kleinian groups starting from classical work of Bers, Maskit and Marden, and then spend most of time explaining Thurston’s framework. If time permits, I should also like to touch upon the continuity/discontinuity of several invariants defined on deformation spaces.

Thomas Koberda (University of Virginia) 
Title: Regularity of groups acting on the circle
Abstract: There is a rich interplay between the degree of regularity of a group action on the circle and the allowable algebraic structure of the group. In this series of talks, I will outline some highlights of this theory, culminating in a construction due to Kim and myself of groups of every possible critical regularity $\alpha \in [1,\infty)$.There is a rich interplay between the degree of regularity of a group action on the circle and the allowable algebraic structure of the group. In this series of talks, I will outline some highlights of this theory, culminating in a construction due to Kim and myself of groups of every possible critical regularity $\alpha \in [1,\infty)$.


If you have any question, please contact me via email hrbaik(at)kaist.ac.kr. 
 
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