This year's concentration area: Arithmetic group theory
The aim of this workshop is to encourage academic activities in the area of geometric topology and promote friendly relations between researchers in this area. Our main focus is knot theory and its relationship to manifold theory. We hope this workshop contributes to acceleration of research in the field.
In this year, we will concentrate on arithmetic group theory and rigidity. The main aim is to introduce the graduate students to this area with applications to geometric topology.
Ki Hyoung Ko (KAIST), Gyo Taek Jin (KAIST) and Suhyoung Choi (KAIST)




January 11^{th} (Monday) 


10:1010:30 
Announcements  
10:3012:00 
Dave Morris 
Introduction to arithmetic group1  
12:101:10 
Lunch 
 
1:102:00 
Taejung Kim  A moduli space of Higgs bundles and a character variety 1  
2:103:00 
Dong Hwa Shin  ycoordinates of elliptic curves  
3:104:00 
JeongRae Kim  Topology and Dynamics of Biological Networks  
4:004:30 
Tea time  
4:305:20 
Youngju Kim  Quasiconformal nonstability for isometry groups in hyperbolic 4space  
January 12^{th} (Tuesday) 

10:2010:30 

Announcements  
10:3012:00 
Dave Morris 
Introduction to arithmetic group2  
12:101:10 
Lunch 
 
1:102:00 
Taejung Kim  A moduli space of Higgs bundles and a character variety 2  
2:103:00 
Seon Hee Lim  Entropy rigidity and measures on the boundary of negatively curved metric spaces  
3:104:00 
Shintaro Kuroki  Equivariant cohomological and cohomological rigidity of toric hyperKahler manifolds  
4:004:30 
Tea time 

4:305:20  Alexander Stoimenow  Around Bennequin's inequality  
5:306:30 
Banquet(Vegetarian)  
January 13^{th} (Wednesday) 
 
10:2010:30 

Announcements  
10:3012:00 
Dave Morris 
Introduction to arithmetic group3  
12:101:10 
Lunch 
 
1:102:00 
Taejung Kim  A moduli space of Higgs bundles and a character variety 3  
2:103:00 
Recess  
3:104:00 
Recess  
4:004:30 
Recess  
4:305:30 
Recess  



You can use :
Electronic File via Notebook + Beam Projector
Manuscript on A4 or letter paper via Document Camera + Beam Projector
Venue
The department of Mathematical Sciences, KAIST, Daejeon, South Korea
Accomodations: We will reserve a room for you in KAIST if possible. Please let us know the type of room desired and
the dates in between January 1014. Send us emails with names and the other informations.
Tour
There will be a. tour of Seoul for foreign speakers. Anyone interested can join us at Kyongbokgung Palace 10: 30 in the morning of Jan 14^{th}. One has to pay fees for yourselves
There will be some lecture fees.
For any inquiries on the workshop, please contact:
KangHyun Choi
Korea
Advanced Institute of Science and Technology
3731 Guseongdong, Yuseonggu,
Daejeon 305701, Republic of Korea
Phone: +82428692772
Email: kchoi1982
at kaist dot ac dot kr
Of course, in general, the answer of this problem is negative (e.g. homotopy complex projective spaces). However, for the important classes in Toric Topology, this problem is still open (e.g. (quasi)toric manifolds).
The cohomological rigidity problem can be also asked to the equivariant cohomology. In this case, Masuda proved that the equivariant cohomology could distinguish toric manifold as algebraic variety. In this talk, we will prove two rigidity theorems of toric hyperKahler manifolds, where the toric hyperKahler manifold is the hyperKahler analogue of toric manifolds.
Roughly, we will prove that the equivariant cohomology distinguishes toric hyperKahler manifolds up to hyperhamiltonian Tisometry, and the (ordinary!) cohomology distinguishes them up to diffeomorphism.
In the first lecture, we will explain a toy model of this equivalence, namely, the equivalence for rank 1 case. In the simplest setting, it will show formal aspects of more complicated cases for a higher rank.
In the second lecture, we will generalize this equivalence to a higher rank. The principal tool for showing this equivalence is the Hitchin's selfduality equation. Moreover, we will also explain the applications of this approach.
In the third lecture, we will study the Dolbeault groupoid, i.e., the moduli space of Higgs bundles, as a dynamical system, i.e., the Hitchin system. We will prove a cohomological criterion for the linearity of Hitchin flows.