The Intensive Lectures on Real Projective Structures
A
workshop on real projective structures and related topics
October
25th to October 27th , 2010
KIAS,
Seoul, KOREA
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 real projective structures and its relationship to
manifold theory. We hope this workshop contributes to acceleration of
research in the field.
Organizers
Inkang Kim (KIAS) and Suhyoung Choi (KAIST)
Confirmed
Participants
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Choi,
Suhyoung
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KAIST
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Kim,
Inkang
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KIAS
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Choi,
Kanghyun
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KAIST
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Lee,
Gye-Seon
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KAIST
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Jeon,
Woojin
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KIAS
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Kim,
Sungwoon
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KIAS
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Overseas
Visitors
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Daniele
Alessandrini
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Max Planck Institute, Bonn
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Programs
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October
25th (Monday)
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10:20-10:30
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Announcements
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10:30-12:00
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Daniele Alessandrini
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Compactification of parameter spaces from a tropical viewpoint
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12:10-1:10
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Lunch
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1:30-2:30
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Suhyoung Choi
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Some notes on the compactification of the deformation spaces of projective structures
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2:40-3:40
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Inkang Kim
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Compactification of real projective structures on surfaces
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3:50-4:50
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Woojin Jeon
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Primitive stability and Bowditch's Q-condition
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October
26th (Tuesday)
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10:20-10:30
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Announcements
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10:30-12:00
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Daniele Alessandrini
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Compactification of parameter spaces from a tropical viewpoint
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12:10-1:10
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Lunch
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1:30-2:30
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Gye-Seon Lee
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Projective Deformations of hyperbolic Coxeter 3-orbifold
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2:40-3:40
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Sungwoon kim
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The simplicial volume of closed manifolds covered by products of hyperbolic planes
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3:50-4:50
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4:50-5:50
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6:00-
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Dinner
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October
27th (Wednesday)
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10:20-10:30
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Announcements
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10:30-12:00
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Daniele Alessandrini
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Compactification of parameter spaces from a tropical viewpoint
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Presentation
You can use
:
Venue
School of Mathematics, KIAS, Seoul, South Korea
Registration
Accomodations:
We will reserve a room for you in KIAS if possible. Please let us
know the type of room desired and
the dates in between
October 25-26. Send us e-mails with names and the other informations.
Registration
Fee
To
be decided later.
Contact
For any
inquiries on the workshop, please contact:
Kang-Hyun
Choi
Korea Advanced Institute of Science and Technology
373-1
Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
Phone:
+82-42-869-2772
Email: kchoi1982 at kaist dot ac dot kr
Abstracts
Gye-Seon Lee: Projective
Deformations of hyperbolic Coxeter 3-orbifold
By using Klein's model for hyperbolic geometry, hyperbolic structures on orbifolds provide examples of real projective structures. By Andreev's theorem, many 3-dimensional reflection orbifolds admit a finite volume hyperbolic structure, and such a hyperbolic structure is unique. However, the induced real projective structure on some such 3-orbifolds deforms into a family of real projective structures that are not induced from hyperbolic structures.
In this talk, I will give new classes of compact hyperbolic reflection 3-orbifolds with such deformations.
Daniele Alessandrini: Compactification of parameter spaces from a tropical viewpoint
The construction of Thurston of compactification of
Teichmüller spaces is only a particular case of a general
construction, called Maslov dequantization, or tropicalization. In the
construction of Thurston this is true at two levels: the construction
of the boundary and the interpretation of the boundary points. In this
mini-course I will explain this relationships, and I will show how to
generalize the construction of Thurston to the parameter spaces of
convex projective structures on Gromov hyperbolic closed manifolds,
using tropical geometry. In the first lecture I will explain the main
ideas behind tropical geometry, the tropicalization of algebraic sets
over algebraically closed fields and the tropicalization of
semi-algebraic sets over real closed fields. In the second lecture I
will explain a general construction of compactification of
semi-algebraic sets that is a generalization of the construction of
Morgan and Shalen, and I will show what happens in the case of
Teichmüller spaces and the spaces of convex projective structures. In
the third lecture I will discuss the interpretation of the boundary
points using tropical geometry.
Woojin Jeon: Primitive stability and Bowditch's Q-condition
The notion of primitive stable representations of a free group is introduced by Y.Minsky
and has its motivation in dynamical action of Out(F_n) on the character variety.
When a free representation is discrete and faithful without parabolics, then it has to be primitive stable.
The proof uses the theory of hyperbolic 3-manifolds and
the Whitehead lemma which is a ciriterion about the primitivity of a cyclically reduced word in F_n.
Moreover, I will talk about some relation between primitive stabiliy and Bowditch's Q-condition.
Sungwoon Kim: The simplicial volume of closed manifolds covered by products of hyperbolic planes
I will introduce the relation between the simplicial volume and the continuous bounded cohomology and talk about the value of the simplicial volume for closed, oriented Riemannian manifolds covered by products of hyperbolic planes.