Time: Wednesday 15:00 ~ 16:00
Location: #4415-6 at E6-1
Location: E6-1 #1409
Speaker: Wouter van Limbeek (University of Michigan)
Language: English
Abstract
Let M be a closed manifold that admits a nontrivial cover diffeomorphic to itself. Which manifolds have such a self-similar structure? Examples are provided by tori, in which case the covering is homotopic to a linear endomorphism. Under the assumption that all iterates of the covering of M are regular, we show that any self-cover is induced by a linear endomorphism of a torus on a quotient of the fundamental group. Under further hypotheses we show that a finite cover of M is a principal torus bundle. We use this to give an application to holomorphic self-covers of Kaehler manifolds.
Speaker: 백형렬 (KAIST)
Language: Korean
Abstract
We give a statistical answer to a variaion of this problem.
Speaker: 신현식 (KAIST)
Language: Korean
Abstract
We report a recent result on the translation length on extension
graphs of RAAGs.
Speaker: 백형렬 (KAIST)
Language: Korean
Abstract
We introduce the geometric topology on the space of Kleinian groups,
and discuss how to understand it with a simple example.
Speaker: 김민훈 (KIAS)
Language: Korean
Abstract
We show that the bipolar filtration of the smooth concordance group of topologically slice knots introduced by Cochran, Harvey and Horn has nontrivial graded quotients at every stage. To detect a nontrivial element in the quotient, the proof uses Cheeger-Gromov $L^2$ $\rho$-invariants and infinitely many Heegaard Floer correction term invariants simultaneously. This is joint work with Jae Choon Cha.
Speaker: TBA
Language: Korean
Abstract
Survey of the paper by Joseph Maher and Giulio Tiozzo V
Speaker: 정홍택 (KAIST)
Language: Korean
Abstract
Survey of the paper by Joseph Maher and Giulio Tiozzo IV
Speaker: 정홍택 (KAIST)
Language: Korean
Abstract
Survey of the paper by Joseph Maher and Giulio Tiozzo III
Speaker: 정성구 (KAIST)
Language: Korean
Abstract
Survey of the paper by Joseph Maher and Giulio Tiozzo II
Speaker: 이계선 (University of Heidelberg)
Language: English
Abstract
There is a classical result first due to Keen known as the collar lemma for hyperbolic surfaces. A consequence of the collar lemma is that if two closed curves A and B on a closed orientable hyperbolizable surface have non-zero geometric intersection number, then there is an explicit lower bound for the length of A in terms of the length of B, which holds for any hyperbolic structure on the surface. By slightly weakening this lower bound, we generalize this statement to hold for all Hitchin representations. This is a joint work with Tengren Zhang.
Speaker: 오상록 (KAIST)
Language: Korean
Abstract
Survey of the paper by Joseph Maher and Giulio Tiozzo I
Speaker: Mladen Bestvina (Distinguished professor at University
of Utah/visiting distinguished professor at KAIST)
Language: English
Location: #2413 at E6-1
Abstract
Probabilistic methods in geometric group theory have recently gained in importance. In the course I will focus on the setting where a countable group G acts on a (possibly nonproper) Gromov hyperbolic space X. Examples include a mapping class group acting on the associated curve complex, or Out(F_n) acting on the complex of free factors, or a group acting on the contact graph of a CAT(0) cube complex it acts on. Under minor assumptions, Maher-Tiozzo show that a random walk on G, projected to X, almost surely converges to a point in the Gromov boundary of X. I will discuss the proof of this theorem. As an application, we will see that "generic" elements of mapping class groups are pseudo-Anosov, and (following Horbez) we will give a random walk proof of the classical theorem of Ivanov classifying subgroups of mapping class groups.
Speaker: Mladen Bestvina (Distinguished professor at University
of Utah/visiting distinguished professor at KAIST)
Language: English
Location: #2413 at E6-1
Abstract
Probabilistic methods in geometric group theory have recently gained in importance. In the course I will focus on the setting where a countable group G acts on a (possibly nonproper) Gromov hyperbolic space X. Examples include a mapping class group acting on the associated curve complex, or Out(F_n) acting on the complex of free factors, or a group acting on the contact graph of a CAT(0) cube complex it acts on. Under minor assumptions, Maher-Tiozzo show that a random walk on G, projected to X, almost surely converges to a point in the Gromov boundary of X. I will discuss the proof of this theorem. As an application, we will see that "generic" elements of mapping class groups are pseudo-Anosov, and (following Horbez) we will give a random walk proof of the classical theorem of Ivanov classifying subgroups of mapping class groups.
Speaker: Mladen Bestvina (Distinguished professor at University
of Utah/visiting distinguished professor at KAIST)
Language: English
Location: #2413 at E6-1
Abstract
Probabilistic methods in geometric group theory have recently gained in importance. In the course I will focus on the setting where a countable group G acts on a (possibly nonproper) Gromov hyperbolic space X. Examples include a mapping class group acting on the associated curve complex, or Out(F_n) acting on the complex of free factors, or a group acting on the contact graph of a CAT(0) cube complex it acts on. Under minor assumptions, Maher-Tiozzo show that a random walk on G, projected to X, almost surely converges to a point in the Gromov boundary of X. I will discuss the proof of this theorem. As an application, we will see that "generic" elements of mapping class groups are pseudo-Anosov, and (following Horbez) we will give a random walk proof of the classical theorem of Ivanov classifying subgroups of mapping class groups.
다음은 이번 학기에 수리과학과에 방문하시는 분들의 방문 기간 안내입니다. 참고하셔서 많은 discussion이 이뤄질 수 있도록 하시면 좋겠습니다.
Visiting Period: April 29 - May 14
Selected Research Topics
Out(F_n), Mapping class groups, hyperbolic and CAT(0)-spaces, bounded cohomology.
Visiting Period: May 11 - 12
Selected Research Topics
Group actions on homogeneous spaces, lattices of Lie groups, dynamics of group actions on trees and buildings, entropy rigidity.
Visiting Period: May 1 - 5
Selected Research Topics
Hyperbolic Geometry, Geometric Group theory, bounded cohomology, mapping class groups, group-theoretic Dehn fillings.
Visiting Period: May 10 - 12
Selected Research Topics
Kleinian groups, Teichmuller spaces, and 3-manifolds.
Visiting Period: May 6 - 14
Selected Research Topics
Hyperbolic geometry, Riemann surfaces, random surfaces, random 3-manifolds.
Visiting Period: May 10 - 13
Selected Research Topics
Mapping class groups, characteristic classes of bundles, 3-manifolds, homology cobordisms.
Visiting Period: May 10 - 12
Selected Research Topics
random walks on mapping class groups, commensurability of hyperbolic manifolds.
Visiting Period: May 5 - 13
Selected Research Topics
Mapping class groups, pseudo-Anosov homeomorphisms, translation surfaces.
If you have any questions, please contact Hyungryul Baik or Hyunsik Shin.