# Previous Talk list

November 13 (Thue), 16:00-17:00

### Surface groups and their normalizers on the dual cube complexes

Location: E6-1 #4415

Speaker: Donggyun Seo (Seoul National University)

Language: English

Abstract

A wallspace, which is named by Haglund-Paulin, has been used as a powerful tool for geometric group theory. The dual cube complex of a wallspace is the CAT(0) cube complex whose pocset structure is identical to the wallspace. In this talk, we will focus on dual cube complexes from the hyperbolic plane with finitely many simple closed geodesics in a finite-area hyperbolic surface, construct a Dehn-twist-like quasi-isometry, and give an answer to the problem suggested by Koberda.

August 23 (Thur), 16:00-17:00

### Non-positively curved cube complexes with hyperbolic fundamental group

Location: E6-1 #4415

Speaker: Federico Vigolo (Oxford University)

Language: English

Abstract

Thanks to Gromov's link condition, it is easy to construct many CAT(0) cube complexes. On the contrary, constructing hyperbolic cube complexes is often a delicate matter. In this talk I will briefly explain the standard technique that is used to show that some Right Angled Coxeter Groups are hyperbolic and I will then introduce a new technique which applies to a larger class of cube complexes (cube complexes with coupled links).

August 14 (Tues), 16:00-17:00

### Kazhdan type theorem for manifolds and complexes

Location: E6-1 #4415

Speaker: Chenxi Wu (Rutger University)

Language: English

Abstract

This is a collaboration with Harry Baik and Farbod Shokrieh. We generalized a classical theorem by Kazhdan on the convergence of canonical metric under a sequence of regular covers to the case of metrizable complexes as well as Riemannian manifolds.

July 12 (Thur), 16:00-17:00

### Nonamenable groups of piecewise projective homeomorphisms

Location: E6-1 #3434

Speaker: Yash Lodha (EPFL)

Language: English

Abstract

Groups of piecewise projective homeomorphisms provide elegant examples of groups that are non amenable, yet do not contain non abelian free subgroups. In this talk I will present a survey of these groups and discuss their striking properties. I will discuss properties such as (non)amenability, finiteness properties, normal subgroup structure, actions by various degrees of regularity and Tarski numbers.

July 5 (Thur), 16:00-17:00

### Rational cobordisms and integral homology

Location: E6-1 #3434

Speaker: Junghwan Park (MPIM)

Language: TBA

Abstract

We show that for any connected sum of lens spaces L there exists a connected sum of lens spaces X such that X is rational homology cobordant to L and if Y is rational homology cobordant to X, then there is an injection from H_1(L; Z) to H_1(Y; Z). Moreover, as a connected sum of lens spaces, X is uniquely determined up to orientation preserving diffeomorphism. As an application, we show that the natural map from the Z/pZ homology cobordism group to the rational homology cobordism group has large cokernel, for each prime p. This is joint work with Paolo Aceto and Daniele Celoria.

June 5 (Tues), 16:30-17:30

### Three-holed sphere groups in PGL(3,R)

Location: E6-1 #4415

Speaker: Jaejeong Lee (KIAS)

Language: Korean

Abstract

Fock and Goncharov (2006) introduced the notion of positive framed PGL(n,R) representations. In this talk we exhibit framed PGL(3,R) representations of the 3-holed sphere group that are "negative" in a certain sense. If we require the boundary holonomies be all quasi-unipotent, then the boundary-embedded and transversal representations in the corresponding relative character variety form an open subset. These examples may be called "relatively Anosov" and properly include the Pappus representations studied by R. Schwartz (1993). If we further restrict to a certain real 1-dimensional subvariety consisting of representations with 2-fold symmetry, then we obtain a PGL(3,R) analogue of the Goldman-Parker conjecture (solved by R. Schwartz in 2001) on the ideal triangle reflection groups in PU(2,1). Joint work in progress with Sungwoon Kim.

June 5 (Tues), 10:30-11:30

### Equivariant K-theory of toric orbifolds

Location: E6-1 #4415

Speaker: Soumen Sarkar (Indian Institute of Technology Madras)

Language: English

Abstract

Toric orbifolds are topological generalization of projective toric varieties. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure an invariant CW-structure of the toric orbifold. In this talk I will discuss 3 different equivariant cohomology theories of toric orbifolds. This is a joint work with V. Uma.

May 16 (Wed), 16:30-17:30

### Rigidity of group actions and geometric group theory

Location: E6-1 #4415

Speaker: Chung Nhân Phú (Sungkyunkwan University)

Language: English

Abstract

In this talk, we present certain rigidity results for group actions via geometric group theory. We will prove a topological version of Popa's measurable cocycle superrigidity theorem for full shifts. In the first part, we provide a new characterization of one end groups via continuous cocycle superrigidity of their full shifts. As a consequence, we have an application in continuous orbit equivalence rigidity. In the second part, we show that every Holder continuous cocycle for the full shifts of every finitely generated group G that has one end, undistorted elements and sub-exponential divergence function is rigidity. This is joint work with Yongle Jiang.

May 15 (Tue), 11:10-12:10

### Convex real projective Dehn fillings

Location: E6-1 #4415

Speaker: Gyeseon Lee (University of Heidelberg)

Language: Korean

Abstract

Thurston's hyperbolic Dehn filling theorem states that if the interior of a compact 3-manifold M with toral boundary admits a complete finite volume hyperbolic structure, then all but finitely many Dehn fillings on each boundary component of M yield 3-manifolds which admit hyperbolic structures. In this talk, I will explain that although Dehn filling is not possible in d-dimensional hyperbolic geometry for d > 3, it is possible in the category of convex real projective d-orbifolds for d = 4, 5, 6. Joint work with Suhyoung Choi and Ludovic Marquis.

May 15 (Tue), 10:00-11:00

### Asymptotic results on affine spheres

Location: E6-1 #4415

Speaker: Nie Xin (KIAS)

Language: English

Abstract

Every properly convex domain in RP^2 carries a pair consisting of a complete Riemannian metric and a holomorphic cubic differential satisfying certain PDE, given by the hyperbolic affine sphere in R^3 projecting to that domain. An intriguing object of study is the interaction between the flat geometry of the cubic differential and the projective geometry of the convex domain. We will explain a local version of a theorem of Dumas and Wolf, showing that if an open subset U of the convex domain is conformal to certain sector region in C with the cubic differential dz^3, then U gives rise to a line segment on the boundary of the convex domain.

April 24 (Tue), 10:30-11:30

### Tangent cones to quasimetric sub-Riemannian spaces and applications

Location: E6-1 #4415

Speaker: Svetlana Selivanova (KAIST)

Language: English

Abstract

A sub-Riemannian space is a manifold with a selected distribution (of "allowed movement directions" represented by the spanning vector fields) of the tangent bundle, which spans by nested commutators, up to some finite order, the whole tangent bundle. Such geometries naturaly arise in nonolonomic mechanics, robotics, thermodynamics, quantum mechanics, neurobiology etc. and are closely related to optimal control problems on the corresponding configuration space. As is well known, there exists an intrinsic Carnot-Caratheodory metric generated by the «allowed» vector fiels. Studying the Gromov's tangent cone to the corresponding metric space is widely used to construct efficient motion planning algorithms for related optimal control systems. We generalize this construction to weighted vector fields, which provides applications to optimal control theory of systems nonlinear on control parameters. Such construction requires, in particular, an extension of Gromov's theory to quasimetric spaces, since the intrinsic C-C metric doesn't exist in this case.

Mar 27 (Tue), 10:30-11:30

### Diffeomorphism groups of critical regularity

Location: E6-1 #4415

Speaker: 김상현 (SNU)

Language: Korean

Abstract

We prove that for each compact connected one-manifold M and for each real number a >=1, there exists a finitely generated group G inside Diff^a(M) such that G admits no injective homomorphisms into the group \cup_{b>a} Diff^b(M). This is a joint work with Thomas Koberda.

Mar 6 (Tue), 10:30-11:30

### Asymptotic translation length on curve complexes

Location: E6-1 #4415

Speaker: 백형렬 (KAIST)

Language: Korean

Abstract

We study the asymptotic translation length on curve complexes of the pseudo-Anosov surface homeomorphisms. We first show that the minimal asymptotic translation length of Torelli groups and pure braid groups are asymptotically 1/\chi(S) where \chi(S) is the Euler characteristic of the surface. If the time permits, we also discuss the asymptotic translation length of pseudo-Anosov monodromies of primitive elements in Thurston’s fibered cone. This talk represents joint work with Hyunshik Shin and Chenxi Wu.

Feb 27 (Tue), 10:30-11:30

### Uniformization theorem and Liouville action for punctured spheres

Location: E6-1 #4415

Speaker: 박진성 (KIAS)

Language: Korean

Abstract

In this talk, I will explain an approach of Poincare to prove the uniformization theorem for punctured spheres, and how it is related to the action functional in the Liouville theory.

### The Zilber-Pink Conjecture and the generalised Cosmetic Surgery Conjecture

Location: E6-1 #3433

Speaker: 전보광 (POSTECH)

Language: TBA

Abstract

In this talk, I will explain how one can generalise the cosmetic surgery conjecture under the assumption of another well-known conjecture in number theory, so called the Zilber-Pink conjecture.

Oct 30 (Tue), 15:00-16:00

### Quasi-isometric invariant of CAT(0) cube complexes

Location: E6-1 #4415

Speaker: 오상록 (KAIST)

Language: 한국어

Abstract

Bestvina, Kleiner and Sageev showed that every 2-quasiflat in a 2-dimensional CAT(0) cube complex is at finite Hausdorff distance from a finite union of 2-dimensional quarter-plane and Huang generalized it to $n$. Using this invariant, several quasi-isometric classification problems in right-angled Artin groups and graph braid groups are solved. In this talk, We discuss how this invariant works when we classify planar graph 2-braid groups up to quasi-isometries.

Oct 24 (Tue), 15:00-16:00

### The set of critical exponents of discrete groups acting on a regular tree

Location: E6-1 #4415

Speaker: 권상훈 (KIAS)

Language: 한국어

Abstract

We discuss the set of critical exponents of discrete groups acting on a regular tree. If the quotient graph is finite, then the critical exponent is an algebraic number. In general, given an arbitrary real number between 0 and the volume entropy of the regular tree, we discuss how we can construct a discrete group whose critical exponent realizes the number. We also study the minimal polynomials of Schottky free discrete groups of rank 2.

September 19 and 26 (Tue), 15:00-16:00

### Geometric inequalities and quasi-local mass for axially symmetric initial data in general relativity (1), (2)

Location: E6-1 #4415 on Sep. 19, and #1409 on Sep. 26

Speaker: 차예슬 Ye Sle Cha (Free University of Berlin)

Language: English

Abstract

In these two talks, I will introduce geometric problems related to mass in general relativity, such as a series of geometric inequalities, and conjectures regarding a notion of quasi-local mass proposed by Bartnik. The geometric inequalities we consider include the angular momentum-mass inequality for axially symmetric initial data for the Einstein equations. Note that the special cases treating maximal data have been proved by Dain et al. Here I will explain how to reduce the general (non-maximal) case to the known maximal case, and then discuss the solvability of the system of Elliptic PDEs arose in the process, for near maximal case. The second part of the talk will mainly provide an introduction to the static/stationary metric extension conjectures, related to Bartnik quasi-local mass. I will briefly discuss some known results for the static metric extension conjecture by Anderson, Anderson/Khuri, Miao et al., and show a local existence theorem for the solutions of axially symmetric, stationary vacuum Einstein equations.

August 23 (Wed), 15:00-16:00

### Dynamics of generalized beta-transformations

Location: E6-1 #4415

Speaker: Chenxi Wu (Rutgers University)

Language: English

Abstract

We study the dynamical properties of the topological generalized beta transformations, which generalizes the concept of generalized beta transformations defined by Gora. In particular, we generalize the result on admissible sequence for unimodular maps to the case of generalized beta maps, and also study the properties of the topological entropy and its Galois conjugates, generalizing some results by Tiozzo. This talk represents an ongoing collaboration with Diana Davis, Kathryn Lindsey and Harry Bray.

August 9 (Wed), 16:00-17:00

### Canonical metric on finite graphs

Location: E6-1 #1409

Speaker: Chenxi Wu (Rutgers University)

Language: English

Abstract

We prove a Kazhdan type theorem for the canonical metrics of finite graphs. Namely, we show that the canonical metric of finite normal coverings of the graph converges when the covering converges, and the limit depends only on the limit of the coverings. We also generalize the argument to higher dimensional simplicial complexes. The proof is mostly based on an analogous argument in the case of Riemann surfaces and Lück's approximation theorem for L^2 cohomology. This is joint work with Farbod Shokrieh.

July 19 (Wed), 15:00-16:00

### The free product structure of diffeomorphism groups

Location: E6-1 #1409

Speaker: Thomas Koberda (University of Virginia)

Language: English

Abstract

I will discuss some aspects of the algebraic structure of finitely generated groups of diffeomorphisms of compact one-manifolds. In particular, we show that if G is not virtually metabelian then (G x Z)*Z cannot act faithfully by C^2 diffeomorphisms on a compact one-manifold. Among the consequences of this result is a completion of the classification of right-angled Artin groups which admit faithful C^{\infty} actions on the circle, a program initiated together with H. Baik and S. Kim. This represents joint work with S. Kim.

June 26 (Mon), 16:00-17:00

### Towers of regular self-covers and linear endomorphisms of tori

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.

June 26 (Mon), 16:00

### Towers of regular self-covers and linear endomorphisms of tori

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.

June 7 (Wed), 15:00

### Is a typical biPerron algebraic unit a pseudo-Anosov dilatation?

Speaker: 백형렬 (KAIST)

Language: Korean

Abstract

We give a statistical answer to a variaion of this problem.

May 31 (Wed), 15:00

### Translation length on extension graphs

Speaker: 신현식 (KAIST)

Language: Korean

Abstract

We report a recent result on the translation length on extension graphs of RAAGs.

May 24 (Wed), 15:00

### Geometric convergence of Kleinian groups

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.

May 17 (Wed), 15:00

### Bipolar filtration of topologically slice knots

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.

April 26 (Wed), 15:00

### Random walks in weakly hyperbolic groups V

Speaker: TBA

Language: Korean

Abstract

Survey of the paper by Joseph Maher and Giulio Tiozzo V

April 12 (Wed), 15:00

### Random walks in weakly hyperbolic groups IV

Speaker: 정홍택 (KAIST)

Language: Korean

Abstract

Survey of the paper by Joseph Maher and Giulio Tiozzo IV

April 5 (Wed), 15:00

### Random walks in weakly hyperbolic groups III

Speaker: 정홍택 (KAIST)

Language: Korean

Abstract

Survey of the paper by Joseph Maher and Giulio Tiozzo III

March 29 (Wed), 15:00

### Random walks in weakly hyperbolic groups II

Speaker: 정성구 (KAIST)

Language: Korean

Abstract

Survey of the paper by Joseph Maher and Giulio Tiozzo II

March 22 (Wed), 15:00

### Collar lemma for Hitchin representations

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.

March 15 (Wed), 15:00

### Random walks in weakly hyperbolic groups I

Speaker: 오상록 (KAIST)

Language: Korean

Abstract

Survey of the paper by Joseph Maher and Giulio Tiozzo I