## Seminar information archive

Seminar information archive ～05/26｜Today's seminar 05/27 | Future seminars 05/28～

#### Mathematical Biology Seminar

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Effect of demographic stochasticity on large amplitude oscillation

**Malay Banerjee**(Department of Mathematics & Statistics, IIT Kanpur)Effect of demographic stochasticity on large amplitude oscillation

[ Abstract ]

Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.

Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.

#### thesis presentations

15:30-16:45 Room #128 (Graduate School of Math. Sci. Bldg.)

#### FMSP Lectures

10:15-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf

**Christian Schnell**(Stony Book University)Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

[ Abstract ]

Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

[ Reference URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf

### 2018/07/17

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Positive flow-spines and contact 3-manifolds (JAPANESE)

**Masaharu Ishikawa**(Keio University)Positive flow-spines and contact 3-manifolds (JAPANESE)

[ Abstract ]

A contact structure is a smooth distribution of hyperplanes on an odd-dimensional manifold that is non-integrable everywhere. In the case of dimension 3, there is a nice relationship between open book decompositions of 3-manifolds and contact structures up to contactomorphisms, called Giroux correspondence. A flow-spine is a spine of a 3-manifold admitting a flow such that it is transverse to the spine and the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. In this talk, we introduce some results in progress that give a correspondence between contact structures and positive flow-spines by regarding Reeb vector fields as flows of spines. This is a joint work with Y. Koda (Hiroshima) and H. Naoe (Tohoku).

A contact structure is a smooth distribution of hyperplanes on an odd-dimensional manifold that is non-integrable everywhere. In the case of dimension 3, there is a nice relationship between open book decompositions of 3-manifolds and contact structures up to contactomorphisms, called Giroux correspondence. A flow-spine is a spine of a 3-manifold admitting a flow such that it is transverse to the spine and the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. In this talk, we introduce some results in progress that give a correspondence between contact structures and positive flow-spines by regarding Reeb vector fields as flows of spines. This is a joint work with Y. Koda (Hiroshima) and H. Naoe (Tohoku).

#### thesis presentations

15:30-16:45 Room #128 (Graduate School of Math. Sci. Bldg.)

#### Infinite Analysis Seminar Tokyo

16:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Operator algebra for statistical model of square ladder (ENGLISH)

**Valerii Sopin:**(Higher School of Economics (Moscow))Operator algebra for statistical model of square ladder (ENGLISH)

[ Abstract ]

In this talk we will define operator algebra for square ladder on the basis

of semi-infinite forms.

Keywords: hard-square model, square ladder, operator algebra, semi-infinite

forms, fermions, quadratic algebra, cohomology, Demazure modules,

Heisenberg algebra.

In this talk we will define operator algebra for square ladder on the basis

of semi-infinite forms.

Keywords: hard-square model, square ladder, operator algebra, semi-infinite

forms, fermions, quadratic algebra, cohomology, Demazure modules,

Heisenberg algebra.

### 2018/07/13

#### Colloquium

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Pluripotential theory and complex dynamics in higher dimension

**DINH Tien Cuong**(National University of Singapore )Pluripotential theory and complex dynamics in higher dimension

[ Abstract ]

Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

### 2018/07/11

#### Operator Algebra Seminars

17:15-18:45 Room #126 (Graduate School of Math. Sci. Bldg.)

Recent progress in the classification of amenable C*-algebras (cont'd)

**George Elliott**(Univ. Toronto)Recent progress in the classification of amenable C*-algebras (cont'd)

### 2018/07/10

#### Algebraic Geometry Seminar

15:30-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

The effective bound of anticanonical volume of Fano threefolds (English)

**Ching-Jui Lai**(NCKU)The effective bound of anticanonical volume of Fano threefolds (English)

[ Abstract ]

According to Mori's program, varieties covered by rational curves are

built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the

dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)

of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical

volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,

where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).

Our aim is to find an effective bound of the anticanonical volume -K^3, which is

not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss

some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.

This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.

According to Mori's program, varieties covered by rational curves are

built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the

dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)

of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical

volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,

where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).

Our aim is to find an effective bound of the anticanonical volume -K^3, which is

not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss

some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.

This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.

#### Lectures

15:00-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the moduli space of flat symplectic surface bundles

**Sam Nariman**(Northwestern University)On the moduli space of flat symplectic surface bundles

[ Abstract ]

There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.

In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of

Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.

There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.

In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of

Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Loose Legendrians and arboreal singularities (ENGLISH)

**Emmy Murphy**(Northwestern University)Loose Legendrians and arboreal singularities (ENGLISH)

[ Abstract ]

Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.

Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.

#### Numerical Analysis Seminar

16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)

Free surface flow using orthogonal basis bubble function finite element method (Japanese)

**Junichi Matsumoto**(AIST)Free surface flow using orthogonal basis bubble function finite element method (Japanese)

### 2018/07/09

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Rigidity results for symplectic curvature flow (ENGLISH)

**Casey Kelleher**(Princeton University)Rigidity results for symplectic curvature flow (ENGLISH)

[ Abstract ]

We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.

We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.

### 2018/07/03

#### Tuesday Seminar on Topology

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)

**Jun Yoshida**(The University of Tokyo)Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)

[ Abstract ]

The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.

The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Surface automorphisms and Salem numbers (English)

**Xun Yu**(Tianjin University)Surface automorphisms and Salem numbers (English)

[ Abstract ]

The entropy of a surface automorphism is either zero or the

logarithm of a Salem number.

In this talk, we will discuss which Salem numbers arise in this way. We

will show that any

supersingular K3 surface in odd characteristic has an automorphism the

entropy of which is

the logarithm of a Salem number of degree 22. In particular, such

automorphisms are

not geometrically liftable to characteristic 0.

The entropy of a surface automorphism is either zero or the

logarithm of a Salem number.

In this talk, we will discuss which Salem numbers arise in this way. We

will show that any

supersingular K3 surface in odd characteristic has an automorphism the

entropy of which is

the logarithm of a Salem number of degree 22. In particular, such

automorphisms are

not geometrically liftable to characteristic 0.

### 2018/07/02

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Distributional limit theorems for intermittent maps (JAPANESE)

**Toru SERA**(Graduate School of Science, Kyoto University)Distributional limit theorems for intermittent maps (JAPANESE)

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Rigidity of certain groups of circle homeomorphisms and Teichmueller spaces (JAPANESE)

**Katsuhiko Matsuzaki**(Waseda University)Rigidity of certain groups of circle homeomorphisms and Teichmueller spaces (JAPANESE)

[ Abstract ]

In this talk, I explain a complex analytic method and its applications

for the study of quasisymmetric homeomorphisms of the circle by extending them to the unit disk quasiconformally.

In RIMS conference "Open Problems in Complex Geometry'' held in 2010,

I gave a talk entitled "Problems on infinite dimensional Teichmueller spaces", and

mentioned several problems on the fixed points of group actions on

the universal Teichmueller space and its subspaces, and the rigidity of conjugation of

certain groups of circle homeomorphisms.

I will report on the development of these problems since then.

In this talk, I explain a complex analytic method and its applications

for the study of quasisymmetric homeomorphisms of the circle by extending them to the unit disk quasiconformally.

In RIMS conference "Open Problems in Complex Geometry'' held in 2010,

I gave a talk entitled "Problems on infinite dimensional Teichmueller spaces", and

mentioned several problems on the fixed points of group actions on

the universal Teichmueller space and its subspaces, and the rigidity of conjugation of

certain groups of circle homeomorphisms.

I will report on the development of these problems since then.

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Convex integration in fluid dynamics (English)

**László Székelyhidi Jr.**(Universität Leipzig)Convex integration in fluid dynamics (English)

[ Abstract ]

In the talk we present the technique of convex integration for constructing weak solutions to various equations in fluid mechanics.

We will focus on the recent resolution of Onsagers conjecture, but also discuss further directions and in particular the applicability to dissipative systems.

In the talk we present the technique of convex integration for constructing weak solutions to various equations in fluid mechanics.

We will focus on the recent resolution of Onsagers conjecture, but also discuss further directions and in particular the applicability to dissipative systems.

### 2018/06/29

#### Colloquium

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Power concavity for parabolic equations (日本語)

**Kazuhiro Ishige**(The University of Tokyo)Power concavity for parabolic equations (日本語)

### 2018/06/27

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

TBA

**Seung-Hyeok Kye**(Seoul National Univ.)TBA

### 2018/06/26

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Varieties with nef diagonal (English)

**Kiwamu Watanabe**(Saitama)Varieties with nef diagonal (English)

[ Abstract ]

For a smooth projective variety $X$, we consider when the diagonal $Δ _X$ is nef as a

cycle on $X \times X$. In particular, we give a classication of complete intersections and smooth

del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for

spherical varieties. This is a joint work with Taku Suzuki.

For a smooth projective variety $X$, we consider when the diagonal $Δ _X$ is nef as a

cycle on $X \times X$. In particular, we give a classication of complete intersections and smooth

del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for

spherical varieties. This is a joint work with Taku Suzuki.

#### Tuesday Seminar of Analysis

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

The Cauchy problem of the drift-diffusion system in R^n (日本語)

**OGAWA Takayoshi**(Tohoku University)The Cauchy problem of the drift-diffusion system in R^n (日本語)

[ Abstract ]

We consider the Cauchy problem of the drift-diffusion system in the whole space. Introducing the scaling critical case, we consider the solvability of the drift-diffusion system in the whole space and give some large time behavior of solutions. This talk is based on a collaboration with Masaki Kurokiba and Hiroshi Wakui.

We consider the Cauchy problem of the drift-diffusion system in the whole space. Introducing the scaling critical case, we consider the solvability of the drift-diffusion system in the whole space and give some large time behavior of solutions. This talk is based on a collaboration with Masaki Kurokiba and Hiroshi Wakui.

### 2018/06/25

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets (JAPANESE)

**Yushi HAMAGUCHI**(Graduate School of Science, Kyoto University)BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets (JAPANESE)

#### Discrete mathematical modelling seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Gap Probabilities and discrete Painlevé equations

**Anton Dzhamay**(University of Northern Colorado)Gap Probabilities and discrete Painlevé equations

[ Abstract ]

It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).

This is joint work with Alisa Knizel (Columbia University)

It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).

This is joint work with Alisa Knizel (Columbia University)

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Cornered Asymptotically Hyperbolic Spaces

**Stephen McKeown**(Princeton University)Cornered Asymptotically Hyperbolic Spaces

[ Abstract ]

This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.

This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.

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