## Seminar information archive

Seminar information archive ～12/09｜Today's seminar 12/10 | Future seminars 12/11～

### 2013/12/10

#### FMSP Lectures

13:00-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Corks, plugs, and local moves of 4-manifolds. (JAPANESE)

**Motoo Tange**(University of Tsukuba)Corks, plugs, and local moves of 4-manifolds. (JAPANESE)

[ Abstract ]

Akbulut and Yasui defined cork, and plug

to produce many exotic pairs.

In this talk, we introduce a plug

with respect to Fintushel-Stern's knot surgery

or more 4-dimensional local moves and

and argue by using Heegaard Fleor theory.

Akbulut and Yasui defined cork, and plug

to produce many exotic pairs.

In this talk, we introduce a plug

with respect to Fintushel-Stern's knot surgery

or more 4-dimensional local moves and

and argue by using Heegaard Fleor theory.

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Quantitative unique continuation principle, local behavior of solutions, and bounds on the density of states for Schr\\"odinger operators (ENGLISH)

**Abel Klein**(UC Irvine)Quantitative unique continuation principle, local behavior of solutions, and bounds on the density of states for Schr\\"odinger operators (ENGLISH)

[ Abstract ]

We establish bounds on the density of states measure for Schr\\"odinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a ``density of states outer-measure'' that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-H\\"older continuity for this density of states outer-measure in one, two, and three dimensions for Schr\\"odinger operators, and in any dimension for discrete Schr\\"odinger operators. Our proofs use a quantitative unique continuation principle and the local behavior of approximate solutions of the stationary Schr\\"odinger equation.

(Joint work with Jean Bourgain.)

References: Jean Bourgain and Abel Klein: Bounds on the density of states for Schr\\"odinger operators. Invent. Math. 194, 41-72 (2013).

We establish bounds on the density of states measure for Schr\\"odinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a ``density of states outer-measure'' that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-H\\"older continuity for this density of states outer-measure in one, two, and three dimensions for Schr\\"odinger operators, and in any dimension for discrete Schr\\"odinger operators. Our proofs use a quantitative unique continuation principle and the local behavior of approximate solutions of the stationary Schr\\"odinger equation.

(Joint work with Jean Bourgain.)

References: Jean Bourgain and Abel Klein: Bounds on the density of states for Schr\\"odinger operators. Invent. Math. 194, 41-72 (2013).

### 2013/12/09

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Donaldson-Tian-Yau 予想と K-安定性について (JAPANESE)

**Toshiki Mabuchi**(Osaka University)Donaldson-Tian-Yau 予想と K-安定性について (JAPANESE)

#### Algebraic Geometry Seminar

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

On birationally tririgid Q-Fano threefolds (JAPANESE)

**Takuzo Okada**(Saga University)On birationally tririgid Q-Fano threefolds (JAPANESE)

[ Abstract ]

I will talk about birational geometry of Q-Fano threefolds. A Mori

fiber space birational to a given Q-Fano threefold is called a birational Mori fiber structure of the threefold. The existence of Q-Fano threefolds with a unique birational Mori fiber structure (resp. with two birational Mori fiber structures) is known. In this talk I will give an example of Q-Fano threefolds with three birational Mori fiber structures and also discuss about the behavior of birational Mori fiber structures in a family.

I will talk about birational geometry of Q-Fano threefolds. A Mori

fiber space birational to a given Q-Fano threefold is called a birational Mori fiber structure of the threefold. The existence of Q-Fano threefolds with a unique birational Mori fiber structure (resp. with two birational Mori fiber structures) is known. In this talk I will give an example of Q-Fano threefolds with three birational Mori fiber structures and also discuss about the behavior of birational Mori fiber structures in a family.

### 2013/12/06

#### Geometry Colloquium

17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Normalized entropy versus volume for pseudo-Anosovs (JAPANESE)

**Sadayoshi KOJIMA**(Tokyo Institute of Technology)Normalized entropy versus volume for pseudo-Anosovs (JAPANESE)

[ Abstract ]

We establish an explicit linear inequality between the normalized entropy of pseudo-Anosov automorphisms and the hyperbolic volume of their mapping tori, based on a recent result by Jean-Marc Schlenker on renormalized volume of quasi-Fuchsian

manifolds. This is a joint work with Greg McShane.

We establish an explicit linear inequality between the normalized entropy of pseudo-Anosov automorphisms and the hyperbolic volume of their mapping tori, based on a recent result by Jean-Marc Schlenker on renormalized volume of quasi-Fuchsian

manifolds. This is a joint work with Greg McShane.

#### FMSP Lectures

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Horospheres: geometry and analysis (II) (ENGLISH)

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

**Simon Gindikin**(Rutgers University)Horospheres: geometry and analysis (II) (ENGLISH)

[ Abstract ]

About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

[ Reference URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

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

#### Colloquium

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

**Naoki Imai**(Graduate School of Mathematical Scinences, The University of Tokyo)Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

#### Colloquium

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

**Naoki Imai**(Graduate School of Mathematical Sciences, The University of Tokyo)Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

### 2013/12/05

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Variational characterizations of exact solutions of the Einstein equation (JAPANESE)

**Sumio Yamada**(Gakushuin University)Variational characterizations of exact solutions of the Einstein equation (JAPANESE)

[ Abstract ]

There are a set of well-known exact solutions to the Einstein equation. The most important one is the Schwarzschild metric, and it models a Ricci-flat space-time, which is asymptotically flat. In addition, there are the Reissner-Nordstrom metric and the Majumdar-Papapetrou metric, which satisfy the Einstein-Maxwell equation, instead of the vacuum Einstein equation. In a jointwork with Marcus Khuri and Gilbert Weinstein, it is shown that those metrics are characterized as the equality

cases of a set of so-called Penrose-type inequalities. The method of proof is a

conformal deformation of Riemannian metrics defined on the space-like slice of the space-time.

There are a set of well-known exact solutions to the Einstein equation. The most important one is the Schwarzschild metric, and it models a Ricci-flat space-time, which is asymptotically flat. In addition, there are the Reissner-Nordstrom metric and the Majumdar-Papapetrou metric, which satisfy the Einstein-Maxwell equation, instead of the vacuum Einstein equation. In a jointwork with Marcus Khuri and Gilbert Weinstein, it is shown that those metrics are characterized as the equality

cases of a set of so-called Penrose-type inequalities. The method of proof is a

conformal deformation of Riemannian metrics defined on the space-like slice of the space-time.

### 2013/12/04

#### Seminar on Probability and Statistics

13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)

A quantile-based likelihood estimator for information theoretic clustering (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/09.html

**HINO, Hideitsu**(University of Tsukuba)A quantile-based likelihood estimator for information theoretic clustering (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/09.html

#### FMSP Lectures

15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Horospheres: geometry and analysis (I) (ENGLISH)

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

**Simon Gindikin**(Rutgers University)Horospheres: geometry and analysis (I) (ENGLISH)

[ Abstract ]

About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

[ Reference URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

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

### 2013/12/03

#### Tuesday Seminar on Topology

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

Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)

**Bruno Martelli**(Univ. di Pisa)Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)

[ Abstract ]

(joint work with A. Kolpakov)

We introduce a simple algorithm which transforms every

four-dimensional cubulation into a cusped finite-volume hyperbolic

four-manifold. Combinatorially distinct cubulations give rise to

topologically distinct manifolds. Using this algorithm we construct

the first examples of finite-volume hyperbolic four-manifolds with one

cusp. More generally, we show that the number of k-cusped hyperbolic

four-manifolds with volume smaller than V grows like C^{V log V} for

any fixed k. As a corollary, we deduce that the 3-torus bounds

geometrically a hyperbolic manifold.

(joint work with A. Kolpakov)

We introduce a simple algorithm which transforms every

four-dimensional cubulation into a cusped finite-volume hyperbolic

four-manifold. Combinatorially distinct cubulations give rise to

topologically distinct manifolds. Using this algorithm we construct

the first examples of finite-volume hyperbolic four-manifolds with one

cusp. More generally, we show that the number of k-cusped hyperbolic

four-manifolds with volume smaller than V grows like C^{V log V} for

any fixed k. As a corollary, we deduce that the 3-torus bounds

geometrically a hyperbolic manifold.

#### FMSP Lectures

13:00-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

### 2013/12/02

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

A smoothing property of the Bergman projection (ENGLISH)

**Anne-Katrin Herbig**(Nagoya University)A smoothing property of the Bergman projection (ENGLISH)

[ Abstract ]

Let $D$ be a bounded domain with smooth boundary in complex space of dimension $n$. Suppose its Bergman projection $B$ maps the Sobolev space of order $k$ continuously into the one of order $m$. Then the following smoothing result holds: the full Sobolev norm of $Bf$ of order $k$ is controlled by $L^2$-derivatives of $f$ taken along a single, distinguished direction (of order up to $m$). This talk is based on joint work with J. D. McNeal and E. J. Straube.

Let $D$ be a bounded domain with smooth boundary in complex space of dimension $n$. Suppose its Bergman projection $B$ maps the Sobolev space of order $k$ continuously into the one of order $m$. Then the following smoothing result holds: the full Sobolev norm of $Bf$ of order $k$ is controlled by $L^2$-derivatives of $f$ taken along a single, distinguished direction (of order up to $m$). This talk is based on joint work with J. D. McNeal and E. J. Straube.

### 2013/11/29

#### FMSP Lectures

10:40-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

#### FMSP Lectures

14:50-16:20 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

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

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

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

### 2013/11/28

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

The prescribed scalar curvature problem for metrics with unit total volume (JAPANESE)

**Shinichiroh MATSUO**(Osaka University)The prescribed scalar curvature problem for metrics with unit total volume (JAPANESE)

[ Abstract ]

In this talk I will talk about the modified Kazdan-Warner problem.

Kazdan and Warner in 1970's completely solved the prescribed scalar curvature problem. In particular, they proved that every function on a manifold with positive Yamabe invariant is the scalar curvature of some metric. Kobayashi in 1987 proposed the modified problem of finding metrics with prescribed scalar curvature and total volume 1. He proved that every function except positive constants on a manifold with positive Yamabe invariant is the scalar curvature of some metricwith total volume 1.

I have recently settled the remaining case. Applying Taubes tequniques to the scalar curvature equations, we can glue two Yamabe metrics to construct metrics with very large scalar curvature and unit total volume, and prove that every positive constant is the scalar curvature of some metric with total volume 1.

In this talk I will talk about the modified Kazdan-Warner problem.

Kazdan and Warner in 1970's completely solved the prescribed scalar curvature problem. In particular, they proved that every function on a manifold with positive Yamabe invariant is the scalar curvature of some metric. Kobayashi in 1987 proposed the modified problem of finding metrics with prescribed scalar curvature and total volume 1. He proved that every function except positive constants on a manifold with positive Yamabe invariant is the scalar curvature of some metricwith total volume 1.

I have recently settled the remaining case. Applying Taubes tequniques to the scalar curvature equations, we can glue two Yamabe metrics to construct metrics with very large scalar curvature and unit total volume, and prove that every positive constant is the scalar curvature of some metric with total volume 1.

#### GCOE Seminars

17:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Inverse problem for the Maxwell equations (ENGLISH)

**Oleg Emanouilov**(Colorado State Univ.)Inverse problem for the Maxwell equations (ENGLISH)

[ Abstract ]

We consider an analog of Caderon's problem for the system of Maxwell equations in a cylindrical domain.

Under some geometrical assumptions on domain we show that from the partial data one can recover the complete set of parameters.

We consider an analog of Caderon's problem for the system of Maxwell equations in a cylindrical domain.

Under some geometrical assumptions on domain we show that from the partial data one can recover the complete set of parameters.

### 2013/11/27

#### Seminar on Probability and Statistics

13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)

Density of solutions to stochastic functional differential equations (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/08.html

**TAKEUCHI, Atsushi**(Osaka City University)Density of solutions to stochastic functional differential equations (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/08.html

### 2013/11/26

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Rational elliptic surfaces and certain line-conic arrangements (JAPANESE)

**Hiroo Tokunaga**(Tokyo Metropolitan University)Rational elliptic surfaces and certain line-conic arrangements (JAPANESE)

[ Abstract ]

Let S be a rational elliptic surface. The generic

fiber of S can be considered as an elliptic curve over

the rational function field of one variable. We can make

use of its group structure in order to cook up a curve C_2 on

S from a given section C_1.

In this talk, we consider certain line-conic arrangements of

degree 7 based on this method.

Let S be a rational elliptic surface. The generic

fiber of S can be considered as an elliptic curve over

the rational function field of one variable. We can make

use of its group structure in order to cook up a curve C_2 on

S from a given section C_1.

In this talk, we consider certain line-conic arrangements of

degree 7 based on this method.

#### Seminar on Mathematics for various disciplines

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

An immersed boundary method for mass transfer across permeable moving interfaces (ENGLISH)

**Huaxiong Huang**(York University)An immersed boundary method for mass transfer across permeable moving interfaces (ENGLISH)

[ Abstract ]

In this talk, we present an immersed boundary method for mass transfer across permeable deformable moving interfaces interacting with the surrounding fluids. One of the key features of our method is the introduction of the mass flux as an independent variable, governed by a non-standard vector transport equation. The flux equation, coupled with the mass transport and the fluid flow equations, allows for a natural implementation of an immersed boundary algorithm when the flux across the interfaces is proportional to the jump in concentration. As an example, the oxygen transfer from red blood cells in a capillary to its wall is used to illustrate the applicability of the proposed method. We show that our method is capable of handling multi-physics problems involving fluid- structure interaction with multiple deformable moving interfaces and (interfacial) mass transfer simultaneously.

This is joint work with X. Gong and Z. Gong.

In this talk, we present an immersed boundary method for mass transfer across permeable deformable moving interfaces interacting with the surrounding fluids. One of the key features of our method is the introduction of the mass flux as an independent variable, governed by a non-standard vector transport equation. The flux equation, coupled with the mass transport and the fluid flow equations, allows for a natural implementation of an immersed boundary algorithm when the flux across the interfaces is proportional to the jump in concentration. As an example, the oxygen transfer from red blood cells in a capillary to its wall is used to illustrate the applicability of the proposed method. We show that our method is capable of handling multi-physics problems involving fluid- structure interaction with multiple deformable moving interfaces and (interfacial) mass transfer simultaneously.

This is joint work with X. Gong and Z. Gong.

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Global Strichartz estimates for Schr\\"odinger equations with long range metrics (JAPANESE)

**Haruya MIZUTANI**(Gakushuin University)Global Strichartz estimates for Schr\\"odinger equations with long range metrics (JAPANESE)

[ Abstract ]

We consider Schr\\"odinger equations on the asymptotically Euclidean space

with the long-range condition on the metric.

We show that if the high energy resolvent has at most polynomial growth with respect to the energy,

then global-in-time Strichartz estimates, outside a large compact set, hold.

Under the non-trapping condition we also discuss global-in-space Strichartz estimates.

This talk is based on a joint work with J.-M. Bouclet (Toulouse University).

We consider Schr\\"odinger equations on the asymptotically Euclidean space

with the long-range condition on the metric.

We show that if the high energy resolvent has at most polynomial growth with respect to the energy,

then global-in-time Strichartz estimates, outside a large compact set, hold.

Under the non-trapping condition we also discuss global-in-space Strichartz estimates.

This talk is based on a joint work with J.-M. Bouclet (Toulouse University).

### 2013/11/25

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On hyperkaehler metrics on holomorphic cotangent bundles on complex reductive Lie groups (JAPANESE)

**Kota Hattori**(The University of Tokyo)On hyperkaehler metrics on holomorphic cotangent bundles on complex reductive Lie groups (JAPANESE)

[ Abstract ]

There exists a complete hyperkaehler metric on the holomorphic cotangent bundle on each complex reductive Lie group. It was constructed by Kronheimer, using hyperkaehler quotient method. In this talk I explain how to describe the Kaehler potentials of these metrics.

There exists a complete hyperkaehler metric on the holomorphic cotangent bundle on each complex reductive Lie group. It was constructed by Kronheimer, using hyperkaehler quotient method. In this talk I explain how to describe the Kaehler potentials of these metrics.

#### Algebraic Geometry Seminar

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

Minimal singular metrics of some line bundles with infinitely generated section rings (JAPANESE)

**Takayuki Koike**(The University of Tokyo)Minimal singular metrics of some line bundles with infinitely generated section rings (JAPANESE)

[ Abstract ]

We consider Hermitian metrics of pseudo-effective line bundles on smooth

projective varieties defined over $\\mathbb{C}$.

Especially we are interested in (possibly singular) Hermitian metrics

with semi-positive curvatures when the section rings are not finitely generated.

We study where and how minimal singular metrics, special Hermitian

metrics with semi-positive curvatures, diverges in the following two situations;

a line bundle admitting no Zariski decomposition even after any

modifications (Nakayama example)

and a nef line bundle $L$ on $X$ satisfying $D \\subset |mL|$ and $|mL-D|

= \\emptyset$ for some divisor $D \\subset X$ and for all $m \\geq 1$ (

Zariski example).

We consider Hermitian metrics of pseudo-effective line bundles on smooth

projective varieties defined over $\\mathbb{C}$.

Especially we are interested in (possibly singular) Hermitian metrics

with semi-positive curvatures when the section rings are not finitely generated.

We study where and how minimal singular metrics, special Hermitian

metrics with semi-positive curvatures, diverges in the following two situations;

a line bundle admitting no Zariski decomposition even after any

modifications (Nakayama example)

and a nef line bundle $L$ on $X$ satisfying $D \\subset |mL|$ and $|mL-D|

= \\emptyset$ for some divisor $D \\subset X$ and for all $m \\geq 1$ (

Zariski example).

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