## Seminar information archive

Seminar information archive ～07/24｜Today's seminar 07/25 | Future seminars 07/26～

### 2012/07/17

#### Tuesday Seminar on Topology

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

Contact structure of mixed links (JAPANESE)

**Mutsuo Oka**(Tokyo University of Science)Contact structure of mixed links (JAPANESE)

[ Abstract ]

A strongly non-degenerate mixed function has a Milnor open book

structures on a sufficiently small sphere. We introduce the notion of

{\\em a holomorphic-like} mixed function

and we will show that a link defined by such a mixed function has a

canonical contact structure.

Then we will show that this contact structure for a certain

holomorphic-like mixed function

is carried by the Milnor open book.

A strongly non-degenerate mixed function has a Milnor open book

structures on a sufficiently small sphere. We introduce the notion of

{\\em a holomorphic-like} mixed function

and we will show that a link defined by such a mixed function has a

canonical contact structure.

Then we will show that this contact structure for a certain

holomorphic-like mixed function

is carried by the Milnor open book.

#### GCOE lecture series

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

An introduction to C*-algebra classification theory (ENGLISH)

**George Elliott**(University of Toronto)An introduction to C*-algebra classification theory (ENGLISH)

#### Tuesday Seminar of Analysis

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

On non-radially symmetric solutions of the Liouville-Gel'fand equation on a two-dimensional annular domain (JAPANESE)

**Toru Kan**(Mathematical institute, Tohoku University)On non-radially symmetric solutions of the Liouville-Gel'fand equation on a two-dimensional annular domain (JAPANESE)

[ Abstract ]

指数関数を非線形項に持つ非線形楕円型方程式(Liouville-Gel'fand方程式)について考察する。特に2次元の円環領域では、この方程式の非球対称な解が球対称解から分岐する形で現れる。本講演では、この分岐解の分岐図上での大域的な構造に関して得られた結果を紹介する。

指数関数を非線形項に持つ非線形楕円型方程式(Liouville-Gel'fand方程式)について考察する。特に2次元の円環領域では、この方程式の非球対称な解が球対称解から分岐する形で現れる。本講演では、この分岐解の分岐図上での大域的な構造に関して得られた結果を紹介する。

#### Lie Groups and Representation Theory

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Dirac induction for graded affine Hecke algebras (ENGLISH)

**Eric Opdam**(Universiteit van Amsterdam)Dirac induction for graded affine Hecke algebras (ENGLISH)

[ Abstract ]

In recent joint work with Dan Ciubotaru and Peter Trapa we

constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.

We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.

In recent joint work with Dan Ciubotaru and Peter Trapa we

constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.

We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.

### 2012/07/14

#### Harmonic Analysis Komaba Seminar

13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On various inequalities characterizing critical Sobolev-Lorentz spaces (JAPANESE)

Boundedness of operators on Hardy spaces with variable exponents

(JAPANESE)

**Hidemitsu Wadade**(Gifu University) 13:30-15:00On various inequalities characterizing critical Sobolev-Lorentz spaces (JAPANESE)

**Yoshihiro Sawano**(Tokyo Metropolitan University) 15:30-17:00Boundedness of operators on Hardy spaces with variable exponents

(JAPANESE)

[ Abstract ]

In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:

First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.

Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.

After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.

In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:

First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.

Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.

After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.

### 2012/07/12

#### Lectures

16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Real time tsunami parameters evaluation (ENGLISH)

**M. Lavrentiev**(Sobolev Institute of Mathematics)Real time tsunami parameters evaluation (ENGLISH)

[ Abstract ]

We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.

We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.

### 2012/07/11

#### Classical Analysis

14:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions (Joint work with N. Nakazono) (JAPANESE)

First order systems of linear ordinary differential equations and

representations of quivers (ENGLISH)

**Seiji Nishioka**(Yamagata University) 14:00-15:30On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions (Joint work with N. Nakazono) (JAPANESE)

**Kazuki Hiroe**(Kyoto University) 16:00-17:30First order systems of linear ordinary differential equations and

representations of quivers (ENGLISH)

### 2012/07/10

#### Tuesday Seminar of Analysis

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

Hadamard variational formula for the Green function

of the Stokes equations with the boundary condition (JAPANESE)

**Erika Ushikoshi**(Mathematical Institute, Tohoku University)Hadamard variational formula for the Green function

of the Stokes equations with the boundary condition (JAPANESE)

#### Tuesday Seminar on Topology

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

Topology in Gravitational Lensing (ENGLISH)

**Marcus Werner**(Kavli IPMU)Topology in Gravitational Lensing (ENGLISH)

[ Abstract ]

General relativity implies that light is deflected by masses

due to the curvature of spacetime. The ensuing gravitational

lensing effect is an important tool in modern astronomy, and

topology plays a significant role in its properties. In this

talk, I will review topological aspects of gravitational lensing

theory: the connection of image numbers with Morse theory; the

interpretation of certain invariant sums of the signed image

magnification in terms of Lefschetz fixed point theory; and,

finally, a new partially topological perspective on gravitational

light deflection that emerges from the concept of optical geometry

and applications of the Gauss-Bonnet theorem.

General relativity implies that light is deflected by masses

due to the curvature of spacetime. The ensuing gravitational

lensing effect is an important tool in modern astronomy, and

topology plays a significant role in its properties. In this

talk, I will review topological aspects of gravitational lensing

theory: the connection of image numbers with Morse theory; the

interpretation of certain invariant sums of the signed image

magnification in terms of Lefschetz fixed point theory; and,

finally, a new partially topological perspective on gravitational

light deflection that emerges from the concept of optical geometry

and applications of the Gauss-Bonnet theorem.

### 2012/07/09

#### Seminar on Geometric Complex Analysis

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

Volume of graded linear series and the existence problem of constant scalar curvature Kaehler metric (JAPANESE)

**Tomoyuki Hisamoto**(Univ. of Tokyo)Volume of graded linear series and the existence problem of constant scalar curvature Kaehler metric (JAPANESE)

[ Abstract ]

We describe the volume of a graded linear series by the Monge-Ampere mass of the associated equilibrium metric. We relate this formula to the question whether the weak geodesic ray associated to a test configuration of given polarized manifold recovers the Donaldson-Futaki invariant.

We describe the volume of a graded linear series by the Monge-Ampere mass of the associated equilibrium metric. We relate this formula to the question whether the weak geodesic ray associated to a test configuration of given polarized manifold recovers the Donaldson-Futaki invariant.

### 2012/07/06

#### Colloquium

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

Large Deviations of Random Graphs and Random Matrices (ENGLISH)

**S.R.Srinivasa Varadhan**(Courant Institute of Mathematical Sciences, New York University)Large Deviations of Random Graphs and Random Matrices (ENGLISH)

[ Abstract ]

A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.

A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.

### 2012/07/04

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

A cohomological Hasse principle of varieties over higher local fields and applications to higher dimensional class field theory (ENGLISH)

**Patrick Forré**(University of Tokyo)A cohomological Hasse principle of varieties over higher local fields and applications to higher dimensional class field theory (ENGLISH)

[ Abstract ]

In this talk I will give an overview of the necessary tools for a description of the class field theory of varieties over higher local fields developed by sevaral mathematicians. On this I will motivate the importance of the proposal and verification of a cohomological Hasse principle for varieties over higher local fields, a generalization of Kato's conjectures, and sketch the recent progress on this.

In this talk I will give an overview of the necessary tools for a description of the class field theory of varieties over higher local fields developed by sevaral mathematicians. On this I will motivate the importance of the proposal and verification of a cohomological Hasse principle for varieties over higher local fields, a generalization of Kato's conjectures, and sketch the recent progress on this.

#### Classical Analysis

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Symmetries of quantum Lax equations for the Painlev\\'e equations (JAPANESE)

**Hajime Nagoya**(Kobe University)Symmetries of quantum Lax equations for the Painlev\\'e equations (JAPANESE)

### 2012/06/27

#### Classical Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Moduli space of meromorphic connections with ramified irregular singularities on principal bundles (JAPANESE)

**Daisuke Yamakawa**(Tokyo Institute of Technology)Moduli space of meromorphic connections with ramified irregular singularities on principal bundles (JAPANESE)

### 2012/06/26

#### Tuesday Seminar of Analysis

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

Absence of embedded eigenvalues for the Schr\\"odinger operator on manifold with ends (JAPANESE)

**Kenichi Ito**(Division of Mathematics, University of Tsukuba)Absence of embedded eigenvalues for the Schr\\"odinger operator on manifold with ends (JAPANESE)

[ Abstract ]

We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of $L^2$-eigenvalues for the Schr\\"odinger operator above some critical value. The critical value is computed from the volume growth rate of the end and the potential behavior at infinity. The end structure is formulated abstractly in terms of some convex function, and the examples include asymptotically Euclidean and hyperbolic ends. The proof consists of a priori superexponential decay estimate for eigenfunctions and the absence of superexponentially decaying eigenfunctions, both of which employs the Mourre-type commutator argument. This talk is based on the recent joint work with E.Skibsted (Aarhus University).

We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of $L^2$-eigenvalues for the Schr\\"odinger operator above some critical value. The critical value is computed from the volume growth rate of the end and the potential behavior at infinity. The end structure is formulated abstractly in terms of some convex function, and the examples include asymptotically Euclidean and hyperbolic ends. The proof consists of a priori superexponential decay estimate for eigenfunctions and the absence of superexponentially decaying eigenfunctions, both of which employs the Mourre-type commutator argument. This talk is based on the recent joint work with E.Skibsted (Aarhus University).

### 2012/06/25

#### Algebraic Geometry Seminar

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

Automorphism groups of Calabi-Yau manifolds of Picard number two (JAPANESE)

**Keiji Oguiso**(Osaka University)Automorphism groups of Calabi-Yau manifolds of Picard number two (JAPANESE)

[ Abstract ]

We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\\"ahler manifolds and birational automorphism groups, as I shall explain. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation for a Calabi-Yau threefold of Picard number two, together with exsistence of rational curve, expected by the cone conjecture.

We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\\"ahler manifolds and birational automorphism groups, as I shall explain. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation for a Calabi-Yau threefold of Picard number two, together with exsistence of rational curve, expected by the cone conjecture.

#### Seminar on Geometric Complex Analysis

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

CR equivalence problem of CR manifolds with slice structure (JAPANESE)

**Atsushi Hayashimoto**(Nagano National College of Technology)CR equivalence problem of CR manifolds with slice structure (JAPANESE)

### 2012/06/20

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

On the reduction modulo p of representations of a quaternion

division algebra over a p-adic field (JAPANESE)

**Kazuki Tokimoto**(University of Tokyo)On the reduction modulo p of representations of a quaternion

division algebra over a p-adic field (JAPANESE)

[ Abstract ]

The p-adic Langlands correspondence and the mod p Langlands correspondence for GL_2(Q_p) are known to be compatible with the reduction modulo p in many cases.

In this talk, we examine whether a similar compatibility exists for the composition of the local Langlands correspondence and the local Jacquet-Langlands correspondence.

The simplest case has already been treated by Vign¥'eras. We deal with more cases.

The p-adic Langlands correspondence and the mod p Langlands correspondence for GL_2(Q_p) are known to be compatible with the reduction modulo p in many cases.

In this talk, we examine whether a similar compatibility exists for the composition of the local Langlands correspondence and the local Jacquet-Langlands correspondence.

The simplest case has already been treated by Vign¥'eras. We deal with more cases.

#### PDE Real Analysis Seminar

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

On the Navier-Stokes Cauchy problem with nondecaying data (ENGLISH)

**Paolo Maremonti**(Seconda Università degli Studi di Napoli)On the Navier-Stokes Cauchy problem with nondecaying data (ENGLISH)

[ Abstract ]

We prove the well posedeness of the Navier-Stokes Cauchy problem for nondecaying initial data u_0 \\in C (R^n) \\cap L^\\infty (R^n), n >= 3. This problem is studied by Giga, Inui and Matsui for n >= 3, and Giga, Matsui and Sawada in the two dimensional case. The aims of our paper are slight different since we also find pointwise estimates for the pressure field. Via a uniqueness theorem, we give a sort of structure theorem to GIM solutions.

We prove the well posedeness of the Navier-Stokes Cauchy problem for nondecaying initial data u_0 \\in C (R^n) \\cap L^\\infty (R^n), n >= 3. This problem is studied by Giga, Inui and Matsui for n >= 3, and Giga, Matsui and Sawada in the two dimensional case. The aims of our paper are slight different since we also find pointwise estimates for the pressure field. Via a uniqueness theorem, we give a sort of structure theorem to GIM solutions.

### 2012/06/19

#### Tuesday Seminar on Topology

17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)

On the universal degenerating family of Riemann surfaces

over the D-M compactification of moduli space (JAPANESE)

**Yukio Matsumoto**(Gakushuin University)On the universal degenerating family of Riemann surfaces

over the D-M compactification of moduli space (JAPANESE)

[ Abstract ]

It is usually understood that over the Deligne-

Mumford compactification of moduli space of Riemann surfaces of

genus > 1, there is a family of stable curves. However, if one tries to

construct this family precisely, he/she must first take a disjoint union

of various types of smooth families of stable curves, and then divide

them by their automorphisms to paste them together. In this talk we will

show that once the smooth families are divided, the resulting quotient

family contains not only stable curves but virtually all types of

degeneration of Riemann surfaces, becoming a kind of universal

degenerating family of Riemann surfaces.

It is usually understood that over the Deligne-

Mumford compactification of moduli space of Riemann surfaces of

genus > 1, there is a family of stable curves. However, if one tries to

construct this family precisely, he/she must first take a disjoint union

of various types of smooth families of stable curves, and then divide

them by their automorphisms to paste them together. In this talk we will

show that once the smooth families are divided, the resulting quotient

family contains not only stable curves but virtually all types of

degeneration of Riemann surfaces, becoming a kind of universal

degenerating family of Riemann surfaces.

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Advances in the charge simulation method (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Hidenori Ogata**(The University of Electro-Communications)Advances in the charge simulation method (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

### 2012/06/18

#### Algebraic Geometry Seminar

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

アルバネーゼ次元最大の複素射影多様体の特殊集合について (JAPANESE)

**Katsutoshi Yamanoi**(Tokyo Institute of Technology)アルバネーゼ次元最大の複素射影多様体の特殊集合について (JAPANESE)

[ Abstract ]

アルバネーゼ次元が最大の複素射影多様体の中に含まれる代数的あるいは超越的な複

素曲線について、

高次元ネヴァンリンナ理論の立場からお話します。

アルバネーゼ次元が最大の複素射影多様体の中に含まれる代数的あるいは超越的な複

素曲線について、

高次元ネヴァンリンナ理論の立場からお話します。

#### Seminar on Geometric Complex Analysis

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

CR Q-curvature flow and CR Paneitz operator on 3-dimensional CR manifolds (JAPANESE)

**Takanari Saotome**(Academia Sinica)CR Q-curvature flow and CR Paneitz operator on 3-dimensional CR manifolds (JAPANESE)

#### Lectures

09:45-12:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Fluctuation of solutions to PDEs with random coefficients (Part 2) (ENGLISH)

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

Weak coupling limits for particles and PDEs (Part 2) (ENGLISH)

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

**James Nolen**(Duke University) 09:45-10:45Fluctuation of solutions to PDEs with random coefficients (Part 2) (ENGLISH)

[ Abstract ]

This is continuation of the previous day's lecture.

[ Reference URL ]This is continuation of the previous day's lecture.

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

**Leonid Ryzhik**(Stanford University) 11:00-12:30Weak coupling limits for particles and PDEs (Part 2) (ENGLISH)

[ Abstract ]

This is continuation of the previous day's lecture.

[ Reference URL ]This is continuation of the previous day's lecture.

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

### 2012/06/17

#### Lectures

09:45-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Fluctuation of solutions to PDEs with random coefficients (Part 1) (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

Weak coupling limits for particles and PDEs (Part 1) (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

Asymptotic spreading for heterogeneous Fisher-KPP reaction-diffusion equations (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

**James Nolen**(Duke University) 09:45-17:30Fluctuation of solutions to PDEs with random coefficients (Part 1) (JAPANESE)

[ Abstract ]

For PDEs with random coefficients, it is interesting to understand whether the solutions exhibit some universal statistical behavior that is independent of the details of the coefficients. In particular, how do solutions fluctuate around the mean behavior? We will discuss this issue in the context of three examples:

(1) Traveling fronts in random media in one dimension.

(2) Elliptic homogenization problems.

(3) Random Hamilton-Jacobi equations.

The relation between PDE tools and probabilistic ideas will be

explained.

[ Reference URL ]For PDEs with random coefficients, it is interesting to understand whether the solutions exhibit some universal statistical behavior that is independent of the details of the coefficients. In particular, how do solutions fluctuate around the mean behavior? We will discuss this issue in the context of three examples:

(1) Traveling fronts in random media in one dimension.

(2) Elliptic homogenization problems.

(3) Random Hamilton-Jacobi equations.

The relation between PDE tools and probabilistic ideas will be

explained.

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

**Leonid Ryzhik**(Stanford Univeristy) 13:00-14:45Weak coupling limits for particles and PDEs (Part 1) (JAPANESE)

[ Abstract ]

Weak random fluctuations in medium parameters may lead to a non-trivial effect after large times and propagation over long distances. We will consider several examples when the large time limit can be treated:

(1) a particle in a weakly random velocity field.

(2) weak random fluctuations of Hamilton equations, and

(3) the linear Scrhoedinger equation with a weak random potential.

The role of long range correlation of the random fluctuations will also be discussed.

[ Reference URL ]Weak random fluctuations in medium parameters may lead to a non-trivial effect after large times and propagation over long distances. We will consider several examples when the large time limit can be treated:

(1) a particle in a weakly random velocity field.

(2) weak random fluctuations of Hamilton equations, and

(3) the linear Scrhoedinger equation with a weak random potential.

The role of long range correlation of the random fluctuations will also be discussed.

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

**Gregoire Nadin**(CNRS / Paris 6) 15:15-17:15Asymptotic spreading for heterogeneous Fisher-KPP reaction-diffusion equations (JAPANESE)

[ Abstract ]

The solutions of the heterogeneous Fisher-KPP equation associated with compactly supported initial data are known to take off from the unstable steady state 0 and to converge to the steady state 1 for large times. The aim of this lecture is to estimate the speed at which the interface between 0 and 1 spreads.

Using the new notion of generalized principal eigenvalues for non-compact elliptic operators, we will derive such estimates which will be proved to be optimal for several classes of heterogeneity such as periodic, almost periodic or random stationary ergodic ones.

[ Reference URL ]The solutions of the heterogeneous Fisher-KPP equation associated with compactly supported initial data are known to take off from the unstable steady state 0 and to converge to the steady state 1 for large times. The aim of this lecture is to estimate the speed at which the interface between 0 and 1 spreads.

Using the new notion of generalized principal eigenvalues for non-compact elliptic operators, we will derive such estimates which will be proved to be optimal for several classes of heterogeneity such as periodic, almost periodic or random stationary ergodic ones.

https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

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