## Seminar information archive

Seminar information archive ～08/17｜Today's seminar 08/18 | Future seminars 08/19～

#### Mathematical Biology Seminar

15:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

When size does matter: Ontogenetic symmetry and asymmetry in energetics

(ENGLISH)

http://staff.science.uva.nl/~aroos/

**Andre M. de Roos**(University of Amsterdam)When size does matter: Ontogenetic symmetry and asymmetry in energetics

(ENGLISH)

[ Abstract ]

Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.

[ Reference URL ]Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.

http://staff.science.uva.nl/~aroos/

#### GCOE Seminars

15:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

When size does matter: Ontogenetic symmetry and asymmetry in energetics (ENGLISH)

http://staff.science.uva.nl/~aroos/

**Andre M. de Roos**(University of Amsterdam)When size does matter: Ontogenetic symmetry and asymmetry in energetics (ENGLISH)

[ Abstract ]

Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.

[ Reference URL ]Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.

http://staff.science.uva.nl/~aroos/

### 2014/03/11

#### GCOE Seminars

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Inverse problem for the waves : stability and convergence matters (ENGLISH)

**Lucie Baudouin**(LAAS-CNRS, equipe MAC)Inverse problem for the waves : stability and convergence matters (ENGLISH)

[ Abstract ]

This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semi-discrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1-d problems.

This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semi-discrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1-d problems.

### 2014/03/10

#### GCOE Seminars

13:30-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The two-dimensional random walk in an isotropic random environment (ENGLISH)

**Erwin Bolthausen**(University of Zurich)The two-dimensional random walk in an isotropic random environment (ENGLISH)

#### Lectures

15:15-16:45 Room #123 (Graduate School of Math. Sci. Bldg.)

Energy fluctuations in the disordered harmonic chain (ENGLISH)

**Marielle Simon**(ENS Lyon, UMPA)Energy fluctuations in the disordered harmonic chain (ENGLISH)

[ Abstract ]

We study the energy diffusion in the disordered harmonic chain of oscillators: the usual Hamiltonian dynamics is provided with random masses and perturbed by a degenerate energy conserving noise. After rescaling space and time diffusively, we prove that energy fluctuations evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and an equivalent definition through the Green-Kubo formula. Since the model is non gradient, and the perturbation is very degenerate, the standard Varadhan's approach is reviewed under new perspectives.

We study the energy diffusion in the disordered harmonic chain of oscillators: the usual Hamiltonian dynamics is provided with random masses and perturbed by a degenerate energy conserving noise. After rescaling space and time diffusively, we prove that energy fluctuations evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and an equivalent definition through the Green-Kubo formula. Since the model is non gradient, and the perturbation is very degenerate, the standard Varadhan's approach is reviewed under new perspectives.

#### GCOE Seminars

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

ELASTIC WAVES IN STRONGLY HETEROGENEOUS PLATES (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/bm01.pdf

**Bernadette Miara**(Univ. Paris-Est)ELASTIC WAVES IN STRONGLY HETEROGENEOUS PLATES (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/bm01.pdf

### 2014/03/06

#### GCOE Seminars

10:10-11:00 Room #002 (Graduate School of Math. Sci. Bldg.)

The Mathematical Model for the Contamination Problems and Related Inverse Problems (ENGLISH)

**J. Cheng**(Fudan Univ.)The Mathematical Model for the Contamination Problems and Related Inverse Problems (ENGLISH)

[ Abstract ]

In this talk, we discuss the motivation for the study of the abnormal diffusion models for the contamination problems. From the practical point of view, several inverse problems proposed and studied Theoretic results, for example, the uniqueness and stability are shown. The possibility of the application of these studies is mentioned.

In this talk, we discuss the motivation for the study of the abnormal diffusion models for the contamination problems. From the practical point of view, several inverse problems proposed and studied Theoretic results, for example, the uniqueness and stability are shown. The possibility of the application of these studies is mentioned.

#### GCOE Seminars

11:10-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Inverse problems with fractional derivatives in the space variable (ENGLISH)

**W. Rundell**(Texas A&M Univ.)Inverse problems with fractional derivatives in the space variable (ENGLISH)

[ Abstract ]

This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.

This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.

#### GCOE Seminars

14:30-15:20 Room #002 (Graduate School of Math. Sci. Bldg.)

Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)

**Y. Luchko**(Beuth Technical University of Applied Sciences)Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)

[ Abstract ]

Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.

In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.

In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.

Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.

In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.

In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.

#### GCOE Seminars

16:20-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

New kind of observations in an inverse parabolic problem (ENGLISH)

**M. Cristofol**(Aix-Marseille Univ.)New kind of observations in an inverse parabolic problem (ENGLISH)

[ Abstract ]

In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.

In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.

### 2014/02/28

#### GCOE Seminars

13:00-14:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)

**Patricia Gaitan**(Aix-Marseille University)Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)

[ Abstract ]

This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.

For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).

This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.

For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).

#### GCOE Seminars

11:00-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)

**Assia Benabdallah**(Aix-Marseille University)Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)

### 2014/02/27

#### GCOE Seminars

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)

**Yves Dermenjian**(Univ. of Marseille)A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)

### 2014/02/18

#### GCOE Seminars

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)

**Yves Dermenjian**(Univ. of Marseille)A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)

### 2014/02/17

#### Lectures

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

Canceled!! (ENGLISH)

**Ratnasingham Shivaji**(The University of North Carolina at Greensboro)Canceled!! (ENGLISH)

[ Abstract ]

Canceled!!

Canceled!!

### 2014/02/15

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Some Hilbert-type inequalities involving the Hardy operator (ENGLISH)

Uniform boundedness of conditinal expectation operators (JAPANESE)

**Batbold Tserendorj**(National University of Mongolia) 13:30-15:00Some Hilbert-type inequalities involving the Hardy operator (ENGLISH)

**Masato Kikuchi**(University of Toyama) 15:30-17:00Uniform boundedness of conditinal expectation operators (JAPANESE)

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Canceled for snow storm: Coble's hypersurface and defining equation of Kummer varieties (JAPANESE)

Generalization of Weierstrass P-functions to quasi-Abelian varieties

Canceled for snow storm: (JAPANESE)

**Yoshihiro Oonishi**(Yamanashi Univ.) 13:30-14:30Canceled for snow storm: Coble's hypersurface and defining equation of Kummer varieties (JAPANESE)

**Atsuko Kogie**(Toyama Univ.) 15:00-16:00Generalization of Weierstrass P-functions to quasi-Abelian varieties

Canceled for snow storm: (JAPANESE)

### 2014/02/13

#### Numerical Analysis Seminar

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)

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

**Mitchell Luskin**(University of Minnesota)Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)

[ Abstract ]

The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.

Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.

[ Reference URL ]The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.

Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.

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

### 2014/02/12

#### Algebraic Geometry Seminar

14:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)

Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)

**Shin-ichi Matsumura**(Kagoshima University) 14:00-15:30An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)

[ Abstract ]

In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics.

This theorem is a powerful generalization of various injectivity and vanishing theorems.

The proof is based on a combination of the theory of harmonic integrals and the L^2-method for the \\dbar-equation.

To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics.

Moreover we obtain L^2-estimates of solutions of the \\dbar-equation, by using the \\check{C}ech complex.

As an application, we obtain a Nadel type vanishing theorem.

In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics.

This theorem is a powerful generalization of various injectivity and vanishing theorems.

The proof is based on a combination of the theory of harmonic integrals and the L^2-method for the \\dbar-equation.

To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics.

Moreover we obtain L^2-estimates of solutions of the \\dbar-equation, by using the \\check{C}ech complex.

As an application, we obtain a Nadel type vanishing theorem.

**Junyan Cao**(KIAS) 16:00-17:30Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)

[ Abstract ]

In this talk, we first prove a version of the Ohsawa-Takegoshi

extension theorem valid for on arbitrary K\\"ahler manifolds, and for

holomorphic line bundles equipped with possibly singular metrics. As an

application, we generalise Berndtsson and Paun 's result about the

pseudo-effectivity of the relative canonical bundles to arbitrary

compact K\\"ahler families.

In this talk, we first prove a version of the Ohsawa-Takegoshi

extension theorem valid for on arbitrary K\\"ahler manifolds, and for

holomorphic line bundles equipped with possibly singular metrics. As an

application, we generalise Berndtsson and Paun 's result about the

pseudo-effectivity of the relative canonical bundles to arbitrary

compact K\\"ahler families.

#### thesis presentations

09:30-10:45 Room #118 (Graduate School of Math. Sci. Bldg.)

A construction of a universal finite type invariant of homology 3-spheres(ホモロジー3球面の普遍有限型不変量のひとつの構成) (JAPANESE)

**清水 達郎**(東京大学大学院数理科学研究科)A construction of a universal finite type invariant of homology 3-spheres(ホモロジー3球面の普遍有限型不変量のひとつの構成) (JAPANESE)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Congruences of Hilbert modular forms over real quadratic fields and the special values of L-functions(実2次体上のHilbert保型形式の合同式とL関数の特殊値) (JAPANESE)

**平野 雄一**(東京大学大学院数理科学研究科)Congruences of Hilbert modular forms over real quadratic fields and the special values of L-functions(実2次体上のHilbert保型形式の合同式とL関数の特殊値) (JAPANESE)

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

On contact submanifolds of the odd dimensional Euclidean space(奇数次元ユークリッド空間の接触部分多様体について) (JAPANESE)

**粕谷 直彦**(東京大学大学院数理科学研究科)On contact submanifolds of the odd dimensional Euclidean space(奇数次元ユークリッド空間の接触部分多様体について) (JAPANESE)

#### thesis presentations

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

特異値間隔分布によるセルオートマトンの分類 (JAPANESE)

**金子 勇治**(東京大学大学院数理科学研究科)特異値間隔分布によるセルオートマトンの分類 (JAPANESE)

### 2014/02/10

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)

(JAPANESE)

**許 本源**(東京大学大学院数理科学研究科)Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)

(JAPANESE)

#### thesis presentations

13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)

**柏原 崇人**(東京大学大学院数理科学研究科)Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)

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