## Seminar information archive

Seminar information archive ～07/13｜Today's seminar 07/14 | Future seminars 07/15～

### 2018/09/21

#### Lectures

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

On the geometry of some p-adic period domains (ENGLISH)

**Laurent Fargues**(CNRS, Institut Mathématique de Jussieu)On the geometry of some p-adic period domains (ENGLISH)

[ Abstract ]

p-adic period spaces have been introduced by Rapoport and Zink as a generalization of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. As an application we can compute the p-adic period space of K3 surfaces with supersingular reduction. The talk will be mainly introductory, presenting the objects showing up in this theorem. This is joint work with Miaofen Chen and Xu Shen.

p-adic period spaces have been introduced by Rapoport and Zink as a generalization of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. As an application we can compute the p-adic period space of K3 surfaces with supersingular reduction. The talk will be mainly introductory, presenting the objects showing up in this theorem. This is joint work with Miaofen Chen and Xu Shen.

### 2018/09/18

#### Lectures

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

Topological epsilon-factors (ENGLISH)

**Alexander Beilinson**(University of Chicago)Topological epsilon-factors (ENGLISH)

[ Abstract ]

I will explain (following mostly my old article arXiv:0610055) how the Kashiwara-Shapira Morse theory construction of the characteristic cycle of a constructible R-sheaf can be refined to yield the cycle with coefficients in the K-theory spectrum K(R). The construction can be viewed as a topological analog of the arithmetic theory of epsilon-factors.

I will explain (following mostly my old article arXiv:0610055) how the Kashiwara-Shapira Morse theory construction of the characteristic cycle of a constructible R-sheaf can be refined to yield the cycle with coefficients in the K-theory spectrum K(R). The construction can be viewed as a topological analog of the arithmetic theory of epsilon-factors.

### 2018/08/24

#### thesis presentations

13:30-14:45 Room #128 (Graduate School of Math. Sci. Bldg.)

#### Operator Algebra Seminars

16:45-18:15 Room #002 (Graduate School of Math. Sci. Bldg.)

Limit profile for the card shuffle by random transpositions

**Lucas Teyssier**(Ecole Normale Superieure)Limit profile for the card shuffle by random transpositions

### 2018/08/08

#### Operator Algebra Seminars

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

$E_0$-semigroups on factors

**Srinivasan Raman**(Chennai Mathematical Institute)$E_0$-semigroups on factors

### 2018/07/31

#### Tuesday Seminar of Analysis

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

Scattering matrices, generalized Fourier transforms and propagation estimates in long-range N-body problems (日本語)

**ASHIDA Sohei**(Kyoto University)Scattering matrices, generalized Fourier transforms and propagation estimates in long-range N-body problems (日本語)

[ Abstract ]

We give a definition of scattering matrices in long-range N-body problems based on the asymptotic behaviors of generalized eigenfunctions and show that these scattering matrices are equivalent to the ones defined by wave-operator approach. We also define generalized Fourier transforms by the asymptotic behaviors of outgoing solutions to nonhomogeneous equations and show that the adjoint operators of them are given by Poisson operators. We also consider new improved propagation estimates for two-cluster scattering channels using projections onto almost invariant subspaces close to two-cluster scattering channels.

We give a definition of scattering matrices in long-range N-body problems based on the asymptotic behaviors of generalized eigenfunctions and show that these scattering matrices are equivalent to the ones defined by wave-operator approach. We also define generalized Fourier transforms by the asymptotic behaviors of outgoing solutions to nonhomogeneous equations and show that the adjoint operators of them are given by Poisson operators. We also consider new improved propagation estimates for two-cluster scattering channels using projections onto almost invariant subspaces close to two-cluster scattering channels.

#### Numerical Analysis Seminar

14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Recent advances on numerical analysis and simulation of invisibility cloaks with metamaterials (English)

**Jichun Li**(University of Nevada Las Vegas)Recent advances on numerical analysis and simulation of invisibility cloaks with metamaterials (English)

[ Abstract ]

In the June 23, 2006's issue of Science magazine, Pendry et al. and Leonhardt independently published their seminar papers on electromagnetic cloaking. Since then, there is a growing interest in using metamaterials to design invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, then I will focus on some time-domain cloaking models we studied in the last few years. Well-posedness study and time-domain finite element method for these models will be presented. I will conclude the talk with some open issues.

In the June 23, 2006's issue of Science magazine, Pendry et al. and Leonhardt independently published their seminar papers on electromagnetic cloaking. Since then, there is a growing interest in using metamaterials to design invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, then I will focus on some time-domain cloaking models we studied in the last few years. Well-posedness study and time-domain finite element method for these models will be presented. I will conclude the talk with some open issues.

### 2018/07/30

#### Tokyo Probability Seminar

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

Parameter estimation of random matrix models via free probability theory (JAPANESE)

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

**Tomohiro Hayase**(Graduate School of Mathematical Sciences, The University of Tokyo)Parameter estimation of random matrix models via free probability theory (JAPANESE)

[ Abstract ]

For random matrix models, the parameter estimation based on the likelihood is not straightforward in particular when there is only one sample matrix. We introduce a new parameter optimization method of random matrix models which works even in such a case not based on the likelihood, instead based on the spectral distribution. We use the spectral distribution perturbed by Cauchy noises because the free deterministic equivalent, which is a tool in free probability theory, allows us to approximate it by a smooth and accessible density function.

In addition, we propose a new rank recovery method for the signal-plus-noise model, and experimentally demonstrate that it recovers the true rank even if the rank is not low; It is a simultaneous rank recovery and parameter estimation procedure.

[ Reference URL ]For random matrix models, the parameter estimation based on the likelihood is not straightforward in particular when there is only one sample matrix. We introduce a new parameter optimization method of random matrix models which works even in such a case not based on the likelihood, instead based on the spectral distribution. We use the spectral distribution perturbed by Cauchy noises because the free deterministic equivalent, which is a tool in free probability theory, allows us to approximate it by a smooth and accessible density function.

In addition, we propose a new rank recovery method for the signal-plus-noise model, and experimentally demonstrate that it recovers the true rank even if the rank is not low; It is a simultaneous rank recovery and parameter estimation procedure.

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

### 2018/07/27

#### Mathematical Biology Seminar

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

Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches

**Somdatta Sinha**(Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches

[ Abstract ]

Malaria has existed in India since antiquity. Different periods of

elimination and control policies have been adopted by the government for

tackling the disease. Malaria parasite was dissevered in India by Sir

Ronald Ross who also developed the simplest mathematical model in early

1900. Malaria modelling has since come through many variations that

incorporated various intrinsic and extrinsic/environmental factors to

describe the disease progression in population. Collection of disease

incidence and prevalence data, however, has been quite variable with both

governmental and non-governmental agencies independently collecting data at

different space and time scales. In this talk I will describe our work on

modelling malaria prevalence using three different approaches. For monthly

prevalence data, I will discuss (i) a regression-based statistical model

based on a specific data-set, and (ii) a general mathematical model that

fits the same data. For more coarse-grained temporal (yearly) data, I will

show graphical analysis that uncovers some useful information from the mass

of data tables. This presentation aims to highlight the suitability of

multiple modelling methods for disease prevalence from variable quality data.

Malaria has existed in India since antiquity. Different periods of

elimination and control policies have been adopted by the government for

tackling the disease. Malaria parasite was dissevered in India by Sir

Ronald Ross who also developed the simplest mathematical model in early

1900. Malaria modelling has since come through many variations that

incorporated various intrinsic and extrinsic/environmental factors to

describe the disease progression in population. Collection of disease

incidence and prevalence data, however, has been quite variable with both

governmental and non-governmental agencies independently collecting data at

different space and time scales. In this talk I will describe our work on

modelling malaria prevalence using three different approaches. For monthly

prevalence data, I will discuss (i) a regression-based statistical model

based on a specific data-set, and (ii) a general mathematical model that

fits the same data. For more coarse-grained temporal (yearly) data, I will

show graphical analysis that uncovers some useful information from the mass

of data tables. This presentation aims to highlight the suitability of

multiple modelling methods for disease prevalence from variable quality data.

### 2018/07/26

#### Numerical Analysis Seminar

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

$L^\infty$ error estimates of the finite element method for elliptic and parabolic equations with the Neumann boundary condition in smooth domains (日本語)

**Takahito Kashiwabara**(University of Tokyo)$L^\infty$ error estimates of the finite element method for elliptic and parabolic equations with the Neumann boundary condition in smooth domains (日本語)

#### thesis presentations

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

### 2018/07/25

#### 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

### 2018/07/24

#### 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

### 2018/07/23

#### Seminar on Geometric Complex Analysis

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

Strange Fatou components of automorphisms of $\mathbb{C}^2$ and Runge embedding of $\mathbb{C} \times \mathbb{C}^*$ into $\mathbb{C}^2$. (ENGLISH)

**Filippo Bracci**(University of Rome Tor Vergata)Strange Fatou components of automorphisms of $\mathbb{C}^2$ and Runge embedding of $\mathbb{C} \times \mathbb{C}^*$ into $\mathbb{C}^2$. (ENGLISH)

[ Abstract ]

The classification of Fatou components for automorphisms of the complex space of dimension greater than $1$ is an interesting and difficult task. Recent deep results prove that the one-dimensional setting is deeply different from the higher dimensional one. Given an automorphism F of $\mathbb{C}^k$, the first bricks in the theory that one would like to understand are invariant Fatou components, namely, those connected open sets $U$, completely invariant under $F$, where the dynamics of $F$ is not chaotic. Among those, we consider “attracting” Fatou components, that is, those components on which the iterates of $F$ converge to a single point. Attracting Fatou components can be recurrent, if the limit point is inside the component or non-recurrent. Recurrent attracting Fatou components are always biholomorphic to $\mathbb{C}^k$, since it was proved by H. Peters, L. Vivas and E. F. Wold that in such a case the point is an attracting (hyperbolic) fixed point, and the Fatou component coincides with the global basin of attraction. Also, as a consequence of works of Ueda and Peters-Lyubich, it is know that all attracting non-recurrent Fatou components of polynomial automorphisms of $\mathbb{C}^2$ are biholomorphic to $\mathbb{C}^2$. One can quite easily find non-simply connected non-recurrent attracting Fatou components in $\mathbb{C}^3$ (mixing a two- dimensional dynamics with a dynamics with non-isolated fixed points in one- variable). In this talk I will explain how to construct a non-recurrent attracting Fatou component in $\mathbb{C}^2$ which is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. This“fantastic beast” is obtained by globalizing, using a result of F. Forstneric, a local construction due to the speaker and Zaitsev, which allows to create a global basin of attraction for an automorphism, and a Fatou coordinate on it. The Fatou coordinate turns out to be a fiber bundle map on $\mathbb{C}$, whose fiber is $\mathbb{C}^*$, then the global basin is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. The most subtle point is to show that such a basin is indeed a Fatou component. This is done exploiting Poschel's results about existence of local Siegel discs and suitable estimates for the Kobayashi distance.

Since attracting Fatou components are Runge, it turns out that this construction gives also an example of a Runge embedding of $\mathbb{C}\times\mathbb{C}^*$ into $\mathbb{C}^2$. Moreover, this example shows an automorphism of $\mathbb{C}^2$ leaving invariant two analytic discs intersecting transversally at the origin.

The talk is based on a joint work with J. Raissy and B. Stensones.

The classification of Fatou components for automorphisms of the complex space of dimension greater than $1$ is an interesting and difficult task. Recent deep results prove that the one-dimensional setting is deeply different from the higher dimensional one. Given an automorphism F of $\mathbb{C}^k$, the first bricks in the theory that one would like to understand are invariant Fatou components, namely, those connected open sets $U$, completely invariant under $F$, where the dynamics of $F$ is not chaotic. Among those, we consider “attracting” Fatou components, that is, those components on which the iterates of $F$ converge to a single point. Attracting Fatou components can be recurrent, if the limit point is inside the component or non-recurrent. Recurrent attracting Fatou components are always biholomorphic to $\mathbb{C}^k$, since it was proved by H. Peters, L. Vivas and E. F. Wold that in such a case the point is an attracting (hyperbolic) fixed point, and the Fatou component coincides with the global basin of attraction. Also, as a consequence of works of Ueda and Peters-Lyubich, it is know that all attracting non-recurrent Fatou components of polynomial automorphisms of $\mathbb{C}^2$ are biholomorphic to $\mathbb{C}^2$. One can quite easily find non-simply connected non-recurrent attracting Fatou components in $\mathbb{C}^3$ (mixing a two- dimensional dynamics with a dynamics with non-isolated fixed points in one- variable). In this talk I will explain how to construct a non-recurrent attracting Fatou component in $\mathbb{C}^2$ which is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. This“fantastic beast” is obtained by globalizing, using a result of F. Forstneric, a local construction due to the speaker and Zaitsev, which allows to create a global basin of attraction for an automorphism, and a Fatou coordinate on it. The Fatou coordinate turns out to be a fiber bundle map on $\mathbb{C}$, whose fiber is $\mathbb{C}^*$, then the global basin is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. The most subtle point is to show that such a basin is indeed a Fatou component. This is done exploiting Poschel's results about existence of local Siegel discs and suitable estimates for the Kobayashi distance.

Since attracting Fatou components are Runge, it turns out that this construction gives also an example of a Runge embedding of $\mathbb{C}\times\mathbb{C}^*$ into $\mathbb{C}^2$. Moreover, this example shows an automorphism of $\mathbb{C}^2$ leaving invariant two analytic discs intersecting transversally at the origin.

The talk is based on a joint work with J. Raissy and B. Stensones.

#### 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

### 2018/07/20

#### FMSP Lectures

**Christian Schnell**(Stony Book University)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

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

### 2018/07/19

#### Applied Analysis

16:00-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent

(Japanese)

**Norihisa Ikoma**(Keio University)Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent

(Japanese)

[ Abstract ]

This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).

This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).

### 2018/07/18

#### Algebraic Geometry Seminar

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

Normal Legendrian singularities (English)

**Jun-Muk Hwang**(KIAS)Normal Legendrian singularities (English)

[ Abstract ]

A germ of a Legendrian subvariety in a holomorphic contact manifold

is called a Legendrian singularity. Legendrian singularities are usually not normal.

We look at some examples of normal Legendrian singularities and discuss their rigidity under deformation.

A germ of a Legendrian subvariety in a holomorphic contact manifold

is called a Legendrian singularity. Legendrian singularities are usually not normal.

We look at some examples of normal Legendrian singularities and discuss their rigidity under deformation.

#### 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

**Christian Schnell**(Stony Book University)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

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.

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