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過去の記録 ～10/03｜本日 10/04 | 今後の予定 10/05～
2018年07月27日(金)
数理人口学・数理生物学セミナー
15:00-16:00 数理科学研究科棟(駒場) 118号室
Somdatta Sinha 氏 (Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)
Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches
Somdatta Sinha 氏 (Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)
Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches
[ 講演概要 ]
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年07月26日(木)
数値解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
柏原崇人 氏 (東京大学大学院数理科学研究科)
滑らかな領域における楕円型・放物型ノイマン境界値問題に対する有限要素法の$L^\infty$誤差評価について (日本語)
柏原崇人 氏 (東京大学大学院数理科学研究科)
滑らかな領域における楕円型・放物型ノイマン境界値問題に対する有限要素法の$L^\infty$誤差評価について (日本語)
[ 講演概要 ]
楕円型および放物型問題に対する$L^\infty$ノルム（最大値ノルム）による汎用的な誤差評価手法の開発については，1970年代のJ.A. Nitsche, A.H. Schatz, L.B. Wahlbinを含む先駆者の研究以来，多くの貢献がなされ，現在では標準的な証明法が確立されたと言える状況にある．一方で，有限要素法で滑らかな領域（曲がった境界を持つ領域）を扱う際は，多角形や多面体領域で近似した上で三角形分割・有限要素空間の導入・定式化を行うのが最も基本的であるが，そのような領域近似（領域摂動）に伴う誤差を考慮した厳密な$L^\infty$誤差解析は，斉次ディリクレ境界条件の場合しか知られていないと思われる．本講演では，ポアソン方程式と熱方程式の非斉次ノイマン問題に対して，領域摂動誤差を考慮した$L^\infty$誤差評価を考察し，$O(h^2 |\log h|)$すなわち領域摂動なしのP1要素の場合と同等の評価が得られたことを報告する．証明の鍵は，汎用的な誤差評価手法において複数回用いられるガラーキン直交性が厳密には成立しなくなるものの，メッシュサイズが0になる極限のもとで漸近的に成り立つことを領域摂動評価を用いて示す点にある．
楕円型および放物型問題に対する$L^\infty$ノルム（最大値ノルム）による汎用的な誤差評価手法の開発については，1970年代のJ.A. Nitsche, A.H. Schatz, L.B. Wahlbinを含む先駆者の研究以来，多くの貢献がなされ，現在では標準的な証明法が確立されたと言える状況にある．一方で，有限要素法で滑らかな領域（曲がった境界を持つ領域）を扱う際は，多角形や多面体領域で近似した上で三角形分割・有限要素空間の導入・定式化を行うのが最も基本的であるが，そのような領域近似（領域摂動）に伴う誤差を考慮した厳密な$L^\infty$誤差解析は，斉次ディリクレ境界条件の場合しか知られていないと思われる．本講演では，ポアソン方程式と熱方程式の非斉次ノイマン問題に対して，領域摂動誤差を考慮した$L^\infty$誤差評価を考察し，$O(h^2 |\log h|)$すなわち領域摂動なしのP1要素の場合と同等の評価が得られたことを報告する．証明の鍵は，汎用的な誤差評価手法において複数回用いられるガラーキン直交性が厳密には成立しなくなるものの，メッシュサイズが0になる極限のもとで漸近的に成り立つことを領域摂動評価を用いて示す点にある．
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 128号室
吉田 純 氏 (東京大学大学院数理科学研究科)
Categories of operators for multicategories with various symmetries
(多彩な対称性を持つマルチ圏のオペレーターの圏)
(JAPANESE)
吉田 純 氏 (東京大学大学院数理科学研究科)
Categories of operators for multicategories with various symmetries
(多彩な対称性を持つマルチ圏のオペレーターの圏)
(JAPANESE)
2018年07月25日(水)
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
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.
[ 参考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年07月24日(火)
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
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.
[ 参考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年07月23日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Filippo Bracci 氏 (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)
Filippo Bracci 氏 (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)
[ 講演概要 ]
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レクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
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.
[ 参考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年07月20日(金)
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
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.
[ 参考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年07月19日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 118号室
生駒 典久 氏 (慶應義塾大学)
Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent
(Japanese)
生駒 典久 氏 (慶應義塾大学)
Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent
(Japanese)
[ 講演概要 ]
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年07月18日(水)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
普段と違う水曜日にセミナーを行います。The seminar will be held on Wednesday. This is a different day from usual.
Jun-Muk Hwang 氏 (KIAS)
Normal Legendrian singularities (English)
普段と違う水曜日にセミナーを行います。The seminar will be held on Wednesday. This is a different day from usual.
Jun-Muk Hwang 氏 (KIAS)
Normal Legendrian singularities (English)
[ 講演概要 ]
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.
数理人口学・数理生物学セミナー
15:00-16:00 数理科学研究科棟(駒場) 118号室
Malay Banerjee 氏 (Department of Mathematics & Statistics, IIT Kanpur)
Effect of demographic stochasticity on large amplitude oscillation
Malay Banerjee 氏 (Department of Mathematics & Statistics, IIT Kanpur)
Effect of demographic stochasticity on large amplitude oscillation
[ 講演概要 ]
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.
博士論文発表会
15:30-16:45 数理科学研究科棟(駒場) 128号室
張 龍傑 氏 (東京大学大学院数理科学研究科)
Mean curvature flow with driving force
(駆動力付きの平均曲率流方程式)
(JAPANESE)
張 龍傑 氏 (東京大学大学院数理科学研究科)
Mean curvature flow with driving force
(駆動力付きの平均曲率流方程式)
(JAPANESE)
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
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.
[ 参考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年07月17日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
石川 昌治 氏 (慶應義塾大学)
Positive flow-spines and contact 3-manifolds (JAPANESE)
Tea: Common Room 16:30-17:00
石川 昌治 氏 (慶應義塾大学)
Positive flow-spines and contact 3-manifolds (JAPANESE)
[ 講演概要 ]
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).
博士論文発表会
15:30-16:45 数理科学研究科棟(駒場) 128号室
三浦 達彦 氏 (東京大学大学院数理科学研究科)
Mathematical analysis of evolution equations in curved thin domains or on moving surfaces
(曲がった薄膜領域や動く曲面上の発展方程式の数学解析)
(ENGLISH)
三浦 達彦 氏 (東京大学大学院数理科学研究科)
Mathematical analysis of evolution equations in curved thin domains or on moving surfaces
(曲がった薄膜領域や動く曲面上の発展方程式の数学解析)
(ENGLISH)
東京無限可積分系セミナー
16:00-17:00 数理科学研究科棟(駒場) 002号室
Valerii Sopin 氏 (Higher School of Economics (Moscow))
Operator algebra for statistical model of square ladder (ENGLISH)
Valerii Sopin 氏 (Higher School of Economics (Moscow))
Operator algebra for statistical model of square ladder (ENGLISH)
[ 講演概要 ]
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年07月13日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 056号室
DINH Tien Cuong 氏 (National University of Singapore )
Pluripotential theory and complex dynamics in higher dimension
DINH Tien Cuong 氏 (National University of Singapore )
Pluripotential theory and complex dynamics in higher dimension
[ 講演概要 ]
Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.
Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.
2018年07月11日(水)
作用素環セミナー
17:15-18:45 数理科学研究科棟(駒場) 126号室
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of amenable C*-algebras (cont'd)
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of amenable C*-algebras (cont'd)
2018年07月10日(火)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 002号室
いつもと部屋が違います。The room is different from usual.
賴青瑞 氏 (国立成功大学)
The effective bound of anticanonical volume of Fano threefolds (English)
いつもと部屋が違います。The room is different from usual.
賴青瑞 氏 (国立成功大学)
The effective bound of anticanonical volume of Fano threefolds (English)
[ 講演概要 ]
According to Mori's program, varieties covered by rational curves are
built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the
dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)
of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical
volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,
where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).
Our aim is to find an effective bound of the anticanonical volume -K^3, which is
not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss
some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.
This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.
According to Mori's program, varieties covered by rational curves are
built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the
dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)
of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical
volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,
where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).
Our aim is to find an effective bound of the anticanonical volume -K^3, which is
not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss
some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.
This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.
講演会
15:00-16:00 数理科学研究科棟(駒場) 128号室
Canceled!! (諸事情により,講演は取りやめとなりました.)
Sam Nariman 氏 (Northwestern University)
On the moduli space of flat symplectic surface bundles
Canceled!! (諸事情により,講演は取りやめとなりました.)
Sam Nariman 氏 (Northwestern University)
On the moduli space of flat symplectic surface bundles
[ 講演概要 ]
There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.
In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of
Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.
There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.
In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of
Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Emmy Murphy 氏 (Northwestern University)
Loose Legendrians and arboreal singularities (ENGLISH)
Tea: Common Room 16:30-17:00
Emmy Murphy 氏 (Northwestern University)
Loose Legendrians and arboreal singularities (ENGLISH)
[ 講演概要 ]
Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.
Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 126号室
松本純一 氏 (産業技術総合研究所)
直交基底気泡関数有限要素法による自由表面流れ
(Japanese)
松本純一 氏 (産業技術総合研究所)
直交基底気泡関数有限要素法による自由表面流れ
(Japanese)
[ 講演概要 ]
非構造格子（三角形と四面体）に適用が可能な直交基底気泡関数要素による有限要素法を用いた2次元浅水流れと3次元気液二相流れについて解説する。2次元浅水流れでは、浅水長波方程式とBoussinesq方程式おける数値安定性を考慮した陽的および陰的有限要素法について説明する。計算例として、浅水長波方程式では風応力を考慮した自由表面問題および河床摩擦を考慮した跳水現象の厳密解との比較、波の分散を考慮したBoussinesq方程式では孤立波の近似解および実験結果と計算結果との比較を示す。3次元気液二相流れでは、界面関数を扱うPhase-FieldモデルとしてAllen-Cahn方程式、Cahn-Hilliard方程式の双方を取り上げ、Navier-Stokes方程式とPhase-Field界面モデルを採用した直交基底気泡関数要素安定化法について解説する。さらに、2次元（2D）浅水流れと3次元（3D）気液二相流れにおける双方向の流れを考慮した結合法について述べ2D-3D連成問題について計算例を示す。
非構造格子（三角形と四面体）に適用が可能な直交基底気泡関数要素による有限要素法を用いた2次元浅水流れと3次元気液二相流れについて解説する。2次元浅水流れでは、浅水長波方程式とBoussinesq方程式おける数値安定性を考慮した陽的および陰的有限要素法について説明する。計算例として、浅水長波方程式では風応力を考慮した自由表面問題および河床摩擦を考慮した跳水現象の厳密解との比較、波の分散を考慮したBoussinesq方程式では孤立波の近似解および実験結果と計算結果との比較を示す。3次元気液二相流れでは、界面関数を扱うPhase-FieldモデルとしてAllen-Cahn方程式、Cahn-Hilliard方程式の双方を取り上げ、Navier-Stokes方程式とPhase-Field界面モデルを採用した直交基底気泡関数要素安定化法について解説する。さらに、2次元（2D）浅水流れと3次元（3D）気液二相流れにおける双方向の流れを考慮した結合法について述べ2D-3D連成問題について計算例を示す。
2018年07月09日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Casey Kelleher 氏 (Princeton University)
Rigidity results for symplectic curvature flow (ENGLISH)
Casey Kelleher 氏 (Princeton University)
Rigidity results for symplectic curvature flow (ENGLISH)
[ 講演概要 ]
We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.
We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.
2018年07月03日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
吉田 純 氏 (東京大学大学院数理科学研究科)
Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)
Tea: Common Room 16:30-17:00
吉田 純 氏 (東京大学大学院数理科学研究科)
Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)
[ 講演概要 ]
The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.
The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
Xun Yu 氏 (Tianjin University)
Surface automorphisms and Salem numbers (English)
Xun Yu 氏 (Tianjin University)
Surface automorphisms and Salem numbers (English)
[ 講演概要 ]
The entropy of a surface automorphism is either zero or the
logarithm of a Salem number.
In this talk, we will discuss which Salem numbers arise in this way. We
will show that any
supersingular K3 surface in odd characteristic has an automorphism the
entropy of which is
the logarithm of a Salem number of degree 22. In particular, such
automorphisms are
not geometrically liftable to characteristic 0.
The entropy of a surface automorphism is either zero or the
logarithm of a Salem number.
In this talk, we will discuss which Salem numbers arise in this way. We
will show that any
supersingular K3 surface in odd characteristic has an automorphism the
entropy of which is
the logarithm of a Salem number of degree 22. In particular, such
automorphisms are
not geometrically liftable to characteristic 0.
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