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過去の記録 ～01/20｜本日 01/21 | 今後の予定 01/22～
2017年10月31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
Yash Lodha 氏 (École Polytechnique Fédérale de Lausanne)
Nonamenable groups of piecewise projective homeomorphisms (ENGLISH)
Tea: Common Room 16:30-17:00
Yash Lodha 氏 (École Polytechnique Fédérale de Lausanne)
Nonamenable groups of piecewise projective homeomorphisms (ENGLISH)
[ 講演概要 ]
Groups of piecewise projective homeomorphisms provide elegant examples of groups that are non amenable, yet do not contain non abelian free subgroups. In this talk I will present a survey of these groups and discuss their striking properties. I will discuss properties such as (non)amenability, finiteness properties, normal subgroup structure, actions by various degrees of regularity and Tarski numbers.
Groups of piecewise projective homeomorphisms provide elegant examples of groups that are non amenable, yet do not contain non abelian free subgroups. In this talk I will present a survey of these groups and discuss their striking properties. I will discuss properties such as (non)amenability, finiteness properties, normal subgroup structure, actions by various degrees of regularity and Tarski numbers.
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
Zhan Li 氏 (Beijing)
ACC for log canonical threshold polytopes (English)
Zhan Li 氏 (Beijing)
ACC for log canonical threshold polytopes (English)
[ 講演概要 ]
We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition. This is a joint work with Jingjun Han and Lu Qi.
We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition. This is a joint work with Jingjun Han and Lu Qi.
離散数理モデリングセミナー
16:30-17:30 数理科学研究科棟(駒場) 126号室
Basile Grammaticos 氏 (Université de Paris VII・XI)
The end of the World (ENGLISH)
Basile Grammaticos 氏 (Université de Paris VII・XI)
The end of the World (ENGLISH)
[ 講演概要 ]
This is not a seminar on astrophysics or cosmology. I am not going to talk about something that will happen in billions of years. I will rather explain the menace to our civilisation and to the human species. Inspired from the works of several authors I will explain the existing risks. I will also present mathematical models which show that a general collapse is possible in the decades that follow.
This is not a seminar on astrophysics or cosmology. I am not going to talk about something that will happen in billions of years. I will rather explain the menace to our civilisation and to the human species. Inspired from the works of several authors I will explain the existing risks. I will also present mathematical models which show that a general collapse is possible in the decades that follow.
離散数理モデリングセミナー
15:30-16:30 数理科学研究科棟(駒場) 126号室
Fon-Che Liu 氏 (National Taiwan University)
A hierarchy of approximate regularity of functions (ENGLISH)
Fon-Che Liu 氏 (National Taiwan University)
A hierarchy of approximate regularity of functions (ENGLISH)
[ 講演概要 ]
A hierarchy of a certain weakly sensed regularity of functions defined on subsets of Euclidean n-space which originated from the well-known Lusin theorem that characterizes measurable functions in terms of approximate continuity will be introduced. Its intimate relations with the ordinary hierarchy of regularity in terms of order of continuous differentiability will be exposed and explained.
A hierarchy of a certain weakly sensed regularity of functions defined on subsets of Euclidean n-space which originated from the well-known Lusin theorem that characterizes measurable functions in terms of approximate continuity will be introduced. Its intimate relations with the ordinary hierarchy of regularity in terms of order of continuous differentiability will be exposed and explained.
FMSPレクチャーズ
16:00-17:00 数理科学研究科棟(駒場) 118号室
V. G. Romanov 氏 (Sobolev Institute of Mathematics)
Some Geometric Aspects in Inverse Problems (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov.pdf
V. G. Romanov 氏 (Sobolev Institute of Mathematics)
Some Geometric Aspects in Inverse Problems (ENGLISH)
[ 講演概要 ]
We consider inverse problems related to recovering coefficients in partial differential equations of the second order. It is supposed that some measurements of solutions to direct problems are produced on convenient sets. A study of some inverse problems for hyperbolic equations leads to geometric problems: recovering a function from its integrals along geodesic lines of the Riemannian metric or recovering the Riemannian metric inside a domain from given distances between arbitrary points of the domain boundary. Our main goal here is to demonstrate how such geometric problems arise for equations of parabolic and elliptic types.
[ 参考URL ]We consider inverse problems related to recovering coefficients in partial differential equations of the second order. It is supposed that some measurements of solutions to direct problems are produced on convenient sets. A study of some inverse problems for hyperbolic equations leads to geometric problems: recovering a function from its integrals along geodesic lines of the Riemannian metric or recovering the Riemannian metric inside a domain from given distances between arbitrary points of the domain boundary. Our main goal here is to demonstrate how such geometric problems arise for equations of parabolic and elliptic types.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov.pdf
2017年10月30日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
伊藤 悠 氏 (京都産業大学 理学部数理科学科)
Integration of controlled rough paths via fractional calculus (JAPANESE)
伊藤 悠 氏 (京都産業大学 理学部数理科学科)
Integration of controlled rough paths via fractional calculus (JAPANESE)
[ 講演概要 ]
本研究は非整数階微積分に基づいたラフパス理論の研究である。非整数階微積分に基づいたラフパス理論の研究は、Y.Hu-D.Nualart(2009)に始まり、ラフ積分と呼ばれるラフパス理論における積分概念に特徴がある。通常のラフ積分は、補正されたRiemann-Stieltjes和の極限として与えられるが、非整数階微積分に基づいたものは、非整数階微分による明示的な表現式として与えられる。本講演では、M.Gubinelli(2004)が導入したラフ積分に対し、そのような表現式を導出するとともに、導出過程において、M.Zähle(1998)の議論が有効に働くことを説明する。
本研究は非整数階微積分に基づいたラフパス理論の研究である。非整数階微積分に基づいたラフパス理論の研究は、Y.Hu-D.Nualart(2009)に始まり、ラフ積分と呼ばれるラフパス理論における積分概念に特徴がある。通常のラフ積分は、補正されたRiemann-Stieltjes和の極限として与えられるが、非整数階微積分に基づいたものは、非整数階微分による明示的な表現式として与えられる。本講演では、M.Gubinelli(2004)が導入したラフ積分に対し、そのような表現式を導出するとともに、導出過程において、M.Zähle(1998)の議論が有効に働くことを説明する。
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
澤田友佑 氏 (名大多元数理)
The bicategory of $W^*$-bimodules
澤田友佑 氏 (名大多元数理)
The bicategory of $W^*$-bimodules
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
加藤 昌英 氏 (上智大学)
Odd dimensional complex analytic Kleinian groups
加藤 昌英 氏 (上智大学)
Odd dimensional complex analytic Kleinian groups
[ 講演概要 ]
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group $G$ of a certain class of discrete subgroups of $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, there is a canonical way to define the region of discontinuity, on which $G$ acts properly discontinuously. General principle in the discussion is to regard $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ as a single point. We can consider the quotient space of the discontinuity region by the action of $G$. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case $n=1$, we explain a new example of compact quotients which is related to a classical Kleinian group.
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group $G$ of a certain class of discrete subgroups of $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, there is a canonical way to define the region of discontinuity, on which $G$ acts properly discontinuously. General principle in the discussion is to regard $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ as a single point. We can consider the quotient space of the discontinuity region by the action of $G$. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case $n=1$, we explain a new example of compact quotients which is related to a classical Kleinian group.
代数幾何学セミナー
10:30-12:00 数理科学研究科棟(駒場) 123号室
Roberto Svaldi 氏 (Cambridge)
Towards birational boundedness of elliptic Calabi-Yau varieties (English)
Roberto Svaldi 氏 (Cambridge)
Towards birational boundedness of elliptic Calabi-Yau varieties (English)
[ 講演概要 ]
I will discuss new results towards the birational boundedness of
low-dimensional elliptic Calabi-Yau varieties, joint work with Gabriele
Di Certo.
Recent work in the minimal model program suggests that pairs with trivial log canonical
class should satisfy some boundedness properties.
I will show that 4-dimensional Calabi-Yau pairs which are not birational to a product are
indeed log birationally bounded. This implies birational boundedness of elliptically fibered
Calabi-Yau manifolds with a section, in dimension up to 5.
If time allows, I will also try to discuss a first approach towards boundedness of rationally
connected CY varieties in low dimension.
I will discuss new results towards the birational boundedness of
low-dimensional elliptic Calabi-Yau varieties, joint work with Gabriele
Di Certo.
Recent work in the minimal model program suggests that pairs with trivial log canonical
class should satisfy some boundedness properties.
I will show that 4-dimensional Calabi-Yau pairs which are not birational to a product are
indeed log birationally bounded. This implies birational boundedness of elliptically fibered
Calabi-Yau manifolds with a section, in dimension up to 5.
If time allows, I will also try to discuss a first approach towards boundedness of rationally
connected CY varieties in low dimension.
2017年10月25日(水)
講演会
11:00-12:00 数理科学研究科棟(駒場) 128号室
Ahmed Abbes 氏 (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
Ahmed Abbes 氏 (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
[ 講演概要 ]
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
2017年10月24日(火)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Christian Klingenberg 氏 (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
Christian Klingenberg 氏 (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
[ 講演概要 ]
We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Simon Markfelder.
We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Simon Markfelder.
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30, Lie群論・表現論セミナーと合同
宮岡 礼子 氏 (東北大学)
ラグランジュ交叉のフレアホモロジーに対する部分多様体論からのアプローチ (JAPANESE)
Tea: Common Room 17:00-17:30, Lie群論・表現論セミナーと合同
宮岡 礼子 氏 (東北大学)
ラグランジュ交叉のフレアホモロジーに対する部分多様体論からのアプローチ (JAPANESE)
[ 講演概要 ]
球面の等径超曲面のガウス写像による像は，複素２次超曲面Q_n(C)の極小ラグランジュ部分多様体の豊富な例を与える．簡単な場合，これはQ_n(C)の実形となり，そのフレアホモロジーは既知である．ここでは相異なる主曲率の個数が3,4,6の場合に得られた結果を報告する．当研究は，入江博（茨城大），Hui Ma（清華大学），大仁田義裕（大阪市大）との共同研究である．
球面の等径超曲面のガウス写像による像は，複素２次超曲面Q_n(C)の極小ラグランジュ部分多様体の豊富な例を与える．簡単な場合，これはQ_n(C)の実形となり，そのフレアホモロジーは既知である．ここでは相異なる主曲率の個数が3,4,6の場合に得られた結果を報告する．当研究は，入江博（茨城大），Hui Ma（清華大学），大仁田義裕（大阪市大）との共同研究である．
Lie群論・表現論セミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30, トポロジー火曜セミナーと合同
宮岡礼子 氏 (東北大学)
ラグランジュ交叉のフレアホモロジーに対する部分多様体論からのアプローチ (JAPANESE)
Tea: Common Room 17:00-17:30, トポロジー火曜セミナーと合同
宮岡礼子 氏 (東北大学)
ラグランジュ交叉のフレアホモロジーに対する部分多様体論からのアプローチ (JAPANESE)
[ 講演概要 ]
球面の等径超曲面のガウス写像による像は，複素２次超曲面Q_n(C)の極小ラグランジュ部分多様体の豊富な例を与える．簡単な場合，これはQ_n(C)の実形となり，そのフレアホモロジーは既知である．ここでは相異なる主曲率の個数が3,4,6の場合に得られた結果を報告するとともに，これらがFOOOの議論から直接得られるものではないことを述べる．当研究は，入江博（茨城大），Hui Ma（清華大学），大仁田義裕（大阪市大）との共同研究である．
球面の等径超曲面のガウス写像による像は，複素２次超曲面Q_n(C)の極小ラグランジュ部分多様体の豊富な例を与える．簡単な場合，これはQ_n(C)の実形となり，そのフレアホモロジーは既知である．ここでは相異なる主曲率の個数が3,4,6の場合に得られた結果を報告するとともに，これらがFOOOの議論から直接得られるものではないことを述べる．当研究は，入江博（茨城大），Hui Ma（清華大学），大仁田義裕（大阪市大）との共同研究である．
2017年10月23日(月)
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
通常と曜日と教室が異なっております。ご注意ください。
Christian Klingenberg 氏 (Wuerzburg University, Germany)
On the numerical discretization of the Euler equations with a gravitational force and applications in astrophysics (English)
通常と曜日と教室が異なっております。ご注意ください。
Christian Klingenberg 氏 (Wuerzburg University, Germany)
On the numerical discretization of the Euler equations with a gravitational force and applications in astrophysics (English)
[ 講演概要 ]
We consider astrophysical systems that are modeled by the multidimensional Euler equations with gravity.
First for the homogeneous Euler equations we look at flow in the low Mach number regime. Here for conventional finite volume discretizations one has excessive dissipation in this regime. We identify inconsistent scaling for low Mach numbers of the numerical fux function as the origin of this problem. Based on the Roe solver a technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations is proposed. We analyze properties of this scheme and demonstrate that its limit yields a discretization of the incompressible limit system.
Next for the Euler equations with gravity we seek well-balanced methods. We describe a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the solutions to these inhomogeneous equations is the special case of stationary solutions with zero velocity, described by a nonlinear PDE, whose solutions are called hydrostatic equilibria. We present well-balanced methods, for which we can ensure robustness, accuracy and stability, since it satisfies discrete entropy inequalities.
We will then present work in progress where we combine the two methods above.
We consider astrophysical systems that are modeled by the multidimensional Euler equations with gravity.
First for the homogeneous Euler equations we look at flow in the low Mach number regime. Here for conventional finite volume discretizations one has excessive dissipation in this regime. We identify inconsistent scaling for low Mach numbers of the numerical fux function as the origin of this problem. Based on the Roe solver a technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations is proposed. We analyze properties of this scheme and demonstrate that its limit yields a discretization of the incompressible limit system.
Next for the Euler equations with gravity we seek well-balanced methods. We describe a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the solutions to these inhomogeneous equations is the special case of stationary solutions with zero velocity, described by a nonlinear PDE, whose solutions are called hydrostatic equilibria. We present well-balanced methods, for which we can ensure robustness, accuracy and stability, since it satisfies discrete entropy inequalities.
We will then present work in progress where we combine the two methods above.
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
台風のため11月27日に延期となりました
細野 元気 氏 (東京大学)
On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
台風のため11月27日に延期となりました
細野 元気 氏 (東京大学)
On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
[ 講演概要 ]
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
阿部 圭宏 氏 (学習院大学 数学科)
2次元離散トーラスの被覆時間の精密評価 (JAPANESE)
阿部 圭宏 氏 (学習院大学 数学科)
2次元離散トーラスの被覆時間の精密評価 (JAPANESE)
[ 講演概要 ]
2次元離散トーラス上を動く単純ランダムウォーク(SRW)を考えます. 被覆時間とはSRWがトーラスのすべての点を訪問し尽くすまでに要する時間です. 被覆時間の第1次オーダーはDembo-Peres-Rosen-Zeitouni(2004)が特定しました. 本講演では筆者が最近得た被覆時間の第2次オーダーの評価を報告します. 本研究は, 2次元トーラス上のBrown運動の被覆時間を第2次オーダーまで精密に評価したBelius-Kistler(2017)の研究の離散版にあたります. 本講演では主結果を述べた後, 対数相関をもつランダム場の研究の中における本研究の位置づけを述べます.
2次元離散トーラス上を動く単純ランダムウォーク(SRW)を考えます. 被覆時間とはSRWがトーラスのすべての点を訪問し尽くすまでに要する時間です. 被覆時間の第1次オーダーはDembo-Peres-Rosen-Zeitouni(2004)が特定しました. 本講演では筆者が最近得た被覆時間の第2次オーダーの評価を報告します. 本研究は, 2次元トーラス上のBrown運動の被覆時間を第2次オーダーまで精密に評価したBelius-Kistler(2017)の研究の離散版にあたります. 本講演では主結果を述べた後, 対数相関をもつランダム場の研究の中における本研究の位置づけを述べます.
2017年10月19日(木)
社会数理コロキウム
17:00-18:30 数理科学研究科棟(駒場) 056号室
18:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
高島 克幸 氏 (三菱電機 情報技術総合研究所)
格子と同種写像に関するアルゴリズムの耐量子暗号への応用 (JAPANESE)
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20171019.pdf
18:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
高島 克幸 氏 (三菱電機 情報技術総合研究所)
格子と同種写像に関するアルゴリズムの耐量子暗号への応用 (JAPANESE)
[ 講演概要 ]
量子計算機の出現に備えて、量子計算機でも効率的に破れない公開鍵暗号の研究が活発に行われています。本講演では、その候補である格子暗号と同種写像暗号について紹介します。Shorの量子アルゴリズムにより、素因数分解問題や離散対数問題が効率的に解けます。更に、Shorアルゴリズムにより、より広いクラスである有限アーベル群に対する隠れ部分群問題が効率的に解けるので、それを避ける数学構造及びその上の計算量仮定、そしてその仮定に基づいた（効率的な）暗号構成が必要になります。本講演では、特に、格子と（楕円曲線間）同種写像という数学構造を利用する方法について概説します。
学生時代に、楕円曲線が暗号に応用されていることを知りました。そして、会社に入って楕円曲線暗号に携わり始めたのは97年でした。それから、世の移ろいと共に、楕円曲線暗号に対する要求も変わり、研究トレンドも変わりました。最近、活発に研究されている耐量子暗号である同種写像暗号は、その一例です。耐量子暗号の重要な候補である格子暗号とともに、最近の研究動向をいささかなりともお伝えするのが、本講演の目的です。
[ 参考URL ]量子計算機の出現に備えて、量子計算機でも効率的に破れない公開鍵暗号の研究が活発に行われています。本講演では、その候補である格子暗号と同種写像暗号について紹介します。Shorの量子アルゴリズムにより、素因数分解問題や離散対数問題が効率的に解けます。更に、Shorアルゴリズムにより、より広いクラスである有限アーベル群に対する隠れ部分群問題が効率的に解けるので、それを避ける数学構造及びその上の計算量仮定、そしてその仮定に基づいた（効率的な）暗号構成が必要になります。本講演では、特に、格子と（楕円曲線間）同種写像という数学構造を利用する方法について概説します。
学生時代に、楕円曲線が暗号に応用されていることを知りました。そして、会社に入って楕円曲線暗号に携わり始めたのは97年でした。それから、世の移ろいと共に、楕円曲線暗号に対する要求も変わり、研究トレンドも変わりました。最近、活発に研究されている耐量子暗号である同種写像暗号は、その一例です。耐量子暗号の重要な候補である格子暗号とともに、最近の研究動向をいささかなりともお伝えするのが、本講演の目的です。
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20171019.pdf
2017年10月17日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Hoài-Minh Nguyên 氏 (École Polytechnique Fédérale de Lausanne)
Some perspectives on negative index materials (English)
Hoài-Minh Nguyên 氏 (École Polytechnique Fédérale de Lausanne)
Some perspectives on negative index materials (English)
[ 講演概要 ]
Negative index materials (NIMs) are artificial structures whose refractive index has negative value over some frequency range. These materials were first investigated theoretically by Veselago in 1964. The existence of NIMs was confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow the construction of NIMs at scales that are interesting for applications. NIMs have attracted a lot of attention from the scientific community, not only because of potentially interesting applications, but also because of challenges in understanding their peculiar properties. Mathematically, the study of NIMs faces two difficulties. First, the equations describing the phenomenon have sign changing coefficients, hence the ellipticity and the compactness are lost in general. Second, the localized resonance, i.e., the field explodes in some regions and remains bounded in some others as the loss goes to 0, might appear. In this talk I will discuss various mathematics techniques used to understand various applications of NIMs such as cloaking and superlensing and to develop new designs for them.
Negative index materials (NIMs) are artificial structures whose refractive index has negative value over some frequency range. These materials were first investigated theoretically by Veselago in 1964. The existence of NIMs was confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow the construction of NIMs at scales that are interesting for applications. NIMs have attracted a lot of attention from the scientific community, not only because of potentially interesting applications, but also because of challenges in understanding their peculiar properties. Mathematically, the study of NIMs faces two difficulties. First, the equations describing the phenomenon have sign changing coefficients, hence the ellipticity and the compactness are lost in general. Second, the localized resonance, i.e., the field explodes in some regions and remains bounded in some others as the loss goes to 0, might appear. In this talk I will discuss various mathematics techniques used to understand various applications of NIMs such as cloaking and superlensing and to develop new designs for them.
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
石井 敦 氏 (筑波大学)
Generalizations of twisted Alexander invariants and quandle cocycle invariants (JAPANESE)
Tea: Common Room 16:30-17:00
石井 敦 氏 (筑波大学)
Generalizations of twisted Alexander invariants and quandle cocycle invariants (JAPANESE)
[ 講演概要 ]
We introduce augmented Alexander matrices, and construct link invariants. An augmented Alexander matrix is defined with an augmented Alexander pair, which gives an extension of a quandle. This framework gives the twisted Alexander invariant and the quandle cocycle invariant. This is a joint work with Kanako Oshiro.
We introduce augmented Alexander matrices, and construct link invariants. An augmented Alexander matrix is defined with an augmented Alexander pair, which gives an extension of a quandle. This framework gives the twisted Alexander invariant and the quandle cocycle invariant. This is a joint work with Kanako Oshiro.
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
Tien Cuong Dinh 氏 (Singapore)
Intersection of currents, dimension excess and complex dynamics (English)
Tien Cuong Dinh 氏 (Singapore)
Intersection of currents, dimension excess and complex dynamics (English)
[ 講演概要 ]
I will discuss dynamical properties of Henon maps in higher dimension, in particular, the equidistribution property of periodic points. Positive closed currents can be seen as an analytic counterpart of effective algebraic cycles. I will explain how a non-generic intersection theory for these currents, possibly with dimension excess, comes into the picture. Other applications of the intersection theory will be also discussed. This is a joint work with Nessim Sibony.
I will discuss dynamical properties of Henon maps in higher dimension, in particular, the equidistribution property of periodic points. Positive closed currents can be seen as an analytic counterpart of effective algebraic cycles. I will explain how a non-generic intersection theory for these currents, possibly with dimension excess, comes into the picture. Other applications of the intersection theory will be also discussed. This is a joint work with Nessim Sibony.
講演会
17:00-18:00 数理科学研究科棟(駒場) 128号室
Guoniu Han 氏 (Université de Strasbourg/CNRS)
Integer partitions and hook length formulas (ENGLISH)
www-irma.u-strasbg.fr/~guoniu/
Guoniu Han 氏 (Université de Strasbourg/CNRS)
Integer partitions and hook length formulas (ENGLISH)
[ 講演概要 ]
Integer partitions were first studied by Euler.
The Ferrers diagram of an integer partition is a very useful tool for
visualizing partitions. A Ferrers diagram is turned into a Young tableau
by filling each cell with a unique integer satisfying some conditions.
The number of Young tableaux is given by the famous hook length formula,
discovered by Frame-Robinson-Thrall.
In this talk, we introduce the hook length expansion technique and
explain how to find old and new hook length formulas for integer
partitions. In particular, we derive an expansion formula for the
powers of the Euler Product in terms of hook lengths, which is also
discovered by Nekrasov-Okounkov and Westburg. We obtain an extension
by adding two more parameters. It appears to be a discrete
interpolation between the Macdonald identities and the generating
function for t-cores. Several other summations involving hook length,
in particular, the Okada-Panova formula, will also be discussed.
[ 参考URL ]Integer partitions were first studied by Euler.
The Ferrers diagram of an integer partition is a very useful tool for
visualizing partitions. A Ferrers diagram is turned into a Young tableau
by filling each cell with a unique integer satisfying some conditions.
The number of Young tableaux is given by the famous hook length formula,
discovered by Frame-Robinson-Thrall.
In this talk, we introduce the hook length expansion technique and
explain how to find old and new hook length formulas for integer
partitions. In particular, we derive an expansion formula for the
powers of the Euler Product in terms of hook lengths, which is also
discovered by Nekrasov-Okounkov and Westburg. We obtain an extension
by adding two more parameters. It appears to be a discrete
interpolation between the Macdonald identities and the generating
function for t-cores. Several other summations involving hook length,
in particular, the Okada-Panova formula, will also be discussed.
www-irma.u-strasbg.fr/~guoniu/
2017年10月16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
須川 敏幸 氏 (東北大学)
Characterizations of hyperbolically $k$-convex domains in terms of hyperbolic metric
須川 敏幸 氏 (東北大学)
Characterizations of hyperbolically $k$-convex domains in terms of hyperbolic metric
[ 講演概要 ]
It is known that a plane domain $X$ with hyperbolic metric $h_X=h_X(z)|dz|$ of constant curvature $-4$ is (Euclidean) convex if and only if $h_X(z)d_X(z)\ge 1/2$, where $d_X(z)$ denotes the Euclidean distance from a point $z$ in $X$ to the boundary of $X$. We will consider spherical and hyperbolic versions of this result. More generally, we consider hyperbolic $k$-convexity (in the sense of Mejia and Minda) in the same line. A key is to observe a detailed behaviour of the hyperbolic density $h_X(z)$ near the boundary.
It is known that a plane domain $X$ with hyperbolic metric $h_X=h_X(z)|dz|$ of constant curvature $-4$ is (Euclidean) convex if and only if $h_X(z)d_X(z)\ge 1/2$, where $d_X(z)$ denotes the Euclidean distance from a point $z$ in $X$ to the boundary of $X$. We will consider spherical and hyperbolic versions of this result. More generally, we consider hyperbolic $k$-convexity (in the sense of Mejia and Minda) in the same line. A key is to observe a detailed behaviour of the hyperbolic density $h_X(z)$ near the boundary.
2017年10月11日(水)
講演会
11:00-12:00 数理科学研究科棟(駒場) 128号室
Ahmed Abbes 氏 (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
Ahmed Abbes 氏 (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
[ 講演概要 ]
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 056号室
Michael Temkin 氏 (The Hebrew University of Jerusalem)
Logarithmic resolution of singularities (ENGLISH)
Michael Temkin 氏 (The Hebrew University of Jerusalem)
Logarithmic resolution of singularities (ENGLISH)
[ 講演概要 ]
The famous Hironaka's theorem asserts that any integral algebraic variety X of characteristic zero can be modified to a smooth variety X_res by a sequence of blowings up. Later it was shown that one can make this compatible with smooth morphisms Y --> X in the sense that Y_res --> Y is the pullback of X_res --> X. In a joint project with D. Abramovich and J. Wlodarczyk, we construct a new algorithm which is compatible with all log smooth morphisms (e.g. covers ramified along exceptional divisors). We expect that this algorithm will naturally extend to an algorithm of resolution of morphisms to log smooth ones. In particular, this should lead to functorial semistable reduction theorems. In my talk I will tell about main ideas of the classical algorithm and will then discuss logarithmic and stack-theoretic modifications we had to make in the new algorithm.
The famous Hironaka's theorem asserts that any integral algebraic variety X of characteristic zero can be modified to a smooth variety X_res by a sequence of blowings up. Later it was shown that one can make this compatible with smooth morphisms Y --> X in the sense that Y_res --> Y is the pullback of X_res --> X. In a joint project with D. Abramovich and J. Wlodarczyk, we construct a new algorithm which is compatible with all log smooth morphisms (e.g. covers ramified along exceptional divisors). We expect that this algorithm will naturally extend to an algorithm of resolution of morphisms to log smooth ones. In particular, this should lead to functorial semistable reduction theorems. In my talk I will tell about main ideas of the classical algorithm and will then discuss logarithmic and stack-theoretic modifications we had to make in the new algorithm.
2017年10月10日(火)
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30
與倉 昭治 氏 (鹿児島大学)
Poset-stratified spaces and some applications (JAPANESE)
Tea: Common Room 17:00-17:30
與倉 昭治 氏 (鹿児島大学)
Poset-stratified spaces and some applications (JAPANESE)
[ 講演概要 ]
A poset-stratified space is a continuous map from a topological space to a poset with the Alexandroff topology. In this talk I will discuss some thoughts about poset-stratified spaces from a naive general-topological viewpoint, some applications such as hyperplane arrangements and poset-stratified space structures of hom-sets, and related topics such as characteristic classes of vector bundles, dependence of maps (by Borsuk) and dependence of cohomology classes (by Thom).
A poset-stratified space is a continuous map from a topological space to a poset with the Alexandroff topology. In this talk I will discuss some thoughts about poset-stratified spaces from a naive general-topological viewpoint, some applications such as hyperplane arrangements and poset-stratified space structures of hom-sets, and related topics such as characteristic classes of vector bundles, dependence of maps (by Borsuk) and dependence of cohomology classes (by Thom).
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