過去の記録

過去の記録 ~10/21本日 10/22 | 今後の予定 10/23~

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

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
[ 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.

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)
[ 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.

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)
[ 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).

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)
[ 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.

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)
[ 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.

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)
[ 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.

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)
[ 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.

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
[ 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.

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)
[ 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.

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)
[ 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。
[ 講演参考URL ]
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)
[ 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.

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)
[ 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.

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)
[ 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.

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)
[ 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.
[ 講演参考URL ]
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
[ 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.

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)
[ 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).

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)
[ 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.

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)
[ 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).

数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 002号室
中野張 氏 (東京工業大学大学院情報理工学院)
線形・非線形放物型偏微分方程式に対するメッシュフリー選点法
[ 講演概要 ]
一般に,後退確率微分方程式や確率最適制御の解は非線形放物型偏微分方程式により記述される.これらの非線形偏微分方程式の多くに対しては,滑らかさが期待できないため古典解ではなく粘性解の枠組みが採用される.よって応用のためは,解くべき偏微分方程式の粘性解に収束し,かつ多次元の問題に適用可能な数値解法が必要とされるが,既存手法の中には未だ決定的なものは存在しない状況である.

本講演では,上述の問題を解決するためにメッシュフリー選点法の適用を提案し,最近の研究成果について報告する.この目的のため,(1) 種々の確率論的問題と放物型偏微分方程式の関係の概説,(2) 粘性解の紹介,(3) 既存数値解法の紹介,(4) 動径基底関数による補間理論の紹介,(5) メッシュフリー選点法の導出,(6) 収束証明に関する結果の紹介,
という流れで話を進める.

また,フィルタリング問題に現れる線形確率偏微分方程式を対象に,メッシュフリー選点法の収束が保証される動径基底関数やグリッド点の具体例について報告する.

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
金光 秋博 氏 (東大数理)
Classification of Mukai pairs with corank 3 (English or Japanese)
[ 講演概要 ]
A Mukai pair $(X,E)$ is a pair of a Fano manifold $X$ and an ample vector bundle $E$ of rank $r$ on $X$ such that $c_1(X)=c_1(E)$. Study of such pairs was proposed by Mukai. It is known that, for a Mukai pair $(X,E)$, the rank $r$ of the bundle $E$ is at most $\dim X +1$, and Mukai conjectured the explicit
classification with $r \geq \dim X$. The above conjecture was solved independently by Fujita, Peternell and Ye-Zhang. Also the classification of Mukai pairs with $r= \dim X -1$ was given by Peternell-Szurek-Wi\'sniewski. In this talk I will give the classification of Mukai pairs with $r= \dim X -2$ and $\dim X \geq 5$.

2017年10月06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) 002号室
宮地晶彦 氏 (東京女子大学)
調和解析における特異積分と実関数論の方法 (JAPANESE)
[ 講演概要 ]
フーリエ級数の収束など古典的な調和解析の問題の多くは、
特異積分の評価の問題に帰着される。特異積分を調べる
実関数論の方法で繰り返し現れるのは最大関数と2乗型関数である。
講演では、特異積分の評価に関わる古典的な方法を振り返りながら、
双線形の特異積分など最近の話題の一端を紹介してみたい。
[ 講演参考URL ]
http://lab.twcu.ac.jp/miyachi/English.html

2017年10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
Athanase Papadopoulos 氏 (IRMA, Université de Strasbourg)
Transitional geometry (ENGLISH)
[ 講演概要 ]
I will describe transitions, that is, paths between hyperbolic and spherical geometry, passing through the Euclidean. This is based on joint work with Norbert A’Campo and recent joint work with A’Campo and Yi Huang.

2017年10月02日(月)

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
Mikael Pichot 氏 (RIMS, Kyoto Univ./McGill Univ.)
Introduction to intermediate rank geometry (English)

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
千葉 優作 氏 (お茶の水女子大学)
The extension of holomorphic functions on a non-pluriharmonic locus
[ 講演概要 ]
Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. In this talk, we show that any holomorphic function defined on a connected open neighborhood of the support of $(i\partial \overline{\partial}\varphi)^{n-3}$ can be extended to the holomorphic function on $\Omega$.

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