過去の記録

過去の記録 ~10/22本日 10/23 | 今後の予定 10/24~

講演会

15:00-16:00   数理科学研究科棟(駒場) 056号室
Alexander Kupers 氏 (Harvard University)
Cellular E_2-algebras and the unstable homology of mapping class groups

[ 講演概要 ]
We discuss joint work with Soren Galatius and Oscar Randal-Williams on the application of higher-algebraic techniques to classical questions about the homology of mapping class groups. This uses a new "multiplicative" approach to homological stability -- in contrast to the "additive" one due to Quillen -- which has the advantage of providing information outside of the stable range.

2018年06月11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
千葉 優作 氏 (お茶の水女子大学)
Cohomology of non-pluriharmonic loci (JAPANESE)
[ 講演概要 ]
In this talk, we study a pseudoconvex counterpart of the Lefschetz hyperplane theorem.
We show a relation between the cohomology of a pseudoconvex domain and the cohomology of the non-pluriharmonic locus of an exhaustive plurisubharmonic function.

2018年06月06日(水)

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
Nicolas Templier 氏 (Cornell University)
On the Ramanujan conjecture for automorphic forms over function fields
[ 講演概要 ]
Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of Bun_G, and on trace formulas. Work with Will Sawin.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of Mathematics と IHES の双方向同時中継で行います.今回はパリからの中継です.)

2018年06月05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
松井 宏樹 氏 (千葉大学)
Topological full groups and generalizations of the Higman-Thompson groups (JAPANESE)
[ 講演概要 ]
For a topological dynamical system on the Cantor set, one can introduce its topological full group, which is a countable subgroup of the homeomorphism group of the Cantor set. The Higman-Thompson group V_n is regarded as the topological full group of the one-sided full shift over n symbols. Replacing the one-sided full shift with other dynamical systems, we obtain variants of the Higman-Thompson group. It is then natural to ask whether those generalized Higman-Thompson groups possess similar (or different) features. I would like to discuss isomorphism classes of these groups, finiteness properties, abelianizations, connections to C*-algebras and their K-theory, and so on.

2018年06月04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) 126号室
三竹 大寿 氏 (東京大学大学院数理科学研究科)
退化粘性ハミルトン・ヤコビ方程式の一意性集合 (JAPANESE)
[ 講演概要 ]
Hamilton-Jacobi (HJ)方程式の初期値問題の解の長時間挙動を考えた時に現れる定常問題を,加法的固有値問題と呼ぶ.この加法的固有値問題の粘性解は,一意性が成り立たないことがよく知られている.力学系におけるAubry-Mather理論と粘性解理論との関係を整理することで発展した弱Kolmogorov-Arnold-Moser (KAM) 理論において,Mather集合またはAubry集合上で一致する粘性解は一意的であることが証明された.つまり,これらの集合は,加法的固有値問題の粘性解の一意性集合の役割を果たす.
最適確率制御問題を考えると自然に現れる退化粘性HJ方程式は,粘性解理論においてより自然な枠組みとして考えることができるが,従来の弱KAM理論では,決定論的な力学系しか扱えないため,取り扱いが困難であった.この点に注目をして,講演者は偏微分方程式論の立場から取り組むことで,弱KAM理論を発展させてきた.本講演では,特に退化粘性HJ方程式の加法的固有値問題の一意性集合について,最近得られた結果について紹介する.
解析のポイントは,対応する一般化されたMather測度を非線形随伴法で構成する点にある.この点での解析手段は,偏微分方程式論において閉じている話題ではあるが,背景に最適確率制御の問題を抱えているため,確率論において一つの新しい題材を提供できればと思っている.なお,本研究はH. V. Tran氏(U. Wisconsin-Madison)との共同研究である.

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
野口潤次郎 氏 (東京大学)
Picardの大定理とManin-Mumford予想(Raynaudの定理) (JAPANESE)
[ 講演概要 ]
Manin-Mumford予想とは,関数体上のMordell予想が解決された後の1960年代後半にManinとMumfordにより(独立に)提示されたもので1983年にM. Raynaudにより『代数体上定義されたアーベル多様体の代数的部分空間$X$内のトージョン点集合$X_{tor}$の$\mathbb{Z}$-閉包は部分群の平行移動の有限和である』という形で解決された.この結果は内容の深さからか多くの研究者の関心を呼び、その後,一般化や種々の別証明がM. Hindry ('88), E. Hrushovski ('96), Pila-Zannier ('08)等により与えられてきた.最後のPila-Zannierがここでの話に関係する.
本講演では,準アーベル多様体に対し拡張されたPicardの大定理(N. '81)を用いて上記Manin-Mumford予想(Raynaudの定理)を準アーベル多様体の場合に証明する.
Nevanlinna理論とDiophantus幾何については,これまで類似の観点からの議論・成果が多くあったが,今回の結果は証明レベルでの直接的な関係で,この様な関係を講演者は永く求めてきた(missing link).その意味で今般の知見は新しいもものであると思う.両理論の間をモデル理論の"o-minimal sets 理論''が取り持つ点も興味深いところと思う.

2018年05月31日(木)

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Olivier Pironneau 氏 (Sorbonne University and Academy of Sciences)
Parallel Computing Methods for Quantitative Finance: the Parareal Algorithm for American Options (English)
[ 講演概要 ]
With parallelism in mind we investigate the parareal method for American contracts both theoretically and numerically. Least-Square Monte-Carlo (LSMC) and parareal time decomposition with two or more levels are used, leading to an efficient parallel implementation which scales linearly with the number of processors and is appropriate to any multiprocessor-memory architecture in its multilevel version. We prove $L^2$ superlinear convergence for an LSMC backward in time computation of American contracts, when the conditional expectations are known, i.e. before Monte-Carlo discretization. In all cases the computing time is increased only by a constant factor, compared to the sequential algorithm on the finest grid, and speed-up is guaranteed when the number of processors is larger than that constant. A numerical implementation will be shown to confirm the theoretical error estimates.

2018年05月30日(水)

代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室
竹内大智 氏 (東京大学数理科学研究科)
Blow-ups and the class field theory for curves (JAPANESE)
[ 講演概要 ]
幾何学的類体論とは、有限体上一変数代数関数体に対する類体論の、係数が一般の完全体の場合への拡張であり、M. Rosenlichtにより証明された定理である。一方1980年代、P. Deligneにより、順分岐の場合の別証明が見いだされた。それは曲線の対称積が、そのJacobi多様体上の射影(或いはアフィン)空間束になることを用いるものである。本講演では対称積のブローアップを考えることで、一般の分岐の場合でも類似の方法で証明できることを説明する。

2018年05月29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
佐藤 光樹 氏 (東京大学大学院数理科学研究科)
A partial order on nu+ equivalence classes (JAPANESE)
[ 講演概要 ]
The nu+ equivalence is an equivalence relation on the knot concordance group. Hom proves that many concordance invariants derived from Heegaard Floer homology are invariant under nu+ equivalence. In this work, we introduce a partial order on nu+ equivalence classes, and study its algebraic and geometrical properties. As an application, we prove that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.

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
Alessandra Sarti 氏 (Universit\'e de Poitiers)
Nikulin configurations on Kummer surfaces (English)
[ 講演概要 ]
A Nikulin configuration is the data of
16 disjoint smooth rational curves on a K3 surface.
According to results of Nikulin this means that the K3 surface
is a Kummer surface and the abelian surface in the Kummer structure
is determined by the 16 curves. An old question of Shioda is about the
existence of non isomorphic Kummer structures on the same Kummer K3
surface.
The question was positively answered and studied by several authors, and
it was shown that the number of non-isomorphic Kummer structures is
finite,
but no explicit geometric construction of such structures was given.
In the talk I will show how to construct explicitely non isomorphic
Kummer structures on generic Kummer K3 surfaces.
This is a joint work with X. Roulleau.

2018年05月28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
中村聡 氏 (東北大学)
A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
[ 講演概要 ]
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.

数理人口学・数理生物学セミナー

15:30-16:30   数理科学研究科棟(駒場) 122号室
Sourav Kumar Sasmal 氏 (Department of Physics and Mathematics, Aoyama Gakuin University)
T-cell mediated adaptive immunity in primary dengue infections
[ 講演概要 ]
Currently, dengue virus (DENV) is the most common mosquito-borne viral disease in the world, which is endemic across tropical Asia, Latin America, and Africa. The global DENV incidence is increasing day by day due to climate changing. According to a report, DENV cases increase almost five times since 1980, than the previous 30 years. Mathematical modeling is a common tool for understanding, studying and analyzing the mechanisms that govern the dynamics of infectious disease. In addition, models can be used to study different mitigation measures to control outbreaks. Here, we present a mathematical model of DENV dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T -cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment effect for DENV in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.

[ 講演参考URL ]
https://www.sciencedirect.com/science/article/pii/S0022519317303211

2018年05月25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
阿部紀行 氏 (東京大学大学院数理科学研究科)
p進簡約群の法p表現 (日本語)
[ 講演概要 ]
近年p進Langlands対応や法p Langlands対応を動機として,p進簡約群の標数pの体の上の表現(法p表現)の研究が行われています.そのような表現論の現状,特に既約表現の分類についてお話しします.

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
普段と違う金曜日にセミナーを行います。The seminar will be held on Friday. This is a different day from usual.
De Qi Zhang 氏 (Singapore)
Endomorphisms of normal projective variety and equivariant-MMP (English)
[ 講演概要 ]
We report some recent joint works on polarized or int-amplified endomorphisms f on a normal projective variety X with mild singularities, and prove the pseudo-effectivity of the anti-canonical divisor of X, and the f-equivariance, after replacing f by its power, for every minimal model program starting from X. Fano varieties and Q-abelian varieties turn out to be building blocks having such symmetries. The ground field is closed and of characteristic 0 or at least 7.

2018年05月24日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
柳田英二 氏 (東京工業大学)
Sign-changing solutions for a one-dimensional semilinear parabolic problem (Japanese)
[ 講演概要 ]
This talk is concerned with a nonlinear parabolic equation on a bounded interval with the homogeneous Dirichlet or Neumann boundary condition. Under rather general conditions on the nonlinearity, we consider the blow-up and global existence of sign-changing solutions. It is shown that there exists a nonnegative integer $k$ such that the solution blows up in finite time if the initial value changes its sign at most $k$ times, whereas there exists a stationary solution with more than $k$ zeros. The proof is based on an intersection number argument combined with a topological method.

2018年05月23日(水)

統計数学セミナー

14:00-15:10   数理科学研究科棟(駒場) 052号室
Lorenzo Mercuri 氏 (University of Milan)
"yuima.law": From mathematical representation of general Lévy processes to a numerical implementation
[ 講演概要 ]
We present a new class called yuima.law that refers to the mathematical description of a general Lévy process used in the formal definition of a general Stochastic Differential Equation. The final aim is to have an object, defined by the user, that contains all possible information about the Lévy process considered. This class creates a link between YUIMA and other R packages available on CRAN that manage specific Lévy processes.

An example of yuima.law is shown based the Mixed Tempered Stable(MixedTS) Lévy processes. A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated.

統計数学セミナー

15:30-16:40   数理科学研究科棟(駒場) 052号室
Emanuele Guidotti 氏 (University of Milan)
Latest Development in yuimaGUI - Interactive Platform for Computational Statistics and Finance

[ 講演概要 ]
The yuimaGUI package provides a user-friendly interface for the yuima package, including additional tools related to Quantitative Finance. It greatly simplifies tasks such as estimation and simulation of stochastic processes, data retrieval, time series clustering, change point and lead-lag analysis. Today we are going to discuss the latest development in yuimaGUI, extending the Platform with multivariate modeling and simulation, Levy processes, Point processes, broader model selection tools and more general distributions thanks to the new yuima-Law object.

2018年05月22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
柳 青 氏 (福岡大学)
A discrete game interpretation for curvature flow equations with dynamic boundary conditions (日本語)
[ 講演概要 ]
A game-theoretic approach to motion by curvature was proposed by Kohn and Serfaty in 2006. They constructed a family of deterministic discrete games, whose value functions converge to the unique solution of the curvature flow equation. In this talk, we develop this method to provide an interpretation for the associated dynamic boundary value problems by including in the game setting a kind of nonlinear reflection near the boundary. We also discuss its applications to the fattening phenomenon. This talk is based on joint work with N. Hamamuki at Hokkaido University.

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
高田 土満 氏 (東京大学大学院数理科学研究科)
無限次元多様体の解析的指数とKK理論 (JAPANESE)
[ 講演概要 ]
Atiyah-Singerの指数定理は,閉多様体上の解析的指数と位相的指数が一致することを主張する,微分トポロジーの金字塔の一つである.私の研究目標は,その指数理論の無限次元多様体版を与えることである.そのためには,できるだけ単純な場合から始めるのが自然であるため,次の問題を考えることにした:円周Tのループ群LTが,「固有かつ余コンパクトに」作用している無限次元多様体に対するLT同変指数理論を,KK理論的な観点から構築せよ.いまだにこの問題の解決には至っていないが,arXiv:1701.06055,arXiv:1709.06205 では,「関数空間」と見なせるHilbert空間を始めとする,解析的指数理論を構築するのに不可欠な対象をいくつか構成した.本講演では,この問題に対する現時点での結果を説明する.

2018年05月21日(月)

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
今週は月曜日にセミナーを行います。13:30-15:00と15:30-17:00の2講演あります。This week's seminar will be held on Monday and consist of two lectures: 13:30-15:00 and 15:30-17:00.
Christopher Hacon 氏 (Utah/Kyoto)
Towards the termination of flips. (English)
[ 講演概要 ]
The minimal model program (MMP) predicts that if $X$ is a smooth complex projective variety which is not uniruled, then there is a finite sequence of "elementary" birational maps
$X=X_0-->X_1-->X_2-->...-->X_n$ known as divisorial contractions and flips whose output $\bar X=X_n$ is a minimal model so that $K_{\bar X}$ is a nef $Q$-divisor i.e it intersects all curves $C\subset \bar X$ non-negatively: $K_{\bar X}\cdot C\geq 0$.
The existence of these birational maps has been established, but in order to complete the MMP, it is necessary to show that flips terminate i.e. there are no infinite sequences of flips. In this talk we will discuss recent results towards the termination of flips.
[ 講演参考URL ]
https://www.math.utah.edu/~hacon/

代数幾何学セミナー

13:30-15:00   数理科学研究科棟(駒場) 122号室
今週は月曜日にセミナーを行います。13:30-15:00と15:30-17:00の2講演あります。This week's seminar will be held on Monday and consist of two lectures: 13:30-15:00 and 15:30-17:00.
Will Donovan 氏 (IPMU)
Perverse sheaves of categories and birational geometry (English)
[ 講演概要 ]
Kapranov and Schechtman have initiated a program to study perverse sheaves of categories, or perverse schobers. It is expected that examples arise from birational geometry, in particular from webs of flops. I explain progress towards constructing these objects for Grothendieck resolutions (work of the above authors with Bondal), and for 3-folds (joint work of myself and Wemyss).

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
井上瑛二 氏 (東京大学)
Kähler-Ricci soliton, K-stability and moduli space of Fano
manifolds (JAPANESE)
[ 講演概要 ]
Kähler-Ricci soliton is a kind of canonical metrics on Fano manifolds and is a natural generalization of Kähler-Einstein metric in view of Kähler-Ricci flow.

In this talk, I will explain the following good geometric features of Fano manifolds admitting Kähler-Ricci solitons:
1. Volume minimization, reductivity and uniqueness results established by Tian&Zhu.
2. Relation to algebraic (modified) K-stability estabilished by Berman&Witt-Niström and Datar&Székelyhidi.
3. Moment map picture for Kähler-Ricci soliton (‘real side’)
4. Moduli stack (‘virtual side’) and moduli space of them

A result in 1 is indispensable for the formulation in 3 and 4, and explains why we should consider solitons, beyond Einstein metrics. I also show an essential idea in the construction of the moduli space of Fano manifolds admitting Kähler-Ricci solitons and give some remarks on technical key point.

2018年05月16日(水)

FMSPレクチャーズ

14:45-15:45   数理科学研究科棟(駒場) 122号室
M.M. Lavrentʼev, Jr. 氏 (Novosibirsk State University)
Some strongly degenerate parabolic equations (joint with Prof. A. Tani) (ENGLISH)
[ 講演概要 ]
We consider some nonlinear 1D parabolic equations with the positive leading coefficient which is not away from zero. "Hyperbolic phenomena" (gradient blowing up phenomena) were reported in literature for such models. We describe special cases of regular solvability for degenerate equations under study.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_MMLavrentev.pdf

2018年05月15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
岡 睦雄 氏 (東京理科大学)
超曲面混合特異点理論とある予想 (JAPANESE)
[ 講演概要 ]
Consider a real algebraic variety of real codimension 2 defined by $V:=\{g(\mathbf x,\mathbf y)=h(\mathbf x,\mathbf y)=0\}$ in $\mathbb C^n=\mathbb R^n\times \mathbb R^n$. Put $\mathbf z=\mathbf x+i\mathbf y$ and consider complex valued real analytic function $f=g+ih$. Replace the variables $x_1,y_1\dots, x_n,y_n$ using the equality $x_j=(z_j+\bar z_j)/2,\, y_j=(z_j-\bar z_j)/2i$. Then $f$ can be understood to be an analytic functions of $z_j,\bar z_j$. We call $f$ a mixed function. In this way, $V=\{f(\mathbf z,\bar{\mathbf z})=0\}$ and we can use the techniques of complex analytic functions and the singularity theory developed there. In this talk, we explain basic properties of the singularity of mixed hyper surface $V(f)$ and give several open questions.

2018年05月14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
山田澄生 氏 (学習院大学)
Harmonic map and the Einstein equation in five dimension (JAPANESE)
[ 講演概要 ]
We present a new method in constructing 5-dimensional stationary solutions to the vacuum Einstein equation. In 1917, H. Weyl expressed the Schwarzschild black hole solution using a cylindical coordinate system, and consequently realized that the metric is completely determined by a harmonic function. Since then, the relation between harmonic maps and the Einstein equation has been explored mostly by physicists, which they call the sigma model of the Einstein equation. In this talk, after explaining the historical background, we demonstrate that in 5D, the Einstein spacetimes can have a wide range of black hole horizons in their topological types. In particular we establish an existence theorem of harmonic maps, which subsequently leads to constructions of 5D spacetimes with black hole horizons of positive Yamabe types, namely $S^3$, $S^2 \times S^1$, and the lens space $L(p,q)$. This is a joint work with Marcus Khuri and Gilbert Weinstein.

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