過去の記録

過去の記録 ~08/18本日 08/19 | 今後の予定 08/20~

2015年10月03日(土)

調和解析駒場セミナー

13:00-18:00   数理科学研究科棟(駒場) 128号室
加藤 睦也 氏 (名古屋大学) 13:30-15:00
Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces
(日本語)
[ 講演概要 ]
$\alpha$--モジュレーション空間($0 \leq \alpha \leq 1$)はGr\"obnerによって導入された空間であり、モジュレーション空間は$\alpha=0$の特別な場合である。
本講演で は$\alpha$--モジュレーション空間と$L^p$--ソボレフ空間($1 \leq p \leq \infty$)との包含関係について紹介する。
モジュレーション空間とソボレフ空間との包含関係は Kobayashi--
Sugimotoによって最適なものが得られており、今 回の結果は$\alpha=0$としたときに彼らのものと完全に一致する。また、時間が許せば局所ハーディー空間と$\alpha$--モジュレーション空間との関係についても紹介したい。
冨田 直人 氏 (大阪大学) 15:30-17:00
最小の滑らかさの仮定の下での多重線形フーリエマルチプライヤーについて
(日本語)
[ 講演概要 ]
線形の場合に,Hormanderのマルチプライヤー定理が主張することは,次元をnとするときに,滑らかさがn/2を超えるソボレフノルムでの適切な評価をマルチプライヤーに課せば,その対応する作用素のL^p-有界性が導かれるというものである.
この結果は,滑らかさをn/2からn/p-n/2に,L^p空間をHardy空間に置き換えることにより,pが1以下の場合にも成り立つことが,Calderon-Torchinskyによって示されている.
ここで現れた滑らかさn/2, n/p-n/2というオーダーは最小であることが知られている.そして,双線形の場合には,この線形の場合に対応する結果を,宮地晶彦氏との共同研究で得ていた.
今回の講演では,さらに,多重線形の場合にも同様の結果が成り立つことをご報告したい.
結果としては,線形,双線形の場合の一般化ではあるが,これらの場合の議論をそのまま焼き直せばよいという単純なものではないことをお話したい.なお,この講演は,L. Grafakos氏,宮地晶彦氏,H. Nguyen氏との共同研究に基づく.

2015年10月02日(金)

幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室
高橋良輔 氏 (名古屋大学 多元数理科学研究科)
ケーラー・リッチソリトンの漸近的安定性 (Japanese)
[ 講演概要 ]
ケーラー・リッチソリトンは,Hamilton のリッチフローのような幾何解析に起源をもつ Fano 多様体上の標準計量であり,ここ数年広範囲に渡って研究されてきた.標準計量の存在は何らかの幾何学的不変式論的安定性と密接に関係することが期待されている.例えば,Donaldsonは,スカラー曲率一定ケーラー計量を許容しかつ自己同型群が離散な任意の偏極多様体は balanced 計量の列を持ち,さらにこの列はスカラー曲率一定ケーラー計量に収束することを証明した.本講演では,同じような結果がケーラー・リッチソリトンに対しても成り立つことを説明する.なお,この結果は Berman-Witt Nystr¥"om の先行結果を一般化するものであり,端的ケーラー計量の漸近的相対 Chow 安定性に関する満渕氏の結果の類似を与えている.

2015年09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
Alan Lauder 氏 (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
[ 講演概要 ]
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.

2015年09月29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
Tuomo Kuusi 氏 (Aalto University)
Nonlocal self-improving properties (English)
[ 講演概要 ]
The classical Gehring lemma for elliptic equations with measurable coefficients states that an energy solution, which is initially assumed to be $W^{1,2}$-Sobolev regular, is actually in a better Sobolev space space $W^{1,q}$ for some $q>2$. This is a consequence of a self-improving property that so-called reverse Hölder inequality implies. In the case of nonlocal equations a self-improving effect appears: Energy solutions are also more differentiable. This is a new, purely nonlocal phenomenon, which is not present in the local case. The proof relies on a nonlocal version of the Gehring lemma involving new exit time and dyadic decomposition arguments. This is a joint work with G. Mingione and Y. Sire.

解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 126号室
Otto Liess 氏 (University of Bologna, Italy)
On the Phragmén-Lindelöf principle for holomorphic functions and factor classes of higher order complex forms in several complex variables
[ 講演概要 ]
In this talk we will discuss maximum principles in unbounded domains in one or several complex variables. We will mainly be interested in these principles for plurisubharmonic (in the one-dimensional case, "subharmonic") or holomorphic functions, when the principles are of
Phragmen-Lindel{\"o}f principle (henceforth called "PL") type. It will turn out that for 2 or more complex variables it will be useful to study our principles together with associated principles for factor classes of complex (0,q) forms with growth type conditions at infinity.
In this abstract we only say something concerning the case of functions. We consider then an open set U in C^n in one or several complex variables. We assume that we are given two real-valued continuous functions f and g on U. We say that PL holds for plurisubharmonic (respectively for holomorphic) functions, if the following implication is true for every plurisubharmonic function $ \rho $ (respectively for every $ \rho $ of form log |h| with h holomorphic) on U: if we know that $ \rho \leq f$ on the boundary of U and if $ (\rho - f)$ is bounded on U, then it must follow that $ \rho \leq g$ on U. ($\rho \leq f$ on the boundary has the following meaning: for ever z in the boundary of U and for every sequence of points y_j in U which tends to z, we have limsup (\rho - f)(y_j) leq 0.) A trivial condition under which PL is true, is when there exists a plurisubharmonic function u on U such that
(*) -g(z) \leq u(z) \leq - f(z) for every z in U.
In fact, if such a function exists, then we can apply the classical maximal principle for unbounded domains to the function $ \rho'= \rho+u$ to obtain at first $ \rho' \leq 0$ and then $ \rho \leq - u \leq g$. It is one of the main goals of the talk to explain how far (*) is from being also a necessary condition for PL. Some examples are intended to justify our approach and applications will be given to problems in convex analysis.

2015年09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
後藤 竜司 氏 (大阪大学)
Flat structures on moduli spaces of generalized complex surfaces
[ 講演概要 ]
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.

東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
齊藤 圭司 氏 (慶應義塾大学理工学部)
低次元系の異常熱輸送現象
[ 講演概要 ]
熱伝導現象は日常的な物理現象であり、よく知られているようにフーリエの法則がもっとも普遍的で重要な法則となる。
フーリエの法則には、エネルギーが拡散方程式に従って拡散するという、ミクロな拡散メカニズムが背景にある。
しかしながら、このような現象は低次元系では一般に成り立たなくなり、異常な拡散が逆に普遍的になる。
低次元系の熱輸送は90年代後半に数値計算の進歩から数値的に示され、最近では実験も存在する。
ある種の可解系も提案され、この分野は現在、実験、物理、数学とそれぞれからのアプローチが可能となった学際的分野に成長した。本講演では、時代をおってこれらの進展を説明するとともに、最近注目されているレビーウォーク拡散からの現象論的解釈、また界面成長を記述するKPZ方程式と密接な関係を示す流体力学的ゆらぎの理論を議論する。

2015年09月25日(金)

談話会・数理科学講演会

16:50-17:50   数理科学研究科棟(駒場) 大講義室号室
Gerhard Huisken 氏 (The Mathematisches Forschungsinstitut Oberwolfach )
Mean curvature flow with surgery
[ 講演概要 ]
We study the motion of hypersurfaces in a Riemannian manifold
with normal velocity equal to the mean curvature of the
evolving hypersurface. In general this quasilinear, parabolic
evolution system may have complicated singularities in finite time.
However, under natural assumptions such as embeddedness of the surface
and positivity of the mean curvature (case of 2-dimensional surfaces)
all singularities can be classified and developing "necks" can be
removed by a surgery procedure similar to techniques employed
by Hamilton and Perelman in the Ricci-flow of Riemannian metrics.
The lecture describes results and techniques for mean curvature flow
with surgery developed in joint work with C. Sinestrari and S. Brendle.
[ 講演参考URL ]
http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken

古典解析セミナー

16:00-17:00   数理科学研究科棟(駒場) 126号室
Damiran Tseveennamjil 氏 (モンゴル生命科学大学)
Twistor理論からみた一般Schlesinger系の合流 (JAPANESE)
[ 講演概要 ]
Grassmann多様体上の一般超幾何関数に対する合流の操作の類似として、一般Schlesinger系を導く線形方程式系の合流を論じる。

2015年09月17日(木)

統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 052号室
Stefano Iacus 氏 (University of Milan)
The use of S4 classes and methods in the Yuima R package
[ 講演概要 ]
In this talk we present the basic concept of S4 classes and methods approach for object oriented programming in R. As a working example, we introduce the structure of the Yuima package for simulation and inference of stochastic differential equations. We will describe the basic classes and objects as well as some recent extensions which allows for Carma and Co-Garch processes handling in Yuima.

東京無限可積分系セミナー

14:00-15:30   数理科学研究科棟(駒場) 002号室
Simon Wood 氏 (The Australian National University)
Classifying simple modules at admissible levels through
symmetric polynomials (ENGLISH)
[ 講演概要 ]
From infinite dimensional Lie algebras such as the Virasoro
algebra or affine Lie (super)algebras one can construct universal
vertex operator algebras. These vertex operator algebras are simple at
generic central charges or levels and only contain proper ideals at so
called admissible levels. The simple quotient vertex operator algebras
at these admissible levels are called minimal model algebras. In this
talk I will present free field realisations of the universal vertex
operator algebras and show how they allow one to elegantly classify
the simple modules over the simple quotient vertex operator algebras
by using a deep connection to symmetric polynomials.

2015年09月11日(金)

FMSPレクチャーズ

17:00-18:30   数理科学研究科棟(駒場) 126号室
Alexander Voronov 氏 (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

2015年09月10日(木)

FMSPレクチャーズ

17:00-18:30   数理科学研究科棟(駒場) 126号室
Alexander Voronov 氏 (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

FMSPレクチャーズ

15:30-16:30   数理科学研究科棟(駒場) 056号室
Zhi Chen 氏 (Hefei University of Technology)
Lifting of maps between surfaces (ENGLISH)
[ 講演概要 ]
The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ZhiChen.pdf

2015年09月09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
Emmanuel Ullmo 氏 (IHES)
The hyperbolic Ax-Lindemann conjecture (English)
[ 講演概要 ]
The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.

2015年09月08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
Monika Muszkieta 氏 (Wroclaw University of Technology)
Duality based approaches to total variation-like flows with applications to image processing (English)
[ 講演概要 ]
During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of di fferentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.
This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.

解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 126号室
水谷治哉 氏 (大阪大学・理学研究科)
長距離型斥力ポテンシャルを持つシュレディンガー方程式の時間大域的ストリッカーツ評価 (Japanese)
[ 講演概要 ]
We will discuss a resent result on global-in-time Strichartz estimates for Schr\"odinger equations with slowly decreasing repulsive potentials. If the potential is of very short-range type, there is a simple method due to Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case. The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet. In particular, we employ both Morawetz type estimates and the methods of micro local analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.

2015年09月02日(水)

FMSPレクチャーズ

17:00-18:30   数理科学研究科棟(駒場) 126号室
Alexander Voronov 氏 (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

2015年08月31日(月)

博士論文発表会

16:30-17:45   数理科学研究科棟(駒場) 128号室
藤城 謙一 氏 (東京大学大学院数理科学研究科)
Approximate Controllability, Non-homogeneous Boundary Value Problems and Inverse Source Problems for Fractional Diffusion Equations(非整数階拡散方程式に対する近似可制御性、非斉次境界値問題およびソース項決定逆問題) (JAPANESE)

2015年08月28日(金)

談話会・数理科学講演会

16:50-17:50   数理科学研究科棟(駒場) 002号室
Athanase Papadopoulos 氏 (Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS)
On the development of Riemann surfaces and moduli (ENGLISH)
[ 講演概要 ]
I will describe a selection of major fundamental ideas in the theory
of Riemann surfaces and moduli, starting from the work of Riemann, and
ending with recent works.

2015年08月07日(金)

統計数学セミナー

14:40-15:50   数理科学研究科棟(駒場) 052号室
生方雅人 氏 (釧路公立大学)
Effectiveness of time-varying minimum value at risk and expected shortfall hedging
[ 講演概要 ]
This paper assesses the incremental value of time-varying minimum value at risk (VaR) and expected shortfall (ES) hedging strategies over unconditional hedging strategy. The conditional futures hedge ratios are calculated through estimation of multivariate volatility models under a skewed and leptokurtic distribution and Monte Carlo simulation for conditional skewness and kurtosis of hedged portfolio returns. We examine DCC-GJR models with or without encompassing realized covariance measure (RCM) from high-frequency data under a multivariate skewed Student's t-distribution. In the out-of-sample analysis with a daily rebalancing approach, the empirical results show that the conditional minimum VaR and ES hedging strategies outperform the unconditional hedging strategy. We find that the use of RCM improves the futures hedging performance for a short hedge, although the degree of improvement is small relative to that when switching from unconditional to conditional.

統計数学セミナー

13:20-14:30   数理科学研究科棟(駒場) 052号室
Yoann Potiron 氏 (University of Chicago)
ESTIMATION OF INTEGRATED QUADRATIC COVARIATION BETWEEN TWO ASSETS WITH ENDOGENOUS SAMPLING TIMES
[ 講演概要 ]
When estimating integrated covariation between two assets based on high-frequency data,simple assumptions are usually imposed on the relationship between the price processes and the observation times. In this paper, we introduce an endogenous 2-dimensional model and show that it is more general than the existing endogenous models of the literature. In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices follow pure-diffusion processes.

2015年07月30日(木)

博士論文発表会

10:30-11:45   数理科学研究科棟(駒場) 128号室
飛澤 和則 氏 (東京大学大学院数理科学研究科)
Theory and application of a meta lambda calculus with cross-level computation (レベル横断的計算機構を持つメタラムダ計算の理論と応用) (JAPANESE)

2015年07月29日(水)

博士論文発表会

16:00-17:15   数理科学研究科棟(駒場) 128号室
鈴木 航介 氏 (東京大学大学院数里科学研究科)
Accelerating convergence and tractability of multivariate numerical integration when the L1-norms of the higher order derivatives of the integrand grow at most exponentially(被積分関数の高階偏微分のL1ノルムの増大度が高々指数的である場合の多次元数値積分の加速的な収束と計算容易性) (JAPANESE)

博士論文発表会

17:30-18:45   数理科学研究科棟(駒場) 128号室
芳木 武仁 氏 (東京大学大学院数理科学研究科)
Research on Walsh figure of merit for higher order convergent Quasi-Monte Carlo integration(高次収束準モンテカルロ積分のためのWalsh figure of meritの研究) (JAPANESE)

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