過去の記録 ~05/28本日 05/29 | 今後の予定 05/30~



10:30-11:30   数理科学研究科棟(駒場) 056号室
Nam Quang Le 氏 (Indiana University)
Global solutions to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations (English)
[ 講演概要 ]
The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger-Wang, Chau-Weinkove and the author solved this global problem under some restrictions on the sign or integrability of the affine mean curvature. In this talk, we explain how to remove these restrictions and obtain global solutions under optimal integrability conditions on the affine mean curvature. Our analysis also covers the case of Abreu's equation arising in complex geometry.


15:30-17:00   数理科学研究科棟(駒場) 122号室
江尻 祥 氏 (東大数理)
On varieties with splittings of relative Frobenius morphisms of Albanese maps
[ 講演概要 ]
Varieties with splittings of Frobenius morphisms are called F-split varieties, which satisfy strong properties such as Kodaira vanishing. However, some important varieties are not F-split. For example, an abelian variety is F-split if and only if its p-rank is maximum. In this talk, we discuss the class of varieties with splittings of relative Frobenius morphisms of Albanese maps, which includes abelian varieties. As a consequence of Sannai and Tanaka's characterization of ordinary abelian varieties, we see that this class also includes F-split varieties. Furthermore, for varieties in this class, we show that the Kodaira vanishing theorem holds, and that Albanese maps are algebraic fiber spaces.


17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
河澄 響矢 氏 (東京大学大学院数理科学研究科)
The Kashiwara-Vergne problem and the Goldman-Turaev Lie bialgebra in genus zero (JAPANESE)
[ 講演概要 ]
In view of results of Goldman and Turaev, the free vector space over the free loops on an oriented surface has a natural Lie bialgebra structure. The Goldman bracket has a formal description by using a special (or symplectic) expansion of the fundamental group of the surface. It is natural to ask for a formal description of the Turaev cobracket. We will show how to obtain a formal description of the Goldman-Turaev Lie bialgebra for genus 0 using a solution of the Kashiwara-Vergne problem. A similar description was recently obtained by Massuyeau using the Kontsevich integral. Moreover we propose a generalization of the Kashiwara-Vergne problem in the context of the Goldman-Turaev Lie bialgebra. This talk is based on a joint work with A. Alekseev, Y. Kuno and F. Naef.


16:50-18:00   数理科学研究科棟(駒場) 052号室
磯貝 孝 氏 (首都大学東京)
[ 講演概要 ]



15:30-17:00   数理科学研究科棟(駒場) 122号室
鈴木拓 氏 (早稲田大学)
Higher order minimal families of rational curves and Fano manifolds with nef Chern characters (Japanese. Writing in English. )
[ 講演概要 ]
In this talk, we introduce higher order minimal families $H_i$ of rational curves
associated to Fano manifolds $X$. We prove that $H_i$ is also a Fano manifold
if the Chern characters of $X$ satisfy some positivity conditions. We also provide
a sufficient condition for Fano manifolds to be covered by higher rational manifolds.


15:30-16:30   数理科学研究科棟(駒場) 002号室
Odo Diekmann 氏 (Utrecht University)
Waning and boosting : on the dynamics of immune status (ENGLISH)
[ 講演概要 ]
A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there.

[1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis
of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388
[2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259
[3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7
[4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47
[ 参考URL ]



10:30-12:00   数理科学研究科棟(駒場) 128号室
島内 宏和 氏 (山梨英和大学)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
[ 講演概要 ]
Herglotz 関数が1つ与えられたとき,対応する radial Loewner 方程式は単位円板から拡張する単連結領域族への等角写像族を定め,それは evolution family と呼ばれる単位円板の自己正則写像族と密接に関係する.本講演では, 与えられた Herglotz 関数に対する radial Loewner flow と evolution family を可視化するアルゴリズムを提示し,近似解の収束性と数値実験結果について紹介する.本研究は,堀田一敬氏(山口大学)との共同研究である.


16:45-18:15   数理科学研究科棟(駒場) 126号室
荒野悠輝 氏 (東大数理)
$C^*$-tensor categories and subfactors for totally disconnected groups


16:50-18:20   数理科学研究科棟(駒場) 128号室
星野壮登 氏 (東京大学大学院数理科学研究科)
Coupled KPZ equations and complex-valued stochastic Ginzburg-Landau equation (日本語)
[ 講演概要 ]
Gubinelli-Imkeller-PerkowskiのParacontrolled calculusによりある種の特異な非線形確率偏微分方程式について解の理論が構築されたが、一般論からは時間局所解の一意存在しか分からない。本講演では、タイトルの2つの方程式について時間大域解の存在について述べる。



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
藤内 翔太 氏 (東京大学大学院数理科学研究科)
CAT(0) properties for orthoscheme complexes (JAPANESE)
[ 講演概要 ]
Gromov showed that a cubical complex is locally CAT(0) if and only if the link of every vertex is a flag complex. Brady and MacCammond introduced an orthoscheme complex as a generalization of cubical complexes. It is, however, difficult to tell whether an orthoscheme complex is (locally) CAT(0) or not. In this talk, I will discuss a translation of Gromov's characterization for orthoscheme complexes. As a generalization of Gromov's characterization, I will show that the orthoscheme complex of locally distributive semilattice is CAT(0) if and only if it is a flag semilattice.



16:45-18:15   数理科学研究科棟(駒場) 126号室
Sorin Popa 氏 (UCLA)
未定 (English)


16:00-17:30   数理科学研究科棟(駒場) 056号室
Murray Muraskin 氏 (University of North Dakota, Grand Forks)
Mathematical Aesthetic Principles and Nonintegrable Systems (ENGLISH)
[ 講演概要 ]
The discussion presents a study of a set of mathematical principles that can be classified as "aesthetic”and shows that these principles can be cast into a set of nonlinear equations. The system of equations is nonintegrable in general. New techniques to handle the nonintegrability feature are discussed. We then illustrate how this system of equations leads to sinusoidal solutions, sine within sine solutions, the phenomenon known as beats, random type oscillations, two and three dimensional lattices, as well as multi wave packet systems. The sinusoidal solutions occur when the arbitrary data associated with the equations causes the equations to be linearized. The sinusoidal behavior totally disappears once the integrability equations are satisfied, illustrating how important the nonintegrability concept is to the development.
[ 参考URL ]



10:30-11:30   数理科学研究科棟(駒場) 268号室
Nguyen Cong Phuc 氏 (Louisiana State University)
The Navier-Stokes equations: stationary existence, conditional regularity, and self-similar singularities (English)
[ 講演概要 ]
In this talk, both stationary and time-dependent Navier-Stokes equations are discussed. The common theme is that the quadratic nonlinearity and the pressure are both treated as weights generally belonging to a Sobolev space of negative order. We obtain the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces that belong to a critical space. This result can be viewed as the stationary counterpart of an existence result obtained by H. Koch and D. Tataru for the free non-stationary Navier-Stokes equations with small initial data in $BMO^{-1}$. In another direction, some new local energy bounds are obtained for the time-dependent Navier-Stokes equations which imply the regularity condition $L_{t}^{\infty}(X)$, where $X$ is a non-endpoint borderline Lorentz space $X=L_{x}^{3, q}, q\not=\infty$. The analysis also allows us to rule out the existence of Leray's backward self-similar solutions to the Navier–Stokes equations with profiles in $L^{12/5}(\mathbb{R}^3)$ or in the Marcinkiewicz space $L^{q, \infty}(\mathbb{R}^{3})$ for any $q \in (12/5, 6)$.
This talk is based on joint work with Tuoc Van Phan and Cristi Guevara.
[ 参考URL ]



15:00-16:00   数理科学研究科棟(駒場) 128号室
Eric Chung 氏 (Chinese Univ. of Hong Kong)
Multiscale simulations of waves and applications (ENGLISH)
[ 講演概要 ]
Numerical simulations of wave propagation in heterogeneous media are important in many applications such as seismic propagation and seismic inversion.
In this talk, we will present a new multiscale approach for seismic wave propagation.
The method is able to compute the solution with much fewer degrees of freedom compared with fine mesh simulation.
The idea is to capture the multiscale features of the solutions by carefully designed multiscale basis functions.
We will also present applications to inverse problems.
[ 参考URL ]


16:00-17:00   数理科学研究科棟(駒場) 128号室
Christian Clason 氏 (University Duisburg-Essen)
Discrete regularization of parameter identification problems (ENGLISH)
[ 講演概要 ]
This talk is concerned with parameter identification problems where a distributed parameter is known a priori to take on values from a given set. This property can be promoted with the aid of a convex regularization term in the Tikhonov functional. We discuss the properties of minimizers of this functional and their numerical computation using a semismooth Newton method.
[ 参考URL ]



10:00-11:00   数理科学研究科棟(駒場) 370号室
Benny Y C Hon 氏 (City Univ. of Hong Kong)
Global-local-integration-based kernel approximation methods: Technical arguments (ENGLISH)
[ 講演概要 ]
We discuss technical details of my talk on 8 Aug. and give also proofs of some main results.
[ 参考URL ]


13:00-14:30   数理科学研究科棟(駒場) 117号室
David Nualart 氏 (Kansas University)
Malliavin calculus and normal approximations



13:00-16:30   数理科学研究科棟(駒場) 117号室
本ワークショップ・レクチャーは統計数学セミナー共催であり,JST CRESTによってサポートされています.
David Nualart 氏 (Kansas University)
Malliavin calculus and normal approximations
[ 講演概要 ]
The purpose of these lectures is to introduce some recent results on the application of Malliavin calculus combined with Stein's method to normal approximation. The Malliavin calculus is a differential calculus on the Wiener space. First, we will present some elements of Malliavin calculus, defining the basic differential operators: the derivative, its adjoint called the divergence operator and the generator of the Ornstein-Uhlenbeck semigroup. The behavior of these operators on the Wiener chaos expansion will be discussed. Then, we will introduce the Stein's method for normal approximation, which leads to general bounds for the Kolmogorov and total variation distances between the law of a Brownian functional and the standard normal distribution. In this context, the integration by parts formula of Malliavin calculus will allow us to express these bounds in terms of the Malliavin operators. We will present the application of this methodology to derive the Fourth Moment Theorem for a sequence of multiple stochastic integrals, and we will discuss some results on the uniform convergence of densities obtained using Malliavin calculus techniques. Finally, examples of functionals of Gaussian processes, such as the fractional Brownian motion, will be discussed.
[ 参考URL ]



16:30-17:30   数理科学研究科棟(駒場) 128号室
Benny Y C Hon 氏 (City Univ. of Hong Kong)
Global-local-integration-based kernel approximation methods (ENGLISH)
[ 参考URL ]


17:30-18:30   数理科学研究科棟(駒場) 128号室
Daniel Gerth 氏 (Tech. Univ. Chemnitz)
On the lifting of deterministic convergence results for inverse problems to the stochastic setting (ENGLISH)
[ 講演概要 ]
In inverse problems, the inevitable measurement noise is modelled either by a deterministic worst-case model or a stochastic one.
The development of convergence theory in both approaches appears to be rather disconnected. In this talk we seek to bridge this gap and show how deterministic result can be transferred into the stochastic setting. The talk is split into two parts. In the first part, after briefly introducing "inverse problems" and the noise models, we examine the particular problem of sparsity-promoting regularization with a Besov-space penalty term to demonstrate the lifting technique. In the second part, we present a generalization of the technique that applies to a large group of regularization methods.
[ 参考URL ]



10:00-17:10   数理科学研究科棟(駒場) 123号室
本ワークショップ・レクチャーは統計数学セミナー共催であり,JST CRESTによってサポートされています.
Nakahiro Yoshida 氏 (University of Tokyo, Institute of Statistical Mathematics, and JST CREST) 10:00-10:50
Asymptotic expansion of variations
Teppei Ogihara 氏 (The Institute of Statistical Mathematics, JST PRESTO, and JST CREST) 11:00-11:50
LAMN property and optimal estimation for diffusion with non synchronous observations
David Nualart 氏 (Kansas University) 13:10-14:00
Approximation schemes for stochastic differential equations driven by a fractional Brownian motion
David Nualart 氏 (Kansas University) 14:10-15:00
Parameter estimation for fractional Ornstein-Uhlenbeck processes
Seiichiro Kusuoka 氏 (Okayama University) 15:20-16:10
Stein's equations for invariant measures of diffusions processes and their applications via Malliavin calculus
Yasushi Ishikawa 氏 (Ehime University) 16:20-17:10
Asymptotic expansion of a nonlinear oscillator with a jump diffusion
[ 参考URL ]



15:00-16:15   数理科学研究科棟(駒場) 118号室
井上 大輔 氏 (東京大学大学院数理科学研究科)
Calabi-Yau 3-folds in Grassmannians and their I-functions (グラスマン多様体に含まれる3 次元カラビ・ヤウ多様体とそれらのI-関数)



15:00-16:00   数理科学研究科棟(駒場) 128号室
Saki Takahashi 氏 (Princeton University)
The ecological dynamics of non-polio enteroviruses: Case studies from China and Japan (ENGLISH)
[ 講演概要 ]
As we approach global eradication of poliovirus (Enterovirus C species), its relatives are rapidly emerging as public health threats. One of these viruses, Enterovirus A71 (EV-A71), has been implicated in large outbreaks of hand, foot, and mouth disease (HFMD), a childhood illness that has had a substantial burden throughout East and Southeast Asia over the past fifteen years. HFMD is typically a self-limiting disease, but a small proportion of EV-A71 infections lead to the development of neurological and systemic complications that can be fatal. EV-A71 also exhibits puzzling spatial characteristics: the virus circulates at low levels worldwide, but has so far been endemic and associated with severe disease exclusively in Asia. In this talk, I will present findings from a recent study that we did to characterize the transmission dynamics of HFMD in China, where over one million cases are reported each year. I will then describe recent efforts to explain the observed multi-annual cyclicity of EV-A71 incidence in Japan and to probe the contributions of other serotypes to the observed burden of HFMD. In closing, I will discuss plans for unifying data and modeling to study this heterogeneity in the endemicity of EV-A71, as well as to broadly better understand the spatial and viral dynamics of this group of infections.



13:00-14:30   数理科学研究科棟(駒場) 052号室
Ajay Jasra 氏 (National University of Singapore)
Multilevel Particle Filters
[ 講演概要 ]
In this talk the filtering of partially observed diffusions,
with discrete-time observations, is considered.
It is assumed that only biased approximations of the diffusion can be
obtained, for choice of an accuracy parameter indexed by $l$.
A multilevel estimator is proposed, consisting of a telescopic sum of
increment estimators associated to the successive levels.
The work associated to $\cO(\varepsilon^2)$ mean-square error between
the multilevel estimator and average with respect to the filtering
distribution is shown to scale optimally, for example as
$\cO(\varepsilon^{-2})$ for optimal rates of convergence of the
underlying diffusion approximation.
The method is illustrated on several examples.



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があります。また13:30--15:00と15:30--17:00に二つの講演があります。This week's seminar will be held on Monday, and we have two seminars from 13:30--15:00 and from 15:30--17:00.
鈴木文顕 氏 (東大数理)
Birational rigidity of complete intersections (English)
[ 講演概要 ]
A complete intersection defined by s hypersurfaces of degree d_1, ... ,d_s in a projective space P^N is Q-Fano, i.e. normal, Q-factorial, terminal and having an ample anti-canonical divisor, if d_1 + ... + d_s is at most N and it has only mild singularities. Then it is rationally-connected by the results of Kollar-Miyaoka-Mori, Zhang and Hacon-Mckernan. A natural question is to determine its rationality. If its dimension or degree is at most 2, then it is rational. How about the remaining cases?

When d_1 + ... + d_s = N, birational rigidity give one of the most effective ways to tackle this problem. We recall that a Q-Fano variety is birationally superrigid if any birational map to the source of another Mori fiber space is isomorphism. It implies that X is non-rational and Bir(X) = Aut(X). After the works of Iskovskih-Manin, Pukhlikov, Chelt'so and de Fernex-Ein-Mustata, de Fernex proved that every smooth hypersurface of degree N in P^N is birationally superrigid for N at least 4. He also proved birational superrigidity of a large class of singular hypersurfaces of this type.

In this talk, we would like to extend de Fernex's results to complete intersections. As a key step, we generalize Pukhlikov's multiplicity bounds of cycles in hypersurfaces to complete intersections.

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