過去の記録 ~05/28本日 05/29 | 今後の予定 05/30~


16:30-18:00   数理科学研究科棟(駒場) 056号室
小守良雄 氏 (九州工業大学大学院情報工学研究院)
Stabilized Runge-Kutta methods for the weak approximation of solutions of stochastic differential equations (日本語)
[ 講演概要 ]
We are concerned with numerical methods which give weak approximations for stiff It\^{o} stochastic differential equations (SDEs). Implicit methods are one of good candidates to deal with such SDEs. In fact, a well-designed implicit method has been recently proposed by Abdulle and his colleagues [Abdulle et al. 2013a]. On the other hand, it is well known that the numerical solution of stiff SDEs leads to a stepsize reduction when explicit methods are used. However, there are some classes of explicit methods that are well suited to solving some types of stiff SDEs. One such class is the class of stochastic orthogonal Runge-Kutta Chebyshev (SROCK) methods [Abdulle et al. 2013b]. SROCK methods reduce to Runge-Kutta Chebyshev methods when applied to ordinary differential equations (ODEs). Another promising class of methods is the class of explicit methods that reduce to explicit exponential Runge-Kutta (RK) methods [Hochbruck et al. 2005, 2010] when applied to semilinear ODEs.
In this talk, we will propose new exponential RK methods which achieve weak order two for multi-dimensional, non-commutative SDEs with a semilinear drift term. We will analytically investigate their stability properties in mean square, and will check their performance in numerical experiments.
(This is a joint work with D. Cohen and K. Burrage.)


16:45-18:15   数理科学研究科棟(駒場) 126号室
Vaughan F. R. Jones 氏 (Vanderbilt University)
Block spin renormalization and R. Thompson's groups F and T



16:50-17:50   数理科学研究科棟(駒場) 056号室
植田一石 氏 (東京大学大学院数理科学研究科)
[ 講演概要 ]



17:00-18:30   数理科学研究科棟(駒場) 002号室
中村あかね 氏 (東大数理)
4次元自励パンルヴェ型方程式と種数2の曲線の退化 (JAPANESE)
[ 講演概要 ]
パンルヴェ型方程式は楕円関数の満たす微分方程式の拡張の一つとして考えられた8種類の2階非線形微分方程式であるが、線形方程式のモノドロミー保存変形、ソリトン方程式の相似簡約、数理物理や表現論との関わりの中で詳しく研究されてきた。個々の側面に着目した差分類似や高階への拡張も多数提案される中、最近4次元パンルヴェ型微分方程式は線形方程式の観点から分類がなされた(Sakai, Kawakami-N.-Sakai, Kawakami)。このセミナーでは4次元パンルヴェ型方程式を自励化して得られる40個の可積分系の方程式をそれらのスペクトラル曲線(種数2の代数曲線である)の退化(浪川-上野型)を調べることで特徴付ける試みについて説明する。



16:45-18:15   数理科学研究科棟(駒場) 122号室
Matthew Cha 氏 (UC Davis)
Gapped ground state phases, topological order and anyons



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
松下 尚弘 氏 (東京大学大学院数理科学研究科)
Box complexes and model structures on the category of graphs (JAPANESE)
[ 講演概要 ]
To determine the chromatic numbers of graphs, so-called the graph
coloring problem, is one of the most classical problems in graph theory.
Box complex is a Z_2-space associated to a graph, and it is known that
its equivariant homotopy invariant is related to the chromatic number.

Csorba showed that for each finite Z_2-CW-complex X, there is a graph
whose box complex is Z_2-homotopy equivalent to X. From this result, I
expect that the usual model category of Z_2-topological spaces is
Quillen equivalent to a certain model structure on the category of
graphs, whose weak equivalences are graph homomorphisms inducing Z_2-
homotopy equivalences between their box complexes.

In this talk, we introduce model structures on the category of graphs
whose weak equivalences are described as above. We also compare our
model categories of graphs with the category of Z_2-topological spaces.



15:30-17:00   数理科学研究科棟(駒場) 122号室
Martí Lahoz 氏 (Institut de Mathématiques de Jussieu )
Rational cohomology tori
[ 講演概要 ]
Complex tori can be topologically characterised among compact Kähler
manifolds by their integral cohomology ring. I will discuss the
structure of compact Kähler manifolds whose rational cohomology ring is
isomorphic to the rational cohomology ring of a torus and give some
examples. This is joint work with Olivier Debarre and Zhi Jiang.
[ 参考URL ]


10:30-12:00   数理科学研究科棟(駒場) 126号室
田邊 晋 氏 (Université Galatasaray)
Amoebas and Horn hypergeometric functions
[ 講演概要 ]
Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.
There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s. In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the
analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.
As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.
This is a collaboration with Timur Sadykov.


16:50-18:20   数理科学研究科棟(駒場) 128号室
中村 ちから 氏 (京都大学数理解析研究所)
Lamplighter random walks on fractals



16:45-18:15   数理科学研究科棟(駒場) 122号室
谷本溶 氏 (東大数理)
Self-adjointness of bound state operators in integrable quantum field theory


17:00-18:00   数理科学研究科棟(駒場) 056号室
関 典史 氏 (東京大学数理科学研究科)
Hodge-Tate weights of p-adic Galois representations and Banach representations of GL_2(Q_p)
[ 講演概要 ]


14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
柿添友輔 氏 (九州大学大学院システム生命科学)
ウイルス感染に伴う時間遅れと保存量の存在:ウイルスダイナミクスの立場から (JAPANESE)
[ 講演概要 ]



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
石川 昌治 氏 (東北大学)
Stable maps and branched shadows of 3-manifolds (JAPANESE)
[ 講演概要 ]
We study what kind of stable map to the real plane a 3-manifold has. It
is known by O. Saeki that there exists a stable map without certain
singular fibers if and only if the 3-manifold is a graph manifold. According to
F. Costantino and D. Thurston, we identify the Stein factorization of a
stable map with a shadow of the 3-manifold under some modification,
where the above singular fibers correspond to the vertices of the shadow. We
define the notion of stable map complexity by counting the number of
such singular fibers and prove that this equals the branched shadow
complexity. With this equality, we give an estimation of the Gromov norm of the
3-manifold by the stable map complexity. This is a joint work with Yuya Koda.



15:30-17:00   数理科学研究科棟(駒場) 122号室
Christopher Hacon 氏 (University of Utah/RIMS)
Boundedness of the KSBA functor of
SLC models (English)
[ 講演概要 ]
Let $X$ be a canonically polarized smooth $n$-dimensional projective variety over $\mathbb C$ (so that $\omega _X$ is ample), then it is well-known that a fixed multiple of the canonical line bundle defines an embedding of $X$ in projective space. It then follows easily that if we fix certain invariants of $X$, then $X$ belongs to finitely many deformation types. Since canonical models are rarely smooth, it is important to generalize this result to canonically polarized $n$-dimensional projectivevarieties with canonical singularities. Moreover, since these varieties specialize to non-normal varieties it is also important to generalize this result to semi-log canonical pairs. In this talk we will explain a strong version of the above result that applies to semi-log canonical pairs.This is joint work with C. Xu and J. McKernan
[ 参考URL ]


10:30-12:00   数理科学研究科棟(駒場) 126号室
早乙女 飛成 氏
The Lyapunov-Schmidt reduction for the CR Yamabe equation on the Heisenberg group (Japanese)
[ 講演概要 ]
We will study CR Yamabe equation for a CR structure on the Heisenberg group which is deformed from the standard structure. By using Lyapunov-Schmidt reduction, it is shown that the perturbation of the standard CR Yamabe solution is a solution to the deformed CR Yamabe equation, under certain conditions of the deformation.


16:50-18:20   数理科学研究科棟(駒場) 128号室
高橋 弘 氏 (日本大学理工学部)


16:30-18:00   数理科学研究科棟(駒場) 056号室
宮武勇登 氏 (名古屋大学大学院工学研究科)
ハミルトン系に対する並列エネルギー保存解法 (日本語)
[ 講演概要 ]
本講演では,ハミルトン系に対するエネルギー保存解法について考える. エネルギー保存解法の研究は,近年になってようやく高精度解法導出の アイデアが提案されつつあるが,高精度化には計算コストの大幅な増大を 伴う.そこで,本講演では,無段式ルンゲクッタ法と呼ばれる数値解法の エネルギー保存条件,次数条件,並列化可能条件をある行列を用いて表現 することで,並列化可能な高精度エネルギー保存解法を導出する.



10:00-11:30   数理科学研究科棟(駒場) 126号室
服部広大 氏 (慶應大学)
The nonuniqueness of tangent cone at infinity of Ricci-flat manifolds (Japanese)
[ 講演概要 ]
For a complete Riemannian manifold (M,g), the Gromov-Hausdorff limit of (M, r^2g) as r to 0 is called the tangent cone at infinity. By the Gromov's Compactness Theorem, there exists tangent cone at infinity for every complete Riemannian manifolds with nonnegative Ricci curvatures. Moreover, if it is Ricci-flat, with Euclidean volume growth and having at least one tangent cone at infinity with a smooth cross section, then it is uniquely determined by the result of Colding and Minicozzi. In this talk I will explain that the assumption of the volume growth is essential for their uniqueness theorem.



16:00-17:30   数理科学研究科棟(駒場) 128号室
横田智巳 氏 (東京理科大学理学部第一部数学科)
準線形退化放物・放物型Keller-Segel 系の時間大域的弱解の存在と有界性: 最大正則性原理からのアプローチ (Japanese)
[ 講演概要 ]
本研究は石田祥子氏(東京理科大学)との共同研究によるものである. Keller-Segel系は細胞性粘菌の集中現象を記述するモデルとして知られており, 近年盛んに研究されている. 本講演では, 拡散と集中を表す項を準線形化した次の方程式系の初期値問題を考える:
$u_t = \Delta u^m - \nabla \cdot (u^{q-1} \nabla v)$,
$v_t = \Delta v - v + u$.
ここで, $m \ge 1$, $q \ge 2$ とする. この問題に対する時間大域的弱解の存在については, 最初にSugiyama-Kunii (2006)によって $q \le m$ という条件が提示され, その後Ishida-Yokota (2012)によって最大正則性原理を用いたアプローチにより$q < m +2/N$ (Nは空間次元)という条件下で示された. しかし, これらの研究において, 解の時間大域的な挙動の解明という観点から重要である「解の有界性」は未解決のまま残されている. なお, $q < m +2/N$ という条件は, $m=1$, $q=2$のときに対応する通常のKeller-Segel系に対する研究から, 初期値の大きさに制限なく時間大域的弱解の存在が言える条件としては最良であると考えられる. 有界領域上のNeumann問題に対しては, Tao-Winkler (2012), Ishida-Seki-Yokota (2014)によって同様の条件の下で時間大域解の存在だけでなく解の有界性まで示されているが, Gagliardo-Nirenbergの補間不等式を繰り返し用いるために計算が複雑であり, 証明の見通しが良いとは言い難い. 本講演では, 特別な場合に対するSenba-Suzuki (2006)の方法を参考に, Ishida-Yokota (2012)による最大正則性原理を用いるアプローチに小さな修正を施すことによって, 解の有界性が容易に導かれることを示す.



16:45-18:15   数理科学研究科棟(駒場) 122号室
David Kerr 氏 (Texas A&M Univ.)
Dynamics, dimension, and $C^*$-algebras



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
赤穂 まなぶ 氏 (首都大学東京)
完全ラグランジュはめ込みのシンプレクティックdisplacementエネルギーについて (JAPANESE)
[ 講演概要 ]
のシンプレクティック面積に関するある不等式を与える. 証明はChekanovが有理
いた技法を, ラグランジュはめ込みのFloerホモロジーに拡張して行う. また時
間が許せば, 我々の不等式とHofer--Zehnderのシンプレクティック容量に関する



10:30-12:00   数理科学研究科棟(駒場) 126号室
糟谷 久矢 氏 (東京工業大学)
Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds (Japanese)
[ 講演概要 ]
By the result of Deligne, Griffiths, Morgan and Sullivan, the Malcev completion of the fundamental group of a compact Kahler manifold is quadratically presented. This fact gives good advances in "Kahler group problem" (Which groups can be the fundamental groups of compact Kahler manifolds?) In this talk, we consider the fundamental groups of compact Sasakian manifolds. We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n >= 2 admits a quadratic presentation by using Morgan's bigradings of Sullivan's minimal models of mixed-Hodge diagrams.


16:50-18:20   数理科学研究科棟(駒場) 128号室
横山 聡 氏 (東京大学大学院数理科学研究科)
On a stochastic Rayleigh-Plesset equation and a certain stochastic Navier-Stokes equation



10:00-11:30   数理科学研究科棟(駒場) 126号室
四之宮佳彦 氏 (静岡大学)
Veech groups of Veech surfaces and periodic points (日本語)
[ 講演概要 ]


16:20-17:30   数理科学研究科棟(駒場) 056号室
足立高徳 氏 (立命館大学)
A Note on Algorithmic Trading based on Some Personal Experience
[ 講演概要 ]
I overview a brief history of HFT based on my 14 years' personal experience of the algorithmic trading business at a wall-street company. Starting with descriptions about layers of the algo business, I mention a stochastic index arbitrage business that I employed in some detail. After reviewing some HFT specific issues such as super short-period alpha, I try to forecast what is going on with HFT in near future.

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