過去の記録 ~08/17本日 08/18 | 今後の予定 08/19~



16:45-18:15   数理科学研究科棟(駒場) 122号室
Marcel Bischoff 氏 (Vanderbilt Univ.)
Conformal field theory, subfactors and planar algebras


16:45-18:15   数理科学研究科棟(駒場) 122号室
Marcel Bischoff 氏 (Vanderbilt Univ.)
Conformal field theory, subfactors and planar algebras (ENGLISH)
[ 講演参考URL ]



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
北山 貴裕 氏 (東京工業大学)
Representation varieties detect essential surfaces (JAPANESE)
[ 講演概要 ]
Extending Culler-Shalen theory, Hara and I presented a way to construct
certain kinds of branched surfaces (possibly without any branch) in a 3-
manifold from an ideal point of a curve in the SL_n-character variety.
There exists an essential surface in some 3-manifold known to be not
detected in the classical SL_2-theory. We show that every essential
surface in a 3-manifold is given by the ideal point of a line in the SL_
n-character variety for some n. The talk is partially based on joint
works with Stefan Friedl and Matthias Nagel, and also with Takashi Hara.



10:30-12:00   数理科学研究科棟(駒場) 126号室
児玉 秋雄 氏
On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)
[ 講演概要 ]
In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.



10:00-11:30   数理科学研究科棟(駒場) 126号室
奥田隆幸 氏 (広島大学)
擬リーマン対称空間上の簡約群の固有な作用とそのコンパクト双対について (日本語)
[ 講演概要 ]
Let G be a non-compact semisimple Lie group. We take a pair of symmetric pairs (G,H) and (G,L) such that the diagonal action of G on G/H \times G/L is proper. In this talk, we show that by taking ``the compact dual of triple (G,H,L)'', we obtain a compact symmetric space M = U/K and its reflective submanifolds S_1 and S_2 satisfying that the intersection of S_1 and gS_2 is discrete in M for any g in U. In particular, we give a classification of such triples (G,H,L).



16:45-18:15   数理科学研究科棟(駒場) 122号室
嶌田洸一 氏 (東大数理)
Approximate unitary equivalence of finite index endomorphisms of the AFD



17:00-18:30   数理科学研究科棟(駒場) 122号室
Anatoly Vershik 氏 (St. Petersburg Department of Steklov Institute of Mathematics)
Random subgroups and representation theory
[ 講演概要 ]
The following problem had been appeared independently in different teams and various reason:
to describe the Borel measures on the lattice of all subgroups of given group, which are invariant with respect to the action of the group by conjugacy. The main interest of course represents nonatomic measures which exist not for any group.
I will explain how these measures connected with characters and representations of the group, and describe the complete list of such measures for infinite symmetric group.


17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea : 17:00-17:30 Common Room
作間 誠 氏 (広島大学)
The Cannon-Thurston maps and the canonical decompositions of punctured surface bundles over the circle (JAPANESE)
[ 講演概要 ]
To each once-punctured-torus bundle over the circle with pseudo-Anosov monodromy,
there are associated two tessellations of the complex plane:
one is the triangulation of a horosphere induced by the canonical decomposition into ideal tetrahedra,
and the other is a fractal tessellation given by the Cannon-Thurston map of the fiber group.
In a joint work with Warren Dicks, I had described the relation between these two tessellations.
This result was recently generalized by Francois Gueritaud to punctured surface bundles
with pseudo-Anosov monodromy where all singuraities of the invariant foliations are at punctures.
In this talk, I will explain Gueritaud's work and related work by Naoki Sakata.



10:30-12:00   数理科学研究科棟(駒場) 126号室
鈴木 雄大 氏 (東京大学)
Cohomology Formula for Obstructions to Asymptotic Chow semistability (JAPANESE)
[ 講演概要 ]
Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. We generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Manfred Lehn 氏 (Mainz/RIMS)
Twisted cubics and cubic fourfolds (English)
[ 講演概要 ]
The moduli scheme of generalised twisted cubics on a smooth
cubic fourfold Y non containing a plane is smooth projective of
dimension 10 and admits a contraction to an 8-dimensional
holomorphic symplectic manifold Z(Y). The latter is shown to be
birational to the Hilbert scheme of four points on a K3 surface if
Y is of Pfaffian type. This is a report on joint work with C. Lehn,
C. Sorger and D. van Straten and with N. Addington.


16:50-18:20   数理科学研究科棟(駒場) 128号室
西岡 國雄 氏 (中央大学商学部)
[ 講演概要 ]
正の定速ドリフトに負の compound Poisson 過程(共通分布は F)を
加えた加法過程 { X (t) } が, 負領域へ到達する最小時刻を T_0 とする.
よく知られた保険会社の収支モデル(Lundberg model) では, T_0 が倒産時刻となる.
我々は, F が "デルタ測度の線形結合 =D" であるとき, 同時分布 
v (x) ={\mathbf E}_x \big[ e^{- \alpha \, T_0 + i \, \beta \, X(T_0) }\, \big],
\quad x \geq 0, \ \alpha \geq 0, \ \beta \in {\mathbb R}^1.
(i) $v(0)$ を Feller の補題を利用して計算,
(ii) $v(x)$ が満たす積分微分方程式を用意し, $v(0)$ から $v(x)$ を導出.

従来は F が指数分布以外では, $v(x)$ の具体型は知られていなかったが,
D は確率測度空間の中の dense subset なので, これにより,
任意の F にたいし近似解が構成でき, 精密な近似定理を得ることが出来た.
更に, F が ``\,実数を径数とするガンマ分布\,''
や ``\,truncated exponential distribution\,'' の場合にも, 新たに
厳密解 $v(x)$ を得ることが出来る.


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.
[ 講演参考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
[ 講演参考URL ]

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