過去の記録

2015年07月17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

Realization of tropical curves in complex tori (Japanese)
[ 講演概要 ]
Tropical curves are combinatorial object satisfying certain harmonicity condition. They reflect properties of holomorphic curves, and rather precise correspondence is known between tropical curves in real affine spaces and holomorphic curves in toric varieties. In this talk we extend this correspondence to the periodic case. Namely, we give a correspondence between periodic plane tropical curves and holomorphic curves in complex tori. This is a joint work with Tony Yue Yu.

東京無限可積分系セミナー

14:00-16:00   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07月16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

ネットワーク曲率流の3重点周りの正則性について (Japanese)
[ 講演概要 ]

2015年07月14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 : 16:30-17:00 Common Room
Carlos Moraga Ferrandiz 氏 (東京大学大学院数理科学研究科, 日本学術振興会)
How homoclinic orbits explain some algebraic relations holding in Novikov rings. (ENGLISH)
[ 講演概要 ]
Given u, a de-Rham cohomology class of degree 1 of a closed manifold M, we consider the space F_u of (closed) Morse 1-forms in this class. In Morse theory, it is important to equip each α in F_u with a descending pseudo-gradient X. The case u=0 yields usual Morse theory, while u ≠ 0 yields Morse-Novikov theory, which is devoted to the understanding of the space of equipped 1-forms (α,X) with α in F_u.
Here, X is a descending pseudo-gradient, which is said to be adapted to α.

The morphism π1(M) → R induced by u (given by the integral of any α in F_u over a loop of M) determines a set of u-negative loops.

We show that for every u-negative g in π1(M), there exists a co-dimension 1 C∞-stratum Sg of F_u which is naturally co-oriented. The stratum Sg is made of elements (α, X) such that X has exactly one homoclinic orbit L whose homotopy class is g.

The goal of this talk is to show that there exists a co-dimension 1 C∞-stratum Sg (0) of Sg which lies in the closure of Sg^2. This result explains geometrically an easy algebraic relation holding in the Novikov ring associated with u.
We will mention how this study generalizes to produce some non-evident symmetric formulas holding in the Novikov ring.

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Lin Wang 氏 (Tsinghua University)
Viscosity solutions of Hamilton-Jacobi equations from a dynamical viewpoint (English)
[ 講演概要 ]
By establishing an implicit variational principle for contact Hamiltonian systems, we detect some properties of viscosity solutions of Hamilton-Jacobi equations of certain Hamilton-Jacobi equations depending on unknown functions, including large time behavior and regularity on certain sets. Besides, I will talk about some connections with contact geometry, thermodynamics and nonholonomic mechanics.

解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Li Yutian 氏 (Department of Mathematics, Hong Kong Baptist University)
Small-time Asymptotics for Subelliptic Heat Kernels (English)
[ 講演概要 ]
Subelliptic operators are the natural generalizations of the Laplace- Beltrami operators, and they play important roles in geometry, several complex variables, probability and physics. As in the classical spectral theory for the elliptic operators, some geometrical properties of the induced subRiemannian geometry can be extracted from the analysis of the heat kernels for subelliptic operators. In this talk we shall review the recent progress in the heat kernel asymptotics for subelliptic operators. We concentrate on the small-time asymptotics of the heat kernel on the diagonal, or equivalently, the asymptotics for the trace. Our interest is to find the exact form of the leading term, and this will lead to a Weyl’s asymptotic formula for the subelliptic operators. This is a joint work with Professor Der-Chen Chang.

Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 122号室
Paul Baum 氏 (Penn State University)
MORITA EQUIVALENCE REVISITED
[ 講演概要 ]
Let X be a complex affine variety and k its coordinate algebra. A k- algebra is an algebra A over the complex numbers which is a k-module (with an evident compatibility between the algebra structure of A and the k-module structure of A). A is not required to have a unit. A k-algebra A is of finite type if as a k-module A is finitely generated. This talk will review Morita equivalence for k-algebras and will then introduce --- for finite type k-algebras ---a weakening of Morita equivalence called geometric equivalence. The new equivalence relation preserves the primitive ideal space (i.e. the set of isomorphism classes of irreducible A-modules) and the periodic cyclic homology of A. However, the new equivalence relation permits a tearing apart of strata in the primitive ideal space which is not allowed by Morita equivalence.

Let G be a connected split reductive p-adic group, The ABPS (Aubert- Baum-Plymen-Solleveld) conjecture states that the finite type algebra which Bernstein assigns to any given Bernstein component in the smooth dual of G, is geometrically equivalent to the coordinate algebra of the associated extended quotient. The second talk will give an exposition of the ABPS conjecture.

2015年07月13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) 126号室

$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains
[ 講演概要 ]
Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.

東京確率論セミナー

16:30-18:20   数理科学研究科棟(駒場) 128号室

Mykhaylo Shkolnikov 氏 (Mathematics Department, Princeton University) 16:30-17:20
On interacting particle systems in beta random matrix theory
[ 講演概要 ]
I will first introduce multilevel Dyson Brownian motions and review how those extend to the setting of beta random matrix theory. Then, I will describe a connection between multilevel Dyson Brownian motions and interacting particle systems on the real line with local interactions. This is the first connection of this kind for values of beta different from 1 and 2. Based on joint work with Vadim Gorin.
Stefan Adams 氏 (Mathematics Institute, Warwick University) 17:30-18:20
Random field of gradients and elasticity
[ 講演概要 ]
Random fields of gradients are a class of model systems arising in the studies of random interfaces, random geometry, field theory, and elasticity theory. These random objects pose challenging problems for probabilists as even an a priori distribution involves strong correlations, and are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena. They emerge in the following three areas, effective models for random interfaces, Gaussian Free Fields (scaling limits), and mathematical models for the Cauchy-Born rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are non-convex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures, the scaling to GFF and strict convexity of the free energy. We present in the talk first results for the free energy and the scaling limit at low temperatures using Gaussian measures and rigorous renormalisation group techniques yielding an analysis in terms of dynamical systems. The key ingredient is a finite range decomposition for parameter dependent families of Gaussian measures. (partly joint work with S. Mueller & R. Kotecky)

2015年07月11日(土)

調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室

An intrinsic square function on weighted Herz spaces with variable exponent
(日本語)
[ 講演概要 ]

あるintrinsic square functionの有界性を各指数に適当な条件を仮定したもとで証明する。本講演の内容は、首都大学東京野井貴弘氏との共同研究に基づく。

Remarks on the strong maximum principle involving p-Laplacian
(日本語)
[ 講演概要 ]
Let $\Omega$ be a bounded domain of ${\bf R}^N (N\ge 1)$.
for the following operator:
$-\Delta_p+a(x)Q(\cdot)$.
Here $1 < p < \infty$, $0\le a\in L^1(\Omega)$, $a\ge 0$ a.e. in $\Omega$, $\Delta_p$ is a p-Laplacian and $Q(\cdot)$ is a nonlinear term satisfying the conditions $[Q_0]$ and $[Q_1]$.
Let $p^* = \max(1, p-1)$ and let $u\in L^1(\Omega)$, $u\ge 0$ a.e. in $\Omega$ such that
$Q(u)\in L^1(\Omega), |\nabla u|\in L^{p^*}_{loc}(\Omega)$
and
$\Delta_pu$ is a Radon measure on $\Omega$.
$-\Delta_pu+a(x)Q(u)\ge 0$ in $\Omega$
in the measure sense:
$\int_E\Delta_pu\le \int_EaQ(u)$
for every Borel set E $\subset$ $\Omega$. Then we prove that if $\tilde{u}=0$ on a set of positive p-capacity in $\Omega$,then $u=0$ a.e. in $\Omega$. Here $\tilde{u}$ is a quasicontinuous representative of $u$.
We also see the sharpness of the condition $[Q_1]$ by
constructing counter-examples.

2015年07月10日(金)

博士論文発表会

13:30-14:45   数理科学研究科棟(駒場) 128号室

On stability of viscosity solutions under non-Euclidean metrics（非ユークリッド距離構造の下での粘性解の安定性） (JAPANESE)

2015年07月09日(木)

東京無限可積分系セミナー

15:00-18:30   数理科学研究科棟(駒場) 056号室

LMO 関手の拡張と形式的 Gauss 積分 (JAPANESE)
[ 講演概要 ]
Cheptea-葉廣-Massuyeau は，閉 3 次元多様体の LMO 不変量の拡張とし
て LMO 関手を導入した．
LMO 関手は「高々 1 個の境界成分を持つ曲面の間の Lagrangian コボルディズ
ムを射とするモノイダル圏」から「ある Jacobi 図の形式的級数を射とするモノ
イダル圏」へのテンソル積を保つ関手である．

べたい．

[ 講演概要 ]
n 次元トンプソン群 nV (n は 1 以上の自然数)は、トンプソン群 V の一般化として Brin により 2004 年に定義された。V がカントール集合 C の自己同相群の部分群として表 されるのに対し、各 nV は C の n 個の直積の、自己同相群の部分群となっている。本講演 では nV のエンド数が 1 であること、また相対エンド数を無限大とする部分群が存在する ことについて述べる。相対エンド数を無限大とする部分群を構成する際の議論から、nV が Haagerup property を持つことが示される。また、nV がコンパクトケーラー多様体の 基本群でないことも示される。これらの結果は、V を扱った Farley の結果の拡張である。

2015年07月08日(水)

作用素環セミナー

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

FMSPレクチャーズ

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 ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

2015年07月07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 : 16:30-17:00 Common Room

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.

2015年07月06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) 126号室

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.

2015年07月03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

[ 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).

2015年07月01日(水)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室

Approximate unitary equivalence of finite index endomorphisms of the AFD
factors

2015年06月30日(火)

Lie群論・表現論セミナー

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.

トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea : 17:00-17:30 Common Room

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.

2015年06月29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) 126号室

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.

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
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.

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

[ 講演概要 ]

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.

$$v (x) ={\mathbf E}_x \big[ e^{- \alpha \, T_0 + i \, \beta \, X(T_0) }\, \big], \quad x \geq 0, \ \alpha \geq 0, \ \beta \in {\mathbb R}^1.$$
の具体型を以下の方法で求めた.
(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.

D は確率測度空間の中の dense subset なので, これにより,

や \,truncated exponential distribution\,'' の場合にも, 新たに

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

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.)

作用素環セミナー

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