過去の記録 ~03/27本日 03/28 | 今後の予定 03/29~


16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
市原 一裕 氏 (日本大学文理学部)
On exceptional surgeries on Montesinos knots
(joint works with In Dae Jong and Shigeru Mizushima) (JAPANESE)
[ 講演概要 ]
I will report recent progresses of the study on exceptional
surgeries on Montesinos knots.
In particular, we will focus on how homological invariants (e.g.
khovanov homology,
knot Floer homology) on knots can be used in the study of Dehn surgery.



16:40-18:10   数理科学研究科棟(駒場) 126号室
Yongnam Lee 氏 (Sogang University)
Slope of smooth rational curves in an anticanonically polarized Fano manifold (ENGLISH)
[ 講演概要 ]
Ross and Thomas introduce the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature metric. Since K-stability implies slope stability, slope stability gives an algebraic obstruction to theexistence of constant scalar curvature. This talk presents a systematic study of slope stability of anticanonically polarized Fano manifolds with respect to smooth rational curves. Especially, we prove that an anticanonically polarized Fano maniold is slope semistable with respect to any free smooth rational curves, and that an anticanonically polarized Fano threefold X with Picard number 1 is slope stable with respect to any smooth rational curves unless X is the project space. It is a joint work with Jun-Muk Hwang and Hosung Kim.


10:30-12:00   数理科学研究科棟(駒場) 128号室
松本 和子 氏 (大阪府立大学)
C^n の Levi 平坦実超曲面への距離の Levi form の退化条件 (JAPANESE)
[ 講演概要 ]
C^nのC^2級の実超曲面への距離のLevi formは、超曲面の定義関数の2階微分から決まるHermite行列と対称行列を用いて表現できることを示す。また、その結果を用いて、距離のLevi formが至る所退化するLevi平坦実超曲面の性質を導く。その直接的な応用として、n次元複素トーラス内の滑らかな境界を持つ擬凸部分領域がSteinになるための条件が得られる。



17:00-18:00   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:30~17:00 (コモンルーム)。

梅原雅顕 氏 (大阪大学大学院理学研究科)
ガウス・ボンネの定理と曲面上の特異点 (JAPANESE)
[ 講演概要 ]
古典的な閉曲面のガウス・ボンネの定理を, 曲面が波面としての特異点を許す場合に拡張します. すると, 古典的なテーマであるにもかかわらず, 曲面の変曲点や位相の情報と, そのガウス写像の特異点の情報との間の関係など, 意外な視点が見えてきます.



16:00-17:30   数理科学研究科棟(駒場) 002号室
Christian Klingenberg 氏 (Wuerzburg 大学 )
Hydrodynamic limit of microscopic particle systems to conservation laws to fluid models
[ 講演概要 ]
In this talk we discuss the hydrodynamic limit of a microscopic description of a fluid to its macroscopic PDE description.

In the first part we consider flow through porous media, i.e. the macroscopic description is a scalar conservation law. Here the new feature is that we allow sudden changes in porosity and thereby the flux may have discontinuities in space. Microscopically this is described through an interacting particle system having only one conserved quantity, namely the total mass. Macroscopically this gives rise to a scalar conservation laws with space dependent flux functions

u_t + f(u, x)_x = 0 .

We are able to derive the PDE together with an entropy condition as a hydrodynamic limit from a microscopic interacting particle system.

In the second part we consider a Hamiltonian system with boundary conditions. Microscopically this is described through a system of coupled oscillators. Macroscopically this will lead to a system of conservation laws, namely the p-system. The proof of the hydrodynamic limit is restricted to smooth solutions. The new feature is that we can derive this with boundary conditions.


16:30-18:00   数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (IPMU)
Random groups and nonarchimedean lattices (JAPANESE)



16:15-17:15   数理科学研究科棟(駒場) 052号室
Richard Hain 氏 (Duke大学)
Universal mixed elliptic motives (ENGLISH)
[ 講演概要 ]
This is joint work with Makoto Matsumoto. A mixed elliptic
motive is a mixed motive (MHS, Galois representation, etc) whose
weight graded quotients are Tate twists of symmetric powers of the the
motive of elliptic curve. A universal mixed elliptic motive is an
object that can be specialized to a mixed elliptic motive for any
elliptic curve and whose specialization to the nodal cubic is a mixed
Tate motive. Universal mixed elliptic motives form a tannakian
category. In this talk I will define universal mixed elliptic motives,
give some fundamental examples, and explain what we know about the
fundamental group of this category. The "geometric part" of this group
is an extension of SL_2 by a prounipotent group that is generated by
Eisenstein series and which has a family of relations for each cusp
form. Although these relations are not known, we have a very good idea
of what they are, thanks to work of Aaron Pollack, who determined
relations between the generators in a very large representation of
this group.


17:30-18:30   数理科学研究科棟(駒場) 056号室
Fabrice Orgogozo 氏 (CNRS, École polytechnique)
[ 講演概要 ]
N. Katz氏の指摘に基づいて、高次順像に於けるℓに対する
ここでは月並みな方法で有るが、A.J.de Jong氏の定理と



16:30-18:00   数理科学研究科棟(駒場) 002号室
松本純一 氏 (産業技術総合研究所)
直交基底気泡関数有限要素法による流体解析と応用計算 (JAPANESE)
[ 講演概要 ]
[ 参考URL ]


16:30-18:00   数理科学研究科棟(駒場) 002号室
松本 純一 氏 (産業技術総合研究所)
直交基底気泡関数有限要素法による流体解析と応用計算 (JAPANESE)
[ 講演概要 ]
[ 参考URL ]


15:00-16:10   数理科学研究科棟(駒場) 000号室
鎌谷 研吾 氏 (東京大学大学院数理科学研究科)
Weak convergence of Markov chain Monte Carlo method and its application to Yuima (JAPANESE)
[ 講演概要 ]
マルコフチェインモンテカルロ(MCMC)法の収束を MCMC法の弱収束の観点から論じる.とくに,MCMC法に対する マルコチェインのエルゴード性からのアプローチとの比較を行う. これらの収束理論の紹介とともに,幾つかの数値実験を統計ソフトフェアRを用いて考察する. また,MCMC法の弱収束とYuimaパッケージに実装されているadaBayes関数との関連を論じる.

[ 参考URL ]



17:00-18:30   数理科学研究科棟(駒場) 126号室
金行壮二 氏 (Sophia University)
Automorphism groups of causal Makarevich spaces (JAPANESE)
[ 講演概要 ]
Let G^ be a simple Lie group of Hermitian type and U^ be a maximal parabolic subgroup of G^ with abelian nilradical. The flag manifold M^= G^/ U^ is the Shilov
boundary of an irreducible bounded symmetric domain of tube type. M^ has the G-invariant causal structure. A causal Makarevich space is, by definition, an open symmetric G-orbit M in M^, endowed with the causal structure induced from that
of the ambient space M^, G being a reductive subgroup of G^. All symmetric cones fall in the class of causal Makarevich spaces.
In this talk, we determine the causal automorphism groups of all causal Makarevich spaces.



16:40-18:10   数理科学研究科棟(駒場) 126号室
Xavier Roulleau 氏 (東大数理)
Genus 2 curve configurations on Fano surfaces (ENGLISH)


10:30-12:00   数理科学研究科棟(駒場) 128号室
久本 智之 氏 (東大数理)
部分多様体に沿ったBergman核の漸近展開 (JAPANESE)
[ 講演概要 ]
射影多様体上の正則直線束があると, 各部分多様体に沿ったBergman核が定義される. 正則直線束のテンソル冪を繰り返し取っていったとき, 対応するBergman核の漸近的振る舞いを調べることは切断の拡張問題と密接な関係がある. 今回の話では漸近展開の主要部を特定し, 拡張問題への応用について触れる.



16:30-18:00   数理科学研究科棟(駒場) 122号室
山下真 氏 (東大数理)
Fixed Points in the Stone-Cech boundary of Groups (ENGLISH)
[ 講演概要 ]
We discuss the class of discrete groups which admit fixed points under the adjoint action on the Stone-Cech boundary. Such groups have vanishing $L^2$-Betti numbers, and nonamenable ones fail to have property (AO).


16:30-18:00   数理科学研究科棟(駒場) 470号室
Birgit Speh 氏 (Cornel University)
Introduction to the cohomology of locally symmetric spaces 2
[ 講演概要 ]
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma $.
If $X_\\Gamma $ is cocompact this cohomology can be expressed as the $(\\bg,K) $-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.

[ 参考URL ]



16:30-17:30   数理科学研究科棟(駒場) 056号室
富安亮子 氏 (高エネルギー加速器研究機構)
On some algebraic properties of CM-types of CM-fields and their
reflex fields (JAPANESE)
[ 講演概要 ]
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.

For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \\rtimes S_n$.
Using properties of the embedding, a set of CM-types $\\Phi$ of $K$ and their
dual CM-types $(K, \\Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual

I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: 16:30 - 17:00 コモンルーム
足助 太郎 氏 (東京大学大学院数理科学研究科)
On Fatou-Julia decompositions (JAPANESE)
[ 講演概要 ]
We will explain that Fatou-Julia decompositions can be
introduced in a unified manner to several kinds of one-dimensional
complex dynamical systems, which include the action of Kleinian groups,
iteration of holomorphic mappings and complex codimension-one foliations.
In this talk we will restrict ourselves mostly to the cases where the
dynamical systems have a certain compactness, however, we will mention
how to deal with dynamical systems without compactness.


16:30-18:00   数理科学研究科棟(駒場) 126号室
Birgit Speh 氏 (Cornel University)
Introduction to the cohomology of locally symmetric spaces
[ 講演概要 ]
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma $.
If $X_\\Gamma $ is cocompact this cohomology can be expressed as the $(g,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.
[ 参考URL ]



16:40-18:10   数理科学研究科棟(駒場) 126号室
金沢 篤 氏 (東大数理)
On Pfaffian Calabi-Yau Varieties and Mirror Symmetry (JAPANESE)
[ 講演概要 ]
We construct new smooth CY 3-folds with 1-dimensional Kaehler moduli and
determine their fundamental topological invariants. The existence of CY
3-folds with the computed invariants was previously conjectured. We then
report mirror symmetry for these non-complete intersection CY 3-folds.
We explicitly build their mirror partners, some of which have 2 LCSLs,
and carry out instanton computations for g=0,1.


10:30-12:00   数理科学研究科棟(駒場) 128号室
吉川 謙一 氏 (京大理)
Singularities and analytic torsion (JAPANESE)



16:30-18:00   数理科学研究科棟(駒場) 126号室
関口次郎 氏 (東京農工大)
一意化方程式の解について (JAPANESE)
[ 講演概要 ]
はじめにこれまでに調べてきた3次元アフィン空間の17種類の単純型斎藤自由因子に沿って対数的極をもつ一意化方程式について概観する。つぎにこれらの斎藤自由因子の補空間の基本群と一意化方程式の関係を論じる。Type Biii)の場合に基本群が可換になる。この場合に一意化方程式の解を初等関数をつかって表示することを試みる。



16:30-18:00   数理科学研究科棟(駒場) 128号室
Catherine Oikonomides 氏 (東大数理)
The C*-algebra of codimension one foliations which are almost without holonomy (ENGLISH)



16:20-17:30   数理科学研究科棟(駒場) 000号室
深澤 正彰 氏 (大阪大学 金融・保険教育研究センター)
R-Yuimaパッケージによるファイナンス高頻度データ解析とシミュレーション (JAPANESE)
[ 講演概要 ]
[ 参考URL ]


10:30-11:30   数理科学研究科棟(駒場) 056号室
Giovanni Pisante 氏 (Department of Mathematics
Hokkaido University)
[ 講演概要 ]
We deal with the system of eikonal equations |ðu/ðx1|=1, |ðu/ðx2|=1 in a planar Lipschitz domain with zero boundary condition. Exploiting the classical pyramidal construction introduced by Cellina, it is easy to prove that there exist infinitely many Lipschitz solutions. Then, the natural problem that has arisen in this framework is to find a way to select and characterize a particular meaningful class of solutions.
We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient. More precisely we select an optimal weighted measure for the jump set of the second derivatives of a given solution v of the system and we prove the existence of minimizers of the corresponding variational problem.

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