過去の記録 ~01/25本日 01/26 | 今後の予定 01/27~



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
Daniel Matei 氏 (IMAR, Bucharest)
Fundamental groups of algebraic varieties (ENGLISH)
[ 講演概要 ]
We discuss restrictions imposed by the complex
structure on fundamental groups of quasi-projective
algebraic varieties with mild singularities.
We investigate quasi-projectivity of various geometric
classes of finitely presented groups.


16:30-18:00   数理科学研究科棟(駒場) 002号室
名古屋靖一郎 氏 (アーク情報システム)
数式処理ソフトを用いた多次元コンパクト差分公式の導出 (JAPANESE)
[ 講演概要 ]
[ 講演参考URL ]


16:30-18:00   数理科学研究科棟(駒場) 126号室
田中雄一郎 氏 (東京大学大学院数理科学研究科)
直交群の無重複表現の幾何と可視的な作用 (JAPANESE)
[ 講演概要 ]
For a connected compact simple Lie group of type B or D,
we find pairs $(V_{1},V_{2})$ of irreducible representations of G such that the tensor product representation $V_{1}¥otimes V_{2}$ is multiplicity-free by a geometric consideration based on
a notion of visible actions on complex manifolds,
introduced by T. Kobayashi. The pairs we find exhaust
all the multiplicity-free pairs by an earlier
combinatorial classification due to Stembridge.



10:30-12:00   数理科学研究科棟(駒場) 126号室
小池 貴之 氏 (東大数理)
Minimal singular metrics of a line bundle admitting no Zariski decomposition (JAPANESE)
[ 講演概要 ]
We give a concrete expression of a minimal singular metric of a big line bundle on a compact Kähler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which have line bundles admitting no Zariski decomposition even after any proper modifications. As an application, we discuss the Zariski closedness of non-nef loci and the openness conjecture of Demailly and Kollar in this class.


15:30-17:00   数理科学研究科棟(駒場) 122号室
江 辰 氏 (東京大学数理科学研究科)
Weak Borisov-Alexeev-Borisov conjecture for 3-fold Mori Fiber spaces (ENGLISH)
[ 講演概要 ]
We investigate $\\epsilon$-klt log Fano 3-folds with some Mori fiber space structure, more precisely, with a del Pezzo fibration structure, or a conic bundle structure over projective plane. We give a bound for the log anti-canonical volume of such pair. The method is constructing non-klt centers and using connectedness lemma. This result is related to birational boundedness of log Fano varieties.



14:50-16:00   数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
村田 昇 氏 (早稲田大学)
スパースコーディングと構造化辞書学習 (JAPANESE)
[ 講演概要 ]
スパースコーディングは,多次元の観測データを複数並べた観測行列を2つの行列の積に分解する問題として,主成分分析・独立成分分析などと統一的な枠組で扱うことができ,その性質の違いは分解される行列に課される制約に依存する. 本講演では,画像を対象とした応用などを例に取り,スパースコーディング特有の性質について議論する. また,他の分解手法にはない特殊な問題として構造化された辞書の学習問題を取り上げ,そのアルゴリズムの性質について議論する.
[ 講演参考URL ]



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
今城洋亮 氏 (京都大学)
Some Uniqueness Theorems for Smoothing Singularities in Special Lagrangian Geometry (JAPANESE)
[ 講演概要 ]
Special Lagrangian submanifolds are area-minimizing Lagrangian submanifolds of Calabi--Yau manifolds. I'll talk mainly about the singularities of two special Lagrangian planes intersecting transversely. I'll determine a class of smoothing models for the singularities.
By some results of Abouzaid and Smith one can determine the smoothing models up to quasi-isomorphism in a Fukaya category. I'll combine it with a technique of Thomas and Yau.



16:30-18:00   数理科学研究科棟(駒場) 118号室
山下真 氏 (Ochanomizu Univ.)
Classification of quantum homogeneous spaces (ENGLISH)


13:00-15:30   数理科学研究科棟(駒場) 006号室
東大数理科学研究科棟 006号室
Mark Podolskij 氏 (Universität Heidelberg)
Limit theorems for ambit processes (ENGLISH)
[ 講演概要 ]
We present some recent limit theorems for high frequency observations of ambit processes. Ambit processes constitute a flexible class of models, which are usually used to describe turbulent motion in physics. Mathematically speaking, they have a continuous moving average structure with additional random component called intermittency. In the first part of the lecture we will demonstrate the asymptotic theory for ambit processes driven by Brownian motion. The second part will deal with Levy driven ambit processes. We will see that these two cases deliver completely different limiting results.

[ 講演参考URL ]



10:30-11:30   数理科学研究科棟(駒場) 056号室
Armin Schikorra 氏 (MPI for Mathematics in the Sciences, Leipzig)
Fractional harmonic maps and applications (ENGLISH)
[ 講演概要 ]
Fractional harmonic mappings are critical points of a generalized Dirichlet Energy where the gradient is replaced with a (non-local) differential operator.
I will present aspects of the regularity theory of (non-local) fractional harmonic maps into manifolds, which extends (and contains) the theory of (poly-)harmonic mappings.
I also will mention, how one can show regularity for critical points of the Moebius (Knot-) Energy, applying the techniques developed in this theory.


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
井上 玲 氏 (千葉大学)
Cluster algebra and complex volume of knots (JAPANESE)
[ 講演概要 ]
The cluster algebra was introduced by Fomin and Zelevinsky around
2000. The characteristic operation in the algebra called `mutation' is
related to various notions in mathematics and mathematical physics. In
this talk I review a basics of the cluster algebra, and introduce its
application to study the complex volume of knot complements in S^3.
Here a mutation corresponds to an ideal tetrahedron.
This talk is based on joint work with Kazuhiro Hikami (Kyushu University).


17:00-18:00   数理科学研究科棟(駒場) 126号室
Benjamin Harris 氏 (Louisiana State University (USA))
Representation Theory and Microlocal Analysis (ENGLISH)
[ 講演概要 ]
Suppose $H\\subset K$ are compact, connected Lie groups, and suppose $\\tau$ is an irreducible, unitary representation of $H$. In 1979, Kashiwara and Vergne proved a simple asymptotic formula for the decomposition of $Ind_H^K\\tau$ by microlocally studying the regularity of vectors in this representation, thought of as vector valued functions on $K$. In 1998, Kobayashi proved a powerful criterion for the discrete decomposability of an irreducible, unitary representation $\\pi$ of a reductive Lie group $G$ when restricted to a reductive subgroup $H$. One of his key ideas was to restrict $\\pi$ to a representation of a maximal compact subgroup $K\\subset G$, view $\\pi$ as a subrepresentation of $L^2(K)$, and then use ideas similar to those developed by Kashiwara and Vergne.

In a recent preprint the speaker wrote with Hongyu He and Gestur Olafsson, the authors consider the possibility of studying induction and restriction to a reductive Lie group $G$ by microlocally studying the regularity of the matrix coefficients of (possibly reducible) unitary representations of $G$, viewed as continuous functions on the (possibly noncompact) Lie group $G$. In this talk, we will outline the main results of this paper and give additional conjectures.



10:30-11:30   数理科学研究科棟(駒場) 056号室
Björn Gustavsson 氏 (KTH Royal Institute of Technology)
Some applications of partial balayage (ENGLISH)
[ 講演概要 ]
Partial balayage is a rather recent tool in potential theory. One of its origins is the construction of quadrature domains for subharmonic functions by Makoto Sakai in the 1970's. It also gives a convenient way of describing weak solutions to a moving boundary problem for Hele-Shaw flow (Laplacian growth), and recently Stephen Gardiner and Tomas Sjödin have used partial balayage to make progress on an inverse problem in potential theory. I plan to discuss some of these, and related, matters.



16:00-17:00   数理科学研究科棟(駒場) 470号室
Fikret Goelgeleyen 氏 (Bulent Ecevit University)
Stability for Inverse problems for Ultrahyperbolic Equations (ENGLISH)
[ 講演概要 ]
In this work, we consider inverse problems of determining a coefficient or a source term in an ultrahyperbolic equation by some lateral boundary data.
We prove Hoelder estimates which are global and local and the key is Carleman estimates.


17:00-18:00   数理科学研究科棟(駒場) 470号室
kazufumi Ito 氏 (North Carolina State University)
Fluid-structure interaction model and Levelset method (ENGLISH)
[ 講演概要 ]
We derive a weak form and weak solution of the level set formulation of Cottet and Maitre for fluid-structure interaction problems with immersed surfaces. The method in particular exhibits appealing mass and energy conservation properties and a variational formulation of Peskin’s Immersed Boundary methods.



17:30-18:30   数理科学研究科棟(駒場) 056号室
Peter Scholze 氏 (ボン大学)
Shimura varieties with infinite level, and torsion in the cohomology of locally symmetric spaces (ENGLISH)
[ 講演概要 ]
We will discuss the p-adic geometry of Shimura varieties with infinite level at p: They are perfectoid spaces, and there is a new period map defined at infinite level. As an application, we will discuss some results on torsion in the cohomology of locally symmetric spaces, and in particular the existence of Galois representations in this setup.

(本講演は「東京北京パリ数論幾何セミナー」として、インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)


16:30-18:00   数理科学研究科棟(駒場) 118号室
磯野優介 氏 (東大数理)
Some prime factorization results for free quantum group factors (JAPANESE)


13:30-14:40   数理科学研究科棟(駒場) 052号室
中谷 朋昭 氏 (北海道大学)
統計解析環境Rにおける多変量GARCHモデルの推定とパッケージ化 (JAPANESE)
[ 講演概要 ]
条件付相関係数型多変量GARCHモデルを推定するためのパッケージccgarch2を紹 介する。ccgarch2は、オープンソースの統計解析環境R用に開発されたアドオン パッケージであるため、幅広いOS上で動作可能である。ccgarch2では、代表的な 条件付相関係数型多変量GARCHモデルであるCCC-GARCH (Bollerslev, 1990)、 DCC-GARCH (Engle, 2002)およびその修正モデルであるcDCC-GARCH (Aielli, 2013)の推定が可能である。このほか、推定されたボラティリティや条件付相関 係数の図示、残差分析などの機能を備えている。報告では、上記の代表的GARCH モデルについて概説した後、ccgarch2の具体的な利用方法と、今後の改良予定に ついて触れる。
[ 講演参考URL ]



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
高瀬 将道 氏 (成蹊大学)
Desingularizing special generic maps (JAPANESE)
[ 講演概要 ]
This is a joint work with Osamu Saeki (IMI, Kyushu University).
A special generic map is a generic map which has only definite
fold as its singularities.
We study the condition for a special generic map from a closed
n-manifold to the p-space (n+1>p), to factor through a codimension
one immersion (or an embedding). In particular, for the cases
where p = 1 and 2 we obtain complete results.
Our techniques are related to Smale-Hirsch theory,
topology of the space of immersions, relation between the space
of topological immersions and that of smooth immersions,
sphere eversions, differentiable structures of homotopy spheres,
diffeomorphism group of spheres, free group actions on the sphere, etc.



13:00-18:00   数理科学研究科棟(駒場) 128号室
加藤睦也 氏 (名古屋大学) 13:30-15:00
The global Cauchy problems for nonlinear dispersive equations on modulation spaces
[ 講演概要 ]
その一方で, 解空間にモジュレーション空間を用いれば

しかし, この事実はシュレディンガー方程式のみでしか述べられていない.
熊ノ郷直人 氏 (工学院大学) 15:30-17:00
[ 講演概要 ]

さらに、この経路積分にお いて微分積分学の基本定理、

[1] N. Kumano-go,
“Feynman path integrals as analysis on path space by time slicing approximation
Bull. Sci. Math. vol. 128 (2004).
[2] D. Fujiwara and N. Kumano-go,
“Smooth functional derivatives in Feynman path integral by time slicing
Bull. Sci. Math. vol. 129 (2005).


[3] N. Kumano-go and D. Fujiwara,
“Phase space Feynman path integrals via piecewise bicharacteristic paths
and their semiclassical approximations”,
Bull. Sci. math. vol. 132 (2008).
[4] N. Kumano-go,
“Phase space Feynman path integrals with smooth functional derivatives
by time slicing approximation”,
Bull. Sci. math. vol. 135 (2011).



16:30-18:00   数理科学研究科棟(駒場) 118号室
Pierre Fima 氏 (Univ. Paris VII)
Graphs of quantum groups and K-amenability (ENGLISH)


16:00-17:00   数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State Univ.)
Determination of the first order terms for elliptic partial differential equations using the partial Cauchy data (ENGLISH)
[ 講演概要 ]
In the bounded domain we consider the variant of the Calderon's problem for the second order partial differential equation with unknown first order terms. Under some geometric condition on domain we prove that the coefficients of this equation can be determined from the partial Cauchy data up to the gauge equivalence.



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
清水 達郎 氏 (東京大学大学院数理科学研究科 )
An invariant of rational homology 3-spheres via vector fields. (JAPANESE)
[ 講演概要 ]
In this talk, we define an invariant of rational homology 3-spheres with
values in a space $\\mathcal A(\\emptyset)$ of Jacobi diagrams by using
vector fields.
The construction of our invariant is a generalization of both that of
the Kontsevich-Kuperberg-Thurston invariant $z^{KKT}$
and that of Fukaya and Watanabe's Morse homotopy invariant $z^{FW}$.
As an application of our invariant, we prove that $z^{KKT}=z^{FW}$ for
integral homology 3-spheres.



10:30-12:00   数理科学研究科棟(駒場) 126号室
菊田 伸 氏 (上智大学)
The limits on boundary of orbifold Kähler-Einstein metrics and orbifold Kähler-Ricci flows over quasi-projective manifolds (JAPANESE)
[ 講演概要 ]
In this talk, we consider a sequence of orbifold Kähler-Einstein metrics of negative Ricci curvature or corresponding orbifold normalized Kähler-Ricci flows on a quasi-projective manifold with ample log-canonical bundle for a simple normal crossing divisor. Tian-Yau, S. Bando and H. Tsuji established that the sequence of orbifold Kähler-Einstein metrics converged to the complete Käler-Einstein metric of negative Ricci curvature on the complement of the boundary divisor. The main purpose of this talk is to show that such a convergence is also true on the boundary for both of the orbifold Kähler-Einstein metrics and the orbifold normalized Kähler-Ricci flows.



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
浅岡 正幸 氏 (京都大学)
A rigidity lemma for cocycles over BS(1,k)-actions (JAPANESE)
[ 講演概要 ]
多様体上のある幾何構造を保つ作用について,その摂動がまた同じ幾何構造を保つという現象がしばしば起きる.本講演では,このような等質作用の持つ剛性を統一的に理解するためのひとつの試みとして,Baumslag-Solitar 群 BS(1,k) = の作用の上のDiff(R^n,0)に値を持つコサイクルに関するある補題から,いくつかの等質作用の剛性定理が導かれることを見たい.

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