過去の記録 ~03/27本日 03/28 | 今後の予定 03/29~


10:30-11:30   数理科学研究科棟(駒場) 056号室
伊藤 翼 氏 (東京工業大学)
Remark on single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a corner (JAPANESE)
[ 講演概要 ]
In this talk, the two dimensional Euler flow under a simple symmetry condition with hyperbolic structure in a unit square $D=\{(x_{1}, x_{2}): 0 < x_{1} + x_{2} < \sqrt{2},\ 0<-x_{1} + x_{2} < \sqrt{2}\}$ is considered.
It is shown that the Lipschitz estimate of the vorticity on the boundary is at most single exponential growth near the stagnation point.
(Joint work with Tsuyoshi Yoneda and Hideyuki Miura.)


16:30-18:00   数理科学研究科棟(駒場) 128号室
Xavier Cabre 氏 (ICREA and UPC, Barcelona)
New isoperimetric inequalities with densities arising in reaction-diffusion problems (English)
[ 講演概要 ]
In joint works with X. Ros-Oton and J. Serra, the study of the
regularity of stable solutions to reaction-diffusion problems
has led us to certain Sobolev and isoperimetric inequalities
with weights.  We will present our results in these new
isoperimetric inequalities with the best constant, that we
establish via the ABP method.  More precisely, we obtain
a new family of sharp isoperimetric inequalities with weights
(or densities) in open convex cones of R^n. Our results apply
to all nonnegative homogeneous weights satisfying a concavity
condition in the cone. Surprisingly, even that our weights are
not radially symmetric, Euclidean balls centered at the origin
(intersected with the cone) minimize the weighted isoperimetric
quotient. As a particular case of our results, we provide with
new proofs of classical results such as the Wulff inequality and
the isoperimetric inequality in convex cones of Lions and Pacella.
Furthermore, we also study the anisotropic isoperimetric problem
for the same class of weights and we prove that the Wulff shape
always minimizes the anisotropic weighted perimeter under the
weighted volume constraint.



10:30-12:00   数理科学研究科棟(駒場) 126号室
大沢健夫 氏 (名古屋大学)
Effective and noneffective extension theorems (Japanese)
[ 講演概要 ]
As an effective extension theorem, I will review the sharp $L^2$ extension theorem explaining the ideas of its proofs due to Blocki and Guan-Zhou. A new proof using the Poincare metric with be given, too. As a noneffective extension theorem, I will talk about an extension theorem from semipositive divisors. It is obtained as an application of an isomorphism theorem which is essentially contained in my master thesis.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Malte Wandel 氏 (RIMS)
Induced Automorphisms on Hyperkaehler Manifolds (ENGLISH)
[ 講演概要 ]
in this talk I want to report on a joint project with Giovanni Mongardi (Milano). We study automorphisms of hyperkaehler manifolds. All known deformation classes of these manifolds contain moduli spaces of stable sheaves on surfaces. If the underlying surface admits a non-trivial automorphism, it is often possible to transfer this automorphism to a moduli space of sheaves. In this way we obtain a big class of interesting examples of automorphisms of hyperkaehler manifolds. I will present a criterion to 'detect' automorphisms in this class and discuss several applications for the classification of automorphisms of manifolds of K3^[n]- and kummer n-type. If time permits I will try to talk about generalisations to O'Grady's sporadic examples.


16:30-18:00   数理科学研究科棟(駒場) 056号室
井元佑介 氏 (九州大学大学院数理学府)
Poisson方程式に対する一般化粒子法の誤差評価 (日本語)
[ 講演概要 ]
SPH法やMPS法に代表される粒子法は, 津波のような移動境界流れに対する数値計算手法の一つとして, 現在幅広く利用されている. 一方で, 近似解の誤差評価といった粒子法の数学的正当化は, 我々の知る限り十分に行われているとは言えない. 
そこで我々は, 誤差評価の第一ステップとして, Poisson方程式に対するある一般化粒子法を導入し, その誤差評価を行った. 提案する粒子法は, SPH法やMPS法を含む, より広いクラスの粒子法を記述することが可能である. 本講演では, 粒子分布の正則性と接続性を導入し, これらの性質を持った粒子分布の下で, 近似解の誤差が重み関数の影響半径に関して2次収束することを示す. 我々の誤差評価では, 従来は工学的な経験則に基づいていた 参照関数の選択や粒子数と影響半径の組合わせの選択などに, 数学的に正当化されたある十分条件を与えていることが重要である.
[ 参考URL ]



16:30-17:30   数理科学研究科棟(駒場) 123号室
西浦博 氏 (東京大学大学院医学研究科)
Estimating the reproduction numbers of emerging infectious diseases: Case studies of Ebola and dengue (JAPANESE)
[ 講演概要 ]
The basic and effective reproduction numbers offer epidemiological
insights into the growth of generations of infectious disease cases,
informing the required control effort. Recently, the renewal process
model has appeared to be a usefu tool for quantifying the reproduction
numbers in real-time using only case data. Here I present methods,
results and pitfalls of the use of renewal process model, presenting
recent case studies of Ebola virus disease epidemic in West Africa and a
massive epidemic of dengue fever in the summer of Japan 2014.
[ 参考URL ]



16:30-18:00   数理科学研究科棟(駒場) 122号室
Yi-Zhi Huang 氏 (Rutgers Univ.)
A program to construct and study conformal field theories (ENGLISH)


16:00-17:00   数理科学研究科棟(駒場) 123号室
Mykhaylo Shkolnikov 氏 (Princeton University)
Intertwinings, wave equations and beta ensembles (ENGLISH)
[ 講演概要 ]
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to wave equations and more general hyperbolic partial differential equations. The talk will be devoted to this recent development, as well as an algebraic perspective on intertwinings which, in particular, gives rise to a novel intertwining in beta random matrix theory. Based on joint works with Vadim Gorin and Soumik Pal.


16:30-17:40   数理科学研究科棟(駒場) 052号室
片山 翔太 氏 (東京工業大学)
Sparse and robust linear regression: Iterative algorithm and its statistical convergence

[ 講演概要 ]
線形回帰モデルにおいて,外れ値にロバストな回帰係数のスパース推定問題を考える. 具体的な手法としては,近年She and Owen (2011)が提案しているように, 外れ値もパラメータとしてモデルに導入し,回帰係数と外れ値を同時にスパースに推定することを考える. 本発表では,回帰係数と外れ値のパラメータを交互に最適化するアルゴリズムを提案し, それによって得られた推定値と真値のL2誤差の確率上界を導出する. これにより,アルゴリズムの初期値の影響がステップサイズの指数オーダで減少するための条件や, L2誤差が0に確率収束するための標本サイズや変数の次元に関する条件が導けた. またこれらの条件は,高次元データの状況でも満たされる可能性があることも確認できた. なお,本研究は統計数理研究所の藤澤洋徳教授との共同研究である.



16:30-18:00   数理科学研究科棟(駒場) 128号室
伊藤 健一 氏 (神戸大学理学研究科)
Stationary scattering theory on manifold with ends (JAPANESE)


16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00-16:30 Common Room
齋藤 昌彦 氏 (University of South Florida)
Quandle knot invariants and applications (JAPANESE)
[ 講演概要 ]
A quandles is an algebraic structure closely related to knots. Homology theories of
quandles have been defined, and their cocycles are used to construct invariants for
classical knots, spatial graphs and knotted surfaces. In this talk, an overview is given
for quandle cocycle invariants and their applications to geometric properties of knots.
The current status of computations, recent developments and open problems will also
be discussed.

Kavli IPMU Komaba Seminar

10:30-11:30   数理科学研究科棟(駒場) 128号室
Naichung Conan Leung 氏 (The Chinese University of Hong Kong)
Donaldson-Thomas theory for Calabi-Yau fourfolds.
[ 講演概要 ]
Donaldson-Thomas theory for Calabi-Yau threefolds is a
complexification of Chern-Simons theory. In this talk I will discuss
my joint work with Cao on the complexification of Donaldson theory.
This work is supported by a RGC grant of HK Government.



13:30-17:00   数理科学研究科棟(駒場) 128号室
Denny Hakim 氏 (首都大学東京) 13:30-14:30
On the Inclusion of Generalized Morrey Spaces and the Boundedness of the Generalized Fractional Maximal Operators (ENGLISH)
[ 講演概要 ]
In this talk, we shall prove a necessary and sufficient condition for an inclusion property of generalized Morrey spaces. We use this property in our proof of the boundedness of the generalized fractional maximal operators on these spaces. Our result also cover the generalized weak Morrey spaces.
This research is a joint work with Y. Sawano, H. Gunawan, K.M. Limanta and A.A. Masta.
Tamara Tararykova 氏 (Cardiff University / Eurasian National University) 14:45-15:45
Hardy-type inequality for 0 < p < 1 and hypodecreasing functions (ENGLISH)
[ 講演概要 ]
Victor Burenkov 氏 (Cardift School of Mathematics / Peoples' Friendship University of Russia / Steklov Institute of Mathematics) 16:00-17:00
Sharp spectral stability estimate for uniformly elliptic differential operators (EMGLISH)
[ 講演概要 ]



15:00-17:00   数理科学研究科棟(駒場) 126号室
戸松玲治 氏 (北大)
Haagerupのbicentralizer論文の紹介 (English)



13:00-15:00   数理科学研究科棟(駒場) 128号室
戸松玲治 氏 (北大)
Haagerupのbicentralizer論文の紹介 (English)


15:00-18:30   数理科学研究科棟(駒場) 002号室
野本 文彦 氏 (東京工業大学大学院理工学研究科数学専攻) 15:00-16:30
非対称 Macdonald 多項式の$t=\infty$への特殊化の明示公式 (JAPANESE)
[ 講演概要 ]
一般のアフィン・ルート系に付随する非対称 Macdonald 多項式のヘッケ・パラメーター t を t = ∞ と特殊化したものを、アフィン・ルート系とアフィン・ワイル群の言葉で組合せ論的に記述する公式が、Orr-Shimozono により得られている。これを踏まえて我々は、上記の特殊化を、有限ルート系と有限ワイル群に付随する量子ブリュアグラフの言葉で記述する明示的な公式を証明した。つまり、アフィン量子群の (典型的な有限次元表現である) 量子ワイル加群の結晶基底の実現を与える量子 Lakshmibai-Seshadri パスのうちである種の明示的条件を満たすもの達全体を考え、それらの次数付き指標 (ウエイトの母関数) を取ったものが、上記の特殊化に他ならないことを証明した。本講演では、得られた明示的公式を例と共に紹介し、証明の概要を説明する。
安東 雅訓 氏 (稚内北星学園大学) 17:00-18:30
約数関数と相異分割 (JAPANESE)
[ 講演概要 ]
超幾何級数での式の特殊化として出てくるものだが, これを整数の分割の母関数として見ることで組合せ論での結果に翻訳し, 全単射法による証明を与える.



13:00-15:00   数理科学研究科棟(駒場) 126号室
戸松玲治 氏 (北大)
Haagerupのbicentralizer論文の紹介 (English)


16:40-17:40   数理科学研究科棟(駒場) 056号室
Fabien Pazuki 氏 (Univ Bordeaux and Univ Copenhagen)
Bad reduction of curves with CM jacobians (English)
[ 講演概要 ]
An abelian variety defined over a number field and having complex multiplication (CM) has potentially good reduction everywhere. If a curve of positive genus which is defined over a number field has good reduction at a given finite place, then so does its jacobian variety. However, the converse statement is false already in the genus 2 case, as can be seen in the entry $[I_0-I_0-m]$ in Namikawa and Ueno's classification table of fibres in pencils of curves of genus 2. In this joint work with Philipp Habegger, our main result states that this phenomenon prevails for certain families of curves.

We prove the following result: Let F be a real quadratic number field. Up to isomorphisms there are only finitely many curves C of genus 2 defined over $\overline{\mathbb{Q}}$ with good reduction everywhere and such that the jacobian Jac(C) has CM by the maximal order of a quartic, cyclic, totally imaginary number field containing F. Hence such a curve will almost always have stable bad reduction at some prime whereas its jacobian has good reduction everywhere. A remark is that one can exhibit an infinite family of genus 2 curves with CM jacobian such that the endomorphism ring is the ring of algebraic integers in a cyclic extension of $\mathbb{Q}$ of degree 4 that contains $\mathbb{Q}(\sqrt{5})$, for example.


14:50-16:20   数理科学研究科棟(駒場) 122号室
若野友一郞 氏 (明治大学現象数理学科)
Adaptive Dynamicsの紹介と、その有限集団への応用 (JAPANESE)
[ 講演概要 ]
本講演では、まず無限集団を仮定する通常のAdaptive Dynamicsを紹介し、
揺らぎの影響を解析的に示すために、無限集団のAdaptive Dynamicsを

[ 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 Common Room
Charles Siegel 氏 (Kavli IPMU)
A Modular Operad of Embedded Curves (ENGLISH)
[ 講演概要 ]
Modular operads were introduced by Getzler and Kapranov to formalize the structure of gluing maps between moduli of stable marked curves. We present a construction of analogous gluing maps between moduli of pluri-log-canonically embedded marked curves, which fit together to give a modular operad of embedded curves. This is joint work with Satoshi Kondo and Jesse Wolfson.


13:00-15:00   数理科学研究科棟(駒場) 126号室
戸松玲治 氏 (北大)
Haagerupのbicentralizer論文の紹介 (ENGLISH)



10:30-12:00   数理科学研究科棟(駒場) 126号室
新田泰文 氏 (東京工業大学)
On strong K-stability of polarized algebraic manifolds (JAPANESE)


13:00-15:00   数理科学研究科棟(駒場) 126号室
戸松玲治 氏 (北大)
Haagerupのbicentralizer論文の紹介 (English)



10:00-11:30   数理科学研究科棟(駒場) 126号室
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 ]
この講演では完全ラグランジュはめ込みの displacement エネルギーと擬正則円盤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 が有理ラグランジュ部分多様体の displacement エネルギーに関する不等式を示す際に用いた技法を, 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考察を述べる.



18:00-19:00   数理科学研究科棟(駒場) 056号室
Ruochuan Liu 氏 (BICMR)
Relative (φ, Γ)-modules (English)
[ 講演概要 ]
In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.
(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.)

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