過去の記録

過去の記録 ~03/30本日 03/31 | 今後の予定 04/01~

2017年03月30日(木)

代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
いつもと曜日が異なりますのでご注意ください.
Haoyu Hu 氏 (東京大学数理科学研究科)
Logarithmic ramifications via pull-back to curves (English)
[ 講演概要 ]
Let X be a smooth variety over a perfect field of characteristic p>0, D a strict normal crossing divisor of X, U the complement of D in X, j:U—>X the canonical injection, and F a locally constant and constructible sheaf of F_l-modules on U (l is a prime number different from p). Using Abbes and Saito’s logarithmic ramification theory, we define a Swan divisor SW(j_!F), which supported on D. Let i:C-->X be a quasi-finite morphism from a smooth curve C to X. Following T. Saito’s idea, we compare the pull-back of SW(j_!F) to C with the Swan divisor of the pull-back of j_!F to C. It answers an expectation of Esnault and Kerz and generalizes the same result of Barrientos for rank 1 sheaves. As an application, we obtain a lower semi-continuity property for Swan divisors of an l-adic sheaf on a smooth fibration, which gives a generalization of Deligne and Laumon’s lower semi-continuity property of Swan conductors of l-adic sheaves on relative curves to higher relative dimensions. This application is a supplement of the semi-continuity of total dimension of vanishing cycles due to T. Saito and the lower semi-continuity of total dimension divisors due to myself and E. Yang.

2017年03月22日(水)

FMSPレクチャーズ

13:00-   数理科学研究科棟(駒場) 117号室
Ian Grojnowski 氏 (University of Cambridge)
Lecture 1: Derived symplectic varieties and the Darboux theorem.
Lecture 2: The moduli of anti-canonically marked del Pezzo surfaces. (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Grojnowski.pdf

2017年03月21日(火)

談話会・数理科学講演会

14:40-15:40   数理科学研究科棟(駒場) 大講義室号室
片岡清臣 氏 (東京大学大学院数理科学研究科)
超局所解析と代数解析を巡って (JAPANESE)
[ 講演概要 ]
1959年に佐藤幹夫により佐藤超関数が創始され1973年にはマイクロ関数を使う擬微分方程式系の解析,いわゆる超局所解析についての決定版である佐藤幹夫・河合隆裕・柏原正樹によるレクチャーノートが出版された.講演者が修士課程に進学したのはちょうどこの直後であり,超局所解析はこの後は群の表現論への応用やファインマン積分の超局所解析など応用が中心となると言われていた.しかしその後,実領域の偏微分方程式系の超局所解析に限っても青木貴史による無限階擬微分作用素の指数解析の理論,柏原正樹・Pierre Schapiraによる層の超局所台の理論という本質的な手法の進展があるだけではなくそれらを応用した新しい超局所解析の手法の進展がある.講演者と関係したものとしてその1つは従来手法では扱えなかった熱方程式やシュレディンガー方程式の超局所解析にも適用できるマイクロ関数解のエネルギー積分不等式法であり,もう1つは初期値・境界値混合問題の超局所解析に導来圏と層のマイクロ台理論を適用する解析法である.本講演ではこれらを概観し,さらに円の連続族を含む曲面の5階偏微分方程式系による解析など代数解析的手法による非線形問題への最近の取り組みも紹介したい.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kiyoomi/index.html

談話会・数理科学講演会

16:00-17:00   数理科学研究科棟(駒場) 大講義室号室
舟木直久 氏 (東京大学大学院数理科学研究科)
確率解析とともに歩んだ40年 --- 統計物理の諸問題に動機づけられて --- (JAPANESE)
[ 講演概要 ]
学生時代に、統計力学、統計物理学の確率論的な定式化に興味を持ち、同時に確率偏微分方程式の問題に取り組みました。これらはその後の私の研究のテーマとなり、一貫して変わることはありませんでした。研究者人生を振り返って多くの方が異口同音に言われることですが、私の場合にも、いくつかの出会いが決定的な役割を果たしました。中でも、Joszef Fritz 氏(ブダペスト)、Herbert Spohn 氏(ミュンヘン)には大きな影響を受け、ミクロな系からマクロな系の挙動を記述する非線形偏微分方程式を導く、いわゆる流体力学極限の問題、あるいは界面の問題に取り組むきっかけとなりました。また、統計物理学の川崎恭治先生から示唆された問題は、現在に至るまで折に触れ形を変え取り組むこととなりました。その対象は確率偏微分方程式により記述されますが、それに数学的意味がついたのは、Martin Hairer 氏(2014年フィールズ賞受賞者)の理論によってです。しかし、数学的に基礎づけられた解に対して物理的に興味深い理論を展開するのは難しく、数学と物理の間にあるギャップは依然として大きいと感じています。談話会では、これまでの自身の研究を振り返り、やり残したことについてもお話しできればと思っています。
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~funaki/

2017年03月10日(金)

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: Common Room 16:30-17:00, Lie群論・表現論セミナーと合同
Lizhen Ji 氏 (University of Michigan)
Satake compactifications and metric Schottky problems (ENGLISH)
[ 講演概要 ]
The quotient of the Poincare upper half plane by the modular group SL(2, Z) is a basic locally symmetric space and also the moduli space of compact Riemann surfaces of genus 1, and it admits two important classes of generalization:

(1) Moduli spaces M_g of compact Riemann surfaces of genus g>1,

(2) Arithmetic locally symmetric spaces Γ \ G/K such as the Siegel modular variety A_g, which is also the moduli of principally polarized abelian varieties of dimension g.

There have been a lot of fruitful work to explore the similarity between these two classes of spaces, and there is also a direct interaction between them through the Jacobian (or period) map J: M_g --> A_g. In this talk, I will discuss some results along these lines related to the Stake compactifications and the Schottky problems on understanding the image J(M_g) in A_g from the metric perspective.

Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同.場所がいつもと異なりますので,ご注意ください.
Lizhen Ji 氏 (University of Michigan, USA)
Satake compactifications and metric Schottky problems (English)
[ 講演概要 ]
The quotient of the Poincare upper half plane by the modular group SL(2, Z) is a basic locally symmetric space and also the moduli space of compact Riemann surfaces of genus 1, and it admits two important classes of generalization:

(1) Moduli spaces M_g of compact Riemann surfaces of genus g>1,

(2) Arithmetic locally symmetric spaces \Gamma \ G/K such as the Siegel modular variety A_g, which is also the moduli of principally polarized abelian varieties of dimension g.

There have been a lot of fruitful work to explore the similarity between these two classes of spaces, and there is also a direct interaction between them through the Jacobian (or period) map J: M_g --> A_g.
In this talk, I will discuss some results along these lines related to the Stake compactifications and the Schottky problems on understanding the image J(M_g) in A_g from the metric perspective.

2017年03月08日(水)

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: Common Room 16:30-17:00
Arthur Soulié 氏 (Université de Strasbourg)
Action of the Long-Moody Construction on Polynomial Functors (ENGLISH)
[ 講演概要 ]
In 2016, Randal-Williams and Wahl proved homological stability with certain twisted coefficients for different families of groups, in particular the one of braid groups. In fact, they obtain the stability for coefficients given by functors satisfying polynomial conditions. We only know few examples of such functors. Among them, we have the functor given by the unreduced Burau representations. In 1994, Long and Moody gave a construction on representations of braid groups which associates a representation of Bn with a representation of Bn+1. This construction complexifies in a sense the initial representation: for instance, starting from a dimension one representation, one obtains the unreduced Burau representation. In this talk, I will present this construction from a functorial point of view. I will explain that the construction of Long and Moody defines an endofunctor, called the Long-Moody functor, between a suitable category of functors. Then, after defining strong polynomial functors in this context, I will prove that the Long-Moody functor increases by one the degree of strong polynomiality of a strong polynomial functor. Thus, the Long-Moody construction will provide new examples of twisted coefficients entering in the framework of Randal-Williams and Wahl.

2017年03月07日(火)

統計数学セミナー

14:00-15:30   数理科学研究科棟(駒場) 052号室
大阪大学基礎工学研究科棟 I407号室 (WEB配信)
Markus Bibinger 氏 (Humboldt-Universität zu Berlin)
Nonparametric change-point analysis of volatility
[ 講演概要 ]
We develop change-point methods for statistics of high-frequency data. The main interest is in the stochastic volatility process of an Itô semi-martingale, the latter being discretely observed over a fixed time horizon. For a local change-point problem under high-frequency asymptotics, we construct a minimax-optimal test to discriminate continuous volatility paths from paths comprising changes. The key example is identification of volatility jumps. We prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. Moreover, we study a different global change-point problem to identify changes in the regularity of the volatility process. In particular, this allows to infer changes in the Hurst parameter of a fractional stochastic volatility process. We establish an asymptotic minimax-optimal test for this problem.

2017年03月06日(月)

複素解析幾何セミナー

10:00-11:30   数理科学研究科棟(駒場) 128号室
いつもと時間が異なります。
Vladimir Matveev 氏 (University of Jena)
Projective and c-projective metric geometries: why they are so similar (ENGLISH)
[ 講演概要 ]
I will show an unexpected application of the standard techniques of integrable systems in projective and c-projective geometry (I will explain what they are and why they were studied). I will show that c-projectively equivalent metrics on a closed manifold generate a commutative isometric $\mathbb{R}^k$-action on the manifold. The quotients of the metrics w.r.t. this action are projectively equivalent, and the initial metrics can be uniquely reconstructed by the quotients. This gives an almost algorithmic way to obtain results in c-projective geometry starting with results in much better developed projective geometry. I will give many application of this algorithmic way including local description, proof of Yano-Obata conjecture for metrics of arbitrary signature, and describe the topology of closed manifolds admitting strictly nonproportional c-projectively equivalent metrics.
Most results are parts of two projects: one is joint with D. Calderbank, M. Eastwood and K. Neusser, and another is joint with A. Bolsinov and S. Rosemann.

2017年02月23日(木)

FMSPレクチャーズ

13:30-15:00   数理科学研究科棟(駒場) 122号室
富安 亮子 氏 (山形大学理学部)
結晶学, 量子ビーム科学分野との連携の中で見たこと, 考えたこと (JAPANESE)
[ 講演概要 ]
結晶学は、結晶を含む固体材料の構造を中心的に扱う学術領域であり、X線・中性子線・電子線等に関わる量子ビーム科学分野から様々な基盤技術が提供されている。
得られた実験データの解析に用いられる様々な手法やソフトウェア、加えて、より一般に結晶構造の記述に関係する議論は、数理結晶学とも呼ばれ、数学者にとっては比較的入りやすい。
話者がこの分野に参入した直接のきっかけは、応用代数分野とよく類似した様々な問題が残っていたことであるので、その辺の数学の話を主に紹介する。得られた定理は、観測誤差を伴うデータ処理において、数学の厳密さをどのように解析アルゴリズムの成功率に反映させるかという問題に直結するもので、話者や高エネ研が配布している結晶学ソフトウェアの基盤となっている。
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_tomiyasu.pdf

2017年02月20日(月)

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: Common Room 16:30-17:00
Jørgen Ellegaard Andersen 氏 (Aarhus University)
The Verlinde formula for Higgs bundles (ENGLISH)
[ 講演概要 ]
In this talk we will present a Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. We further present a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. We will explain how all these dimensions fit into a one parameter family of 2D TQFT's, encoded in a one parameter family of Frobenius algebras, which we will construct.

2017年02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
Danielle Hilhorst 氏 (CNRS / University of Paris-Sud)
Diffusive and inviscid traveling wave solution of the Fisher-KPP equation
(ENGLISH)
[ 講演概要 ]
Our purpose is to study the limit of traveling wave solutions of the Fisher-KPP equation as the diffusion coefficient tends to zero. More precisely, we consider monotone traveling waves which connect the stable steady state to the unstable one. It is well known that there exists a positive constant c* such that there does not exist any traveling wave solution if c < c* and a unique (up to translation) monotone traveling wave solution of wave speed c for each c > c*.

We consider the corresponding inviscid ordinary differential equation where the diffusion coefficient is equal to zero and show that it possesses a unique traveling wave solution. We then fix c > 0 arbitrary and prove the convergence of the travelling wave of the parabolic equation with velocity c to that of the corresponding traveling wave solution of the inviscid problem.

Further research should involve a similar problem for monostable systems.

This is joint work with Yong Jung Kim.

2017年02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) 128号室
Qi'an Guan 氏 (北京大学)
A Characterization of regular points by Ohsawa-Takegoshi Extension Theorem (ENGLISH)
[ 講演概要 ]
In this talk, we will present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa-Takegoshi extension theorem holds. We also present a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.
This is joint work with Dr. Zhenqian Li.

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
横山 聡 氏 (東京大学大学院数理科学研究科)
Sharp interface limit for stochastically perturbed mass conserving Allen-Cahn equation

2017年02月10日(金)

代数幾何学セミナー

14:00-15:30   数理科学研究科棟(駒場) 002号室
Chenyang Xu 氏 (Beijing International Center of Mathematics Research)
Stability theory of a klt singularity II (English)
[ 講演概要 ]
In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In the talks, we will discuss a series of recent works started by Chi Li, and then by Harold Blum, Yuchen Liu and myself, in which we want to establish an algebro-geometric stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. metric tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

2017年02月09日(木)

離散数理モデリングセミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Dinh Tran 氏 (University of New South Wales, Sydney, Australia)
Growth of degrees of lattice equations and its signatures over finite fields (ENGLISH)
[ 講演概要 ]
We study growth of degrees of autonomous and non-autonomous lattice equations, some of which are known to be integrable. We present a conjecture that helps us to prove polynomial growth of a certain class of equations including $Q_V$ and its non-autonomous generalization. In addition, we also study growth of degrees of several non-integrable equations. Exponential growth of degrees of these equations is also proved subject to a conjecture. Our technique is to determine the ambient degree growth of the equations and a conjectured growth of their common factors at each vertex, allowing the true degree growth to be found. Moreover, our results can also be used for mappings obtained as periodic reductions of integrable lattice equations. We also study signatures of growth of degrees of lattice equations over finite fields.

2017年02月07日(火)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 117号室
Chenyang Xu 氏 (Beijing International Center of Mathematics Research)
Stability theory of a klt singularity I (English)
[ 講演概要 ]
In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In the talks, we will discuss a series of recent works started by Chi Li, and then by Harold Blum, Yuchen Liu and myself, in which we want to establish an algebro-geometric stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. metric tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

2017年02月03日(金)

博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 118号室
林 達也 氏 (東京大学大学院数理科学研究科)
Mathematical modeling for synchronization of cardiac muscle cells (心筋細胞の拍動同期現象に関する数理モデル)
(JAPANESE)

博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 118号室
梅崎 直也 氏 (東京大学大学院数理科学研究科)
Characteristic class and the ε-factor of an étale sheaf (エタール層の特性類とε因子) (JAPANESE)

博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 118号室
吉川 祥 氏 (東京大学大学院数理科学研究科)
On modularity of elliptic curves over abelian totally real fields (総実アーベル拡大体上の楕円曲線の保型性について)
(JAPANESE)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室
大内 元気 氏 (東京大学大学院数理科学研究科)
Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces (K3曲面の導来自己同型を用いた超ケーラー多様体上の正エントロピー自己同型の構成について) (JAPANESE)

博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 122号室
Otani Yul 氏 (東京大学大学院数理科学研究科)
Entanglement Entropy in Algebraic Quantum Field Theory (代数的場の量子論におけるエンタングルメント・エントロピー)
(JAPANESE)

博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 122号室
窪田 陽介 氏 (東京大学大学院数理科学研究科)
A Categorical Approach for Freeness of Group Actions on C*-algebras (C*-環への群作用の自由性に対する圏論的アプローチ)
(JAPANESE)

博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室
増本 周平 氏 (東京大学大学院数理科学研究科)
Applications of Fraïssé theory to operator algebras (Fraïssé理論の作用素環への応用) (JAPANESE)

博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 126号室
野村 亮介 氏 (東京大学大学院数理科学研究科)
Study of the Kähler-Ricci Flow and its Application in Algebraic Geometry (ケーラー・リッチ流の研究とその代数幾何学における応用)
(JAPANESE)

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