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過去の記録
過去の記録 ～03/27｜本日 03/28 | 今後の予定 03/29～
2020年03月26日(木)
談話会・数理科学講演会
16:00-17:00 数理科学研究科棟(駒場) 117号室
延期
河野 俊丈 氏 (東京大学大学院数理科学研究科)
モノドロミー表現とその高次圏への拡張 (JAPANESE)
延期
河野 俊丈 氏 (東京大学大学院数理科学研究科)
モノドロミー表現とその高次圏への拡張 (JAPANESE)
2020年03月02日(月)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 002号室
諸事情により中止を決定しました。Cancelled.
Evgeny Shinder 氏 (The University of Sheffield)
Semiorthogonal decompositions for singular varieties (English)
諸事情により中止を決定しました。Cancelled.
Evgeny Shinder 氏 (The University of Sheffield)
Semiorthogonal decompositions for singular varieties (English)
[ 講演概要 ]
I will define the semiorthogonal decomposition for derived categories of singular projective varieties due to Professor Kawamata, into finite-dimensional algebras, generalizing the concept of an exceptional collection in the smooth case. I will present known constructions of these for nodal curves (Burban), torsion-free toric surfaces (Karmazyn-Kuznetsov-Shinder) and two nodal threefolds (Kawamata). I will also explain obstructions coming from the K_{-1} group, and how it translates to maximal nonfactoriality in the nodal threefold case. This is joint work with M.Kalck and N.Pavic.
I will define the semiorthogonal decomposition for derived categories of singular projective varieties due to Professor Kawamata, into finite-dimensional algebras, generalizing the concept of an exceptional collection in the smooth case. I will present known constructions of these for nodal curves (Burban), torsion-free toric surfaces (Karmazyn-Kuznetsov-Shinder) and two nodal threefolds (Kawamata). I will also explain obstructions coming from the K_{-1} group, and how it translates to maximal nonfactoriality in the nodal threefold case. This is joint work with M.Kalck and N.Pavic.
2020年02月28日(金)
PDE実解析研究会
16:00-17:00 数理科学研究科棟(駒場) 370号室
通常の曜日・時刻・教室と異なります。
Maximilian Moser 氏 (University of Regensburg)
Convergence of the Allen-Cahn equation with a nonlinear Robin-boundary condition to mean curvature flow with constant contact angle (English)
通常の曜日・時刻・教室と異なります。
Maximilian Moser 氏 (University of Regensburg)
Convergence of the Allen-Cahn equation with a nonlinear Robin-boundary condition to mean curvature flow with constant contact angle (English)
[ 講演概要 ]
In this talk I will present a result for the sharp interface limit of the Allen-Cahn equation with a nonlinear Robin boundary condition in a two-dimensional domain, in the situation where an interface has developed and intersects the boundary. The boundary condition is designed in such a way that one obtains as the limit problem the mean curvature flow with constant contact angle. Convergence using strong norms is shown for contact angles close to 90° and small times, when a smooth solution to the limit problem exists. For the proof the method of de Mottoni and Schatzman is used: we construct an approximate solution for the Allen-Cahn system using asymptotic expansions based on the solution to the limit problem. Then we estimate the difference of the exact and approximate solution with a spectral estimate for the linearized (at the approximate solution) Allen-Cahn operator.
This is joint work with Helmut Abels from Regensburg.
In this talk I will present a result for the sharp interface limit of the Allen-Cahn equation with a nonlinear Robin boundary condition in a two-dimensional domain, in the situation where an interface has developed and intersects the boundary. The boundary condition is designed in such a way that one obtains as the limit problem the mean curvature flow with constant contact angle. Convergence using strong norms is shown for contact angles close to 90° and small times, when a smooth solution to the limit problem exists. For the proof the method of de Mottoni and Schatzman is used: we construct an approximate solution for the Allen-Cahn system using asymptotic expansions based on the solution to the limit problem. Then we estimate the difference of the exact and approximate solution with a spectral estimate for the linearized (at the approximate solution) Allen-Cahn operator.
This is joint work with Helmut Abels from Regensburg.
2020年02月21日(金)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 370号室
いつもと曜日・時間・部屋が異なります
Jakub Witaszek 氏 (Michigan)
Keel's theorem and quotients in mixed characteristic (English)
http://www-personal.umich.edu/~jakubw/
いつもと曜日・時間・部屋が異なります
Jakub Witaszek 氏 (Michigan)
Keel's theorem and quotients in mixed characteristic (English)
[ 講演概要 ]
In trying to understand characteristic zero varieties one can apply a wide range of techniques coming from analytic methods such as vanishing theorems. More complicated though they are, positive characteristic varieties come naturally with Frobenius action which sometimes allows for imitating analytic proofs or even showing results which are false over complex numbers. Of all the three classes, the mixed characteristic varieties are the most difficult to understand as they represent the worst of both worlds: one lacks the analytic methods as well the Frobenius action.
What is key for many applications of Frobenius in positive characteristic (to birational geometry, moduli theory, constructing quotients, etc.) is the fact that every universal homeomorphism of algebraic varieties factors through a power of Frobenius. In this talk I will discuss an analogue of this fact (and applications thereof) in mixed characteristic.
[ 講演参考URL ]In trying to understand characteristic zero varieties one can apply a wide range of techniques coming from analytic methods such as vanishing theorems. More complicated though they are, positive characteristic varieties come naturally with Frobenius action which sometimes allows for imitating analytic proofs or even showing results which are false over complex numbers. Of all the three classes, the mixed characteristic varieties are the most difficult to understand as they represent the worst of both worlds: one lacks the analytic methods as well the Frobenius action.
What is key for many applications of Frobenius in positive characteristic (to birational geometry, moduli theory, constructing quotients, etc.) is the fact that every universal homeomorphism of algebraic varieties factors through a power of Frobenius. In this talk I will discuss an analogue of this fact (and applications thereof) in mixed characteristic.
http://www-personal.umich.edu/~jakubw/
2020年02月18日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
中止となりました（数値解析セミナーとの共催）
Alessio Porretta 氏 (Tor Vergata university of Rome)
Long time behavior of mean field games systems (English)
中止となりました（数値解析セミナーとの共催）
Alessio Porretta 氏 (Tor Vergata university of Rome)
Long time behavior of mean field games systems (English)
[ 講演概要 ]
I will review several aspects related to the long time ergodic behavior of mean field game systems: the turnpike property, the exponential rate of convergence, the role of monotonicity of the couplings, the convergence of u up to translations, the limit of the vanishing discounted problem, the long time behavior of the master equation. All those aspects have independent interest and are correlated at the same time.
I will review several aspects related to the long time ergodic behavior of mean field game systems: the turnpike property, the exponential rate of convergence, the role of monotonicity of the couplings, the convergence of u up to translations, the limit of the vanishing discounted problem, the long time behavior of the master equation. All those aspects have independent interest and are correlated at the same time.
東京無限可積分系セミナー
15:00-16:00 数理科学研究科棟(駒場) 002号室
Vincent Pasquier 氏 (IPhT Saclay)
Hydrodynamics of a one dimensional lattice gas.
(ENGLISH)
Vincent Pasquier 氏 (IPhT Saclay)
Hydrodynamics of a one dimensional lattice gas.
(ENGLISH)
[ 講演概要 ]
The simplest boxball model is a one dimensional lattice gas obtained as
a certain (cristal) limit of the six vertex model where the evolution
determined by the transfer matrix becomes deterministic. One can
study its thermodynamics in and out of equilibrium and we shall present
preliminary results in this direction.
Collaboration with Atsuo Kuniba and Grégoire Misguich.
The simplest boxball model is a one dimensional lattice gas obtained as
a certain (cristal) limit of the six vertex model where the evolution
determined by the transfer matrix becomes deterministic. One can
study its thermodynamics in and out of equilibrium and we shall present
preliminary results in this direction.
Collaboration with Atsuo Kuniba and Grégoire Misguich.
2020年02月17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
満渕 俊樹 氏 (大阪大学)
Precompactness of the moduli space of pseudo-normed graded algebras
満渕 俊樹 氏 (大阪大学)
Precompactness of the moduli space of pseudo-normed graded algebras
[ 講演概要 ]
Graded algebras (such as canonical rings) coming from the spaces of sections of polarized algebraic varieties are studied by many mathematicians. On the other hand, the pseudo-norm project proposed by S.-T. Yau and C.-Y. Chi gives us a new differential geometric aspect of the Torelli type theorem.
In this talk, we give the details of how the geometry of pseudo-normed graded algebras allows us to obtain a natural compactification of the moduli space of pseudo-normed graded algebras.
(1) For a sequence of pseudo-normed graded algebras (of the same type), the above precompactness gives us some limit different from the Gromov-Hausdorff limit in Riemannian geometry.
(2) As an example of our construction, we have the Deligne-Mumford compactification, in which the notion of the orthogonal direct sum of pseudo-normed spaces comes up naturally. We also have a higher dimensional analogue by using weight filtration.
Graded algebras (such as canonical rings) coming from the spaces of sections of polarized algebraic varieties are studied by many mathematicians. On the other hand, the pseudo-norm project proposed by S.-T. Yau and C.-Y. Chi gives us a new differential geometric aspect of the Torelli type theorem.
In this talk, we give the details of how the geometry of pseudo-normed graded algebras allows us to obtain a natural compactification of the moduli space of pseudo-normed graded algebras.
(1) For a sequence of pseudo-normed graded algebras (of the same type), the above precompactness gives us some limit different from the Gromov-Hausdorff limit in Riemannian geometry.
(2) As an example of our construction, we have the Deligne-Mumford compactification, in which the notion of the orthogonal direct sum of pseudo-normed spaces comes up naturally. We also have a higher dimensional analogue by using weight filtration.
離散数理モデリングセミナー
16:30-18:30 数理科学研究科棟(駒場) 126号室
Sanjay Ramassamy 氏 (IPhT, CEA Saclay)
Cluster algebras, dimer models and geometric dynamics
Sanjay Ramassamy 氏 (IPhT, CEA Saclay)
Cluster algebras, dimer models and geometric dynamics
[ 講演概要 ]
Cluster algebras were introduced by Fomin and Zelevinsky at the beginning of the 21st century and have since then been related to several areas of mathematics. In this talk I will describe cluster algebras coming from quivers and give two concrete situations were they arise. The first is the bipartite dimer model coming from statistical mechanics. The second is in several dynamics on configurations of points/lines/circles/planes.
This is based on joint work with Niklas Affolter (TU Berlin), Max Glick (Google) and Pavlo Pylyavskyy (University of Minnesota).
Cluster algebras were introduced by Fomin and Zelevinsky at the beginning of the 21st century and have since then been related to several areas of mathematics. In this talk I will describe cluster algebras coming from quivers and give two concrete situations were they arise. The first is the bipartite dimer model coming from statistical mechanics. The second is in several dynamics on configurations of points/lines/circles/planes.
This is based on joint work with Niklas Affolter (TU Berlin), Max Glick (Google) and Pavlo Pylyavskyy (University of Minnesota).
2020年02月14日(金)
FMSPレクチャーズ
17:00-18:00 数理科学研究科棟(駒場) 128号室
Piermarco Cannarsa 氏 (University of Rome Tor Vergata)
Bilinear control for evolution equations of parabolic type (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cannarsa200214.pdf
Piermarco Cannarsa 氏 (University of Rome Tor Vergata)
Bilinear control for evolution equations of parabolic type (ENGLISH)
[ 講演概要 ]
Recently, in a series of joint papers with F. Alabau-Boussouira and C. Urbani, I have studied the response of an evolution equation on a Hilbert space to the action of a bilinear control. As is well-known, a bilinear control is a scalar function of time multiplying one of the coefficient of the equation (usually, a lower order term). Therefore, this is a nonlinear control problem, even if the equation is linear in the state variable.
For such a problem, exact controllability is out of question, due to a well-known negative result by Ball, Marsden, and Slemrod back in the 80’s.
In this talk, equations of parabolic type will be considered, meaning that the infinitesimal generator - of the strongly continuous semigroup which drives the system - is assumed to be a self-adjoint accretive operator. It will be explained how, under some conditions relating the spectrum of the generator to the control coefficient, one can locally stabilise the system to the solution associated with the ground state at a doubly exponential speed, or even attain such a ground-state solution in finite time. Applications to concrete parabolic problems will also be provided.
[ 講演参考URL ]Recently, in a series of joint papers with F. Alabau-Boussouira and C. Urbani, I have studied the response of an evolution equation on a Hilbert space to the action of a bilinear control. As is well-known, a bilinear control is a scalar function of time multiplying one of the coefficient of the equation (usually, a lower order term). Therefore, this is a nonlinear control problem, even if the equation is linear in the state variable.
For such a problem, exact controllability is out of question, due to a well-known negative result by Ball, Marsden, and Slemrod back in the 80’s.
In this talk, equations of parabolic type will be considered, meaning that the infinitesimal generator - of the strongly continuous semigroup which drives the system - is assumed to be a self-adjoint accretive operator. It will be explained how, under some conditions relating the spectrum of the generator to the control coefficient, one can locally stabilise the system to the solution associated with the ground state at a doubly exponential speed, or even attain such a ground-state solution in finite time. Applications to concrete parabolic problems will also be provided.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cannarsa200214.pdf
2020年02月13日(木)
離散数理モデリングセミナー
16:30-18:30 数理科学研究科棟(駒場) 126号室
Sanjay Ramassamy 氏 (IPhT, CEA Saclay)
Embeddings adapted to two-dimensional models of statistical mechanics (English)
Sanjay Ramassamy 氏 (IPhT, CEA Saclay)
Embeddings adapted to two-dimensional models of statistical mechanics (English)
[ 講演概要 ]
A discrete model of statistical mechanics in 2D (for example simple random walk on the infinite square grid) can be defined on a graph without specifying a particular embedding of this graph. However, when stating that such a model converges to a conformally invariant object in the scaling limit, one needs to specify an embedding of the graph. For models which possess a local move, such as a star-triangle transformation, one would like the choice of the embedding to be compatible with that local move.
In this talk I will present a candidate for an embedding adapted to the 2D dimer model (a.k.a. random perfect matchings) on bipartite graphs, that is, graphs whose faces all have an even degree. This embedding is obtained by considering centers of circle patterns with the combinatorics of the graph on which the dimer model lives.
This is based on joint works with Dmitry Chelkak (École normale supérieure), Richard Kenyon (Yale University), Wai Yeung Lam (Université du Luxembourg) and Marianna Russkikh (MIT).
A discrete model of statistical mechanics in 2D (for example simple random walk on the infinite square grid) can be defined on a graph without specifying a particular embedding of this graph. However, when stating that such a model converges to a conformally invariant object in the scaling limit, one needs to specify an embedding of the graph. For models which possess a local move, such as a star-triangle transformation, one would like the choice of the embedding to be compatible with that local move.
In this talk I will present a candidate for an embedding adapted to the 2D dimer model (a.k.a. random perfect matchings) on bipartite graphs, that is, graphs whose faces all have an even degree. This embedding is obtained by considering centers of circle patterns with the combinatorics of the graph on which the dimer model lives.
This is based on joint works with Dmitry Chelkak (École normale supérieure), Richard Kenyon (Yale University), Wai Yeung Lam (Université du Luxembourg) and Marianna Russkikh (MIT).
2020年02月12日(水)
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 126号室
Lorenzo Mercuri 氏 (University of Milan)
Handling the underlying noise of Stochastic Differential Equations in YUIMA project
Lorenzo Mercuri 氏 (University of Milan)
Handling the underlying noise of Stochastic Differential Equations in YUIMA project
[ 講演概要 ]
Some advances in the implementation of advanced mathematical tools and numerical methods for an object of class yuima.law are presented and discussed. An object of yuima.law-class refers to the mathematical description of the underlying noise specified in the formal definition of a general Stochastic Differential Equation. Its aim is to create a link between YUIMA and other R packages available on CRAN for managing specific Lévy noises. Here we present as examples the simulation and the estimation of a CARMA(p,q) and Point Process regression models.
Some advances in the implementation of advanced mathematical tools and numerical methods for an object of class yuima.law are presented and discussed. An object of yuima.law-class refers to the mathematical description of the underlying noise specified in the formal definition of a general Stochastic Differential Equation. Its aim is to create a link between YUIMA and other R packages available on CRAN for managing specific Lévy noises. Here we present as examples the simulation and the estimation of a CARMA(p,q) and Point Process regression models.
2020年02月05日(水)
Lie群論・表現論セミナー
15:00-16:00 数理科学研究科棟(駒場) 126号室
Simon Gindikin 氏 (Rutgers University)
Direct inversion of the horospherical transform on Riemannian symmetric spaces (English)
Simon Gindikin 氏 (Rutgers University)
Direct inversion of the horospherical transform on Riemannian symmetric spaces (English)
[ 講演概要 ]
It was a problem of Gelfand to find an inversion of the horospherical transform directly and as a result to find directly the Plancherel formula.
I will give such an inversion and it gives a formula different from Harish-Chandra's one.
It was a problem of Gelfand to find an inversion of the horospherical transform directly and as a result to find directly the Plancherel formula.
I will give such an inversion and it gives a formula different from Harish-Chandra's one.
2020年01月31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
茅原 涼平 氏 (東京大学大学院数理科学研究科)
SO(3)-invariant G2-geometry
(SO(3)-不変 G2-幾何学)
茅原 涼平 氏 (東京大学大学院数理科学研究科)
SO(3)-invariant G2-geometry
(SO(3)-不変 G2-幾何学)
博士論文発表会
10:45-12:00 数理科学研究科棟(駒場) 118号室
石橋 典 氏 (東京大学大学院数理科学研究科)
Geometry of cluster modular groups
(クラスターモジュラー群の幾何学)
石橋 典 氏 (東京大学大学院数理科学研究科)
Geometry of cluster modular groups
(クラスターモジュラー群の幾何学)
博士論文発表会
12:45-14:00 数理科学研究科棟(駒場) 118号室
渡部 淳 氏 (東京大学大学院数理科学研究科)
Fibred Cusp b-Pseudodifferential Operators and Its Applications
(Fibred Cusp b-擬微分作用素とその応用)
渡部 淳 氏 (東京大学大学院数理科学研究科)
Fibred Cusp b-Pseudodifferential Operators and Its Applications
(Fibred Cusp b-擬微分作用素とその応用)
博士論文発表会
14:15-15:30 数理科学研究科棟(駒場) 118号室
田森 宥好 氏 (東京大学大学院数理科学研究科)
Classification and construction of minimal representations
(極小表現の分類と構成)
田森 宥好 氏 (東京大学大学院数理科学研究科)
Classification and construction of minimal representations
(極小表現の分類と構成)
博士論文発表会
9:15-10:30 数理科学研究科棟(駒場) 122号室
岩井 雅崇 氏 (東京大学大学院数理科学研究科)
Studies on singular Hermitian metrics and their applications in algebraic geometry
（特異エルミート計量の研究と代数幾何学への応用）
岩井 雅崇 氏 (東京大学大学院数理科学研究科)
Studies on singular Hermitian metrics and their applications in algebraic geometry
（特異エルミート計量の研究と代数幾何学への応用）
博士論文発表会
10:45-12:00 数理科学研究科棟(駒場) 122号室
陳 韋中 氏 (東京大学大学院数理科学研究科)
Boundedness of Weak Fano Pairs with Alpha-invariants and Volumes Bounded Below
(体積とα不変量が下に有界な弱Fano対の有界性)
陳 韋中 氏 (東京大学大学院数理科学研究科)
Boundedness of Weak Fano Pairs with Alpha-invariants and Volumes Bounded Below
(体積とα不変量が下に有界な弱Fano対の有界性)
博士論文発表会
12:45-14:00 数理科学研究科棟(駒場) 122号室
加藤 大輝 氏 (東京大学大学院数理科学研究科)
Wild ramification, the nearby cycle complexes, and the characteristic cycles of ℓ-adic sheaves
(ℓ進層の暴分岐、隣接サイクル複体、特性サイクルについて)
加藤 大輝 氏 (東京大学大学院数理科学研究科)
Wild ramification, the nearby cycle complexes, and the characteristic cycles of ℓ-adic sheaves
(ℓ進層の暴分岐、隣接サイクル複体、特性サイクルについて)
博士論文発表会
14:15-15:30 数理科学研究科棟(駒場) 122号室
長岡 大 氏 (東京大学大学院数理科学研究科)
Studies of compactifications of affine homology 3-cells into del Pezzo fibrations
(Del Pezzoファイブレーションへのアフィンホモロジー3-胞体のコンパクト化の研究)
長岡 大 氏 (東京大学大学院数理科学研究科)
Studies of compactifications of affine homology 3-cells into del Pezzo fibrations
(Del Pezzoファイブレーションへのアフィンホモロジー3-胞体のコンパクト化の研究)
博士論文発表会
9:15-10:30 数理科学研究科棟(駒場) 126号室
千葉 悠喜 氏 (東京大学大学院数理科学研究科)
Discontinuous Galerkin method for elliptic problems
(楕円型問題に対する不連続Galerkin法)
千葉 悠喜 氏 (東京大学大学院数理科学研究科)
Discontinuous Galerkin method for elliptic problems
(楕円型問題に対する不連続Galerkin法)
博士論文発表会
10:45-12:00 数理科学研究科棟(駒場) 126号室
平良 晃一 氏 (東京大学大学院数理科学研究科)
Spectral and scattering theory for generalized Schrödinger operators
(一般化シュレディンガー作用素に関するスペクトル理論と散乱理論)
平良 晃一 氏 (東京大学大学院数理科学研究科)
Spectral and scattering theory for generalized Schrödinger operators
(一般化シュレディンガー作用素に関するスペクトル理論と散乱理論)
博士論文発表会
12:45-14:00 数理科学研究科棟(駒場) 126号室
中井 拳吾 氏 (東京大学大学院数理科学研究科)
Machine-learning Construction of a Model and Refined Regularity Criterion on Fluid Equations
(流体方程式の機械学習によるモデリングと解の正則性の判定条件)
中井 拳吾 氏 (東京大学大学院数理科学研究科)
Machine-learning Construction of a Model and Refined Regularity Criterion on Fluid Equations
(流体方程式の機械学習によるモデリングと解の正則性の判定条件)
博士論文発表会
14:15-15:30 数理科学研究科棟(駒場) 126号室
鈴木 拓海 氏 (東京大学大学院数理科学研究科)
Penalized Least Squares Approximation Methods and Their Applications to Stochastic Processes
(罰則付き最小二乗近似法と確率過程への応用)
鈴木 拓海 氏 (東京大学大学院数理科学研究科)
Penalized Least Squares Approximation Methods and Their Applications to Stochastic Processes
(罰則付き最小二乗近似法と確率過程への応用)
2020年01月30日(木)
博士論文発表会
10:45-12:00 数理科学研究科棟(駒場) 118号室
浅尾 泰彦 氏 (東京大学大学院数理科学研究科)
Magnitude homology and Vietoris-Rips homology of geodesic metric spaces
（測地的距離空間のマグニチュードホモロジー及びヴィートリス・リップスホモロジー）
浅尾 泰彦 氏 (東京大学大学院数理科学研究科)
Magnitude homology and Vietoris-Rips homology of geodesic metric spaces
（測地的距離空間のマグニチュードホモロジー及びヴィートリス・リップスホモロジー）
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