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過去の記録 ～01/27｜本日 01/28 | 今後の予定 01/29～
2023年01月31日(火)
代数幾何学セミナー
14:30-16:00 数理科学研究科棟(駒場) ハイブリッド開催/002号室
いつもと時間が異なります.
Shiji Lyu 氏 (プリンストン大学)
Some properties of splinters via ultrapower (English)
いつもと時間が異なります.
Shiji Lyu 氏 (プリンストン大学)
Some properties of splinters via ultrapower (English)
[ 講演概要 ]
A Noetherian (reduced) ring is called a splinter if it is a direct summand of every finite ring extension of it. This notion is related to various interesting notions of singularities, but far less properties are known about splinters.
In this talk, we will discuss the question of "regular ascent"; in the simplest (but already essential) form, we ask, for a Noetherian splinter R, is the polynomial ring R[X] always a splinter. We will see how ultrapower, a construction mainly belonging to model theory, is involved.
A Noetherian (reduced) ring is called a splinter if it is a direct summand of every finite ring extension of it. This notion is related to various interesting notions of singularities, but far less properties are known about splinters.
In this talk, we will discuss the question of "regular ascent"; in the simplest (but already essential) form, we ask, for a Noetherian splinter R, is the polynomial ring R[X] always a splinter. We will see how ultrapower, a construction mainly belonging to model theory, is involved.
2023年02月06日(月)
応用解析セミナー
16:00-18:10 数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催（通常と開催曜日が異なりますのでご注意下さい）
Marek Fila 氏 (Comenius University) 16:00-17:00
Solutions with moving singularities for nonlinear diffusion equations (ENGLISH)
Fast diffusion equation: uniqueness of solutions with a moving singularity (ENGLISH)
https://forms.gle/nKa4XATuuGPwZWbUA
対面・オンラインハイブリッド開催（通常と開催曜日が異なりますのでご注意下さい）
Marek Fila 氏 (Comenius University) 16:00-17:00
Solutions with moving singularities for nonlinear diffusion equations (ENGLISH)
[ 講演概要 ]
We give a survey of results on solutions with singularities moving along a prescribed curve for equations of fast diffusion or porous medium type. These results were obtained in collaboration with J.R. King, P. Mackova, J. Takahashi and E. Yanagida.
Petra Mackova 氏 (Comenius University) 17:10-18:10We give a survey of results on solutions with singularities moving along a prescribed curve for equations of fast diffusion or porous medium type. These results were obtained in collaboration with J.R. King, P. Mackova, J. Takahashi and E. Yanagida.
Fast diffusion equation: uniqueness of solutions with a moving singularity (ENGLISH)
[ 講演概要 ]
This talk focuses on open questions in the area of the uniqueness of distributional solutions of the fast diffusion equation with a given source term. The existence of different sets of such solutions is known from previous research, and the natural next issue is to examine their uniqueness. Assuming that the source term is a measure, the existence of different classes of solutions is known, however, their uniqueness is an open problem. The existence of a class of asymptotically radially symmetric solutions with a singularity that moves along a prescribed curve was proved by M. Fila, J. Takahashi, and E. Yanagida. More recently, it has been established by M. Fila, P. M., J. Takahashi, and E. Yanagida that these solutions solve the corresponding problem with a moving Dirac source term. In this talk, we discuss the uniqueness of these solutions. This is a joint work with M. Fila.
[ 参考URL ]This talk focuses on open questions in the area of the uniqueness of distributional solutions of the fast diffusion equation with a given source term. The existence of different sets of such solutions is known from previous research, and the natural next issue is to examine their uniqueness. Assuming that the source term is a measure, the existence of different classes of solutions is known, however, their uniqueness is an open problem. The existence of a class of asymptotically radially symmetric solutions with a singularity that moves along a prescribed curve was proved by M. Fila, J. Takahashi, and E. Yanagida. More recently, it has been established by M. Fila, P. M., J. Takahashi, and E. Yanagida that these solutions solve the corresponding problem with a moving Dirac source term. In this talk, we discuss the uniqueness of these solutions. This is a joint work with M. Fila.
https://forms.gle/nKa4XATuuGPwZWbUA
代数幾何学セミナー
13:00-14:30 数理科学研究科棟(駒場) 123号室
レクチャーシリーズ第２回目
Chenyang Xu 氏 (プリンストン大学)
K-stability of Fano varieties. (English)
レクチャーシリーズ第２回目
Chenyang Xu 氏 (プリンストン大学)
K-stability of Fano varieties. (English)
[ 講演概要 ]
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.
In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.
In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.
2023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
対面・オンラインのハイブリッド形式で行います。オンライン参加される場合は参考URLからご登録ください。
野口 潤次郎 氏 (東京大学)
多変数複素解析入門講義法 (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
対面・オンラインのハイブリッド形式で行います。オンライン参加される場合は参考URLからご登録ください。
野口 潤次郎 氏 (東京大学)
多変数複素解析入門講義法 (Japanese)
[ 講演概要 ]
微積分は，主に1変数の理論を講義するが，後半で多変数の内容を入れる．同じ様に，複素解析（函数論）でも，一変数の後につなぎよく，多変数の講義を段差なく行えるようにしたい．
モデルケースとして'リーマンの写像定理'がある．現在多くの教科書に書かれているモンテルの定理による初等的な証明(1922, Fejér--Riesz)まで，もとのリーマンの学位論文(1851)から約70年の歳月がかかている．
岡理論・多変数関数論基礎についてみると，Oka IX (1953)より本年でやはり70年たつが，あまり'初等化'の方面へは進展していないように思う．こここでは，学部の複素解析のコースで'リーマンの写像定理'の後に，段差無く完全証明付きで岡理論・多変数関数論基礎を講義する展開を考える．
初等化には，岡のオリジナル法(1943未発表, IX 1953)を第1連接定理に基づき展開するのが適当であることを紹介したい．学部講義の数学内容に日本人による成果が入ることで，学生のモチベーションに好効果を与えるであろうことも期待したい．
時間が許せば，擬凸問題解決の岡のオリジナル法と別証明とされるGrauertの証明との間のFredholm定理をめぐる類似性についても述べたい．
[ 参考URL ]微積分は，主に1変数の理論を講義するが，後半で多変数の内容を入れる．同じ様に，複素解析（函数論）でも，一変数の後につなぎよく，多変数の講義を段差なく行えるようにしたい．
モデルケースとして'リーマンの写像定理'がある．現在多くの教科書に書かれているモンテルの定理による初等的な証明(1922, Fejér--Riesz)まで，もとのリーマンの学位論文(1851)から約70年の歳月がかかている．
岡理論・多変数関数論基礎についてみると，Oka IX (1953)より本年でやはり70年たつが，あまり'初等化'の方面へは進展していないように思う．こここでは，学部の複素解析のコースで'リーマンの写像定理'の後に，段差無く完全証明付きで岡理論・多変数関数論基礎を講義する展開を考える．
初等化には，岡のオリジナル法(1943未発表, IX 1953)を第1連接定理に基づき展開するのが適当であることを紹介したい．学部講義の数学内容に日本人による成果が入ることで，学生のモチベーションに好効果を与えるであろうことも期待したい．
時間が許せば，擬凸問題解決の岡のオリジナル法と別証明とされるGrauertの証明との間のFredholm定理をめぐる類似性についても述べたい．
https://forms.gle/hYT2hVhDE3q1wDSh6
2023年02月17日(金)
代数幾何学セミナー
10:00-11:30 数理科学研究科棟(駒場) 123号室
レクチャーシリーズ第３回
Chenyang Xu 氏 (プリンストン大学)
K-stability of Fano varieties. ( English)
レクチャーシリーズ第３回
Chenyang Xu 氏 (プリンストン大学)
K-stability of Fano varieties. ( English)
[ 講演概要 ]
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.
In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.
In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.
2023年02月20日(月)
代数幾何学セミナー
10:00-11:30 数理科学研究科棟(駒場) 056号室
レクチャーシリーズ第４回目
Chenyang Xu 氏 (プリンストン大学)
K-stability of Fano varieties. (English)
レクチャーシリーズ第４回目
Chenyang Xu 氏 (プリンストン大学)
K-stability of Fano varieties. (English)
[ 講演概要 ]
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.
In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.
In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.
2023年02月22日(水)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催（通常と開催曜日が異なりますのでご注意下さい）
Alessio Porretta 氏 (University of Rome Tor Vergata)
Long time decay of Fokker-Planck equations with confining drift (ENGLISH)
https://forms.gle/SCyZWtfC5bNGadxE8
対面・オンラインハイブリッド開催（通常と開催曜日が異なりますのでご注意下さい）
Alessio Porretta 氏 (University of Rome Tor Vergata)
Long time decay of Fokker-Planck equations with confining drift (ENGLISH)
[ 講演概要 ]
The convergence to equilibrium of Fokker-Planck equations with confining drift is a classical issue, starting with the basic model of the Ornstein-Uhlenbeck process. I will discuss a new approach to obtain estimates on the time decay rate, which applies to both local and nonlocal diffusions. This is based on duality arguments and oscillation estimates for transport-diffusion equations, which are reminiscent of coupling methods used in probabilistic approaches.
[ 参考URL ]The convergence to equilibrium of Fokker-Planck equations with confining drift is a classical issue, starting with the basic model of the Ornstein-Uhlenbeck process. I will discuss a new approach to obtain estimates on the time decay rate, which applies to both local and nonlocal diffusions. This is based on duality arguments and oscillation estimates for transport-diffusion equations, which are reminiscent of coupling methods used in probabilistic approaches.
https://forms.gle/SCyZWtfC5bNGadxE8
2023年03月07日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 128号室
Ricardo Correa da Silva 氏 (Friedrich-Alexander-Universität Erlangen-Nürnberg)
Structure and Inclusions of Twisted Araki-Woods Algebras (English)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ricardo Correa da Silva 氏 (Friedrich-Alexander-Universität Erlangen-Nürnberg)
Structure and Inclusions of Twisted Araki-Woods Algebras (English)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
