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過去の記録 ～12/07｜本日 12/08 | 今後の予定 12/09～
2024年12月09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
鈴木 良明 氏 (新潟大学)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
鈴木 良明 氏 (新潟大学)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
[ 講演概要 ]
Heisenberg Bieberbach多様体とは、Heisenberg群とユニタリ群との半直積における離散かつ捩れの無い部分群によってHeisenberg群を割って得られるコンパクト商のことである。この商多様体は、Heisenberg群を自身の離散部分群で割ったコンパクト商(Heisenberg冪零多様体)をさらに有限群で割った空間になっている。この講演では3次元Heisenberg Bieberbach多様体上のFolland-Stein作用素と呼ばれるCR幾何由来の微分作用素の固有値と固有空間について考察する。Heisenberg Bieberbach多様体の被覆空間であるHeisenberg冪零多様体に対しては、2004年にFollandが表現論の手法を用いてFolland-Stein作用素の固有値と固有関数が明示的に求めている。Follandの結果を応用し、3次元Heisenberg Bieberbach多様体のいくつかの例に対してもFolland-Stein作用素の固有値と固有関数を求めることができることを紹介する。特に固有空間の次元も求めることができ、Weylの法則が成り立つことも紹介したい。
[ 参考URL ]Heisenberg Bieberbach多様体とは、Heisenberg群とユニタリ群との半直積における離散かつ捩れの無い部分群によってHeisenberg群を割って得られるコンパクト商のことである。この商多様体は、Heisenberg群を自身の離散部分群で割ったコンパクト商(Heisenberg冪零多様体)をさらに有限群で割った空間になっている。この講演では3次元Heisenberg Bieberbach多様体上のFolland-Stein作用素と呼ばれるCR幾何由来の微分作用素の固有値と固有空間について考察する。Heisenberg Bieberbach多様体の被覆空間であるHeisenberg冪零多様体に対しては、2004年にFollandが表現論の手法を用いてFolland-Stein作用素の固有値と固有関数が明示的に求めている。Follandの結果を応用し、3次元Heisenberg Bieberbach多様体のいくつかの例に対してもFolland-Stein作用素の固有値と固有関数を求めることができることを紹介する。特に固有空間の次元も求めることができ、Weylの法則が成り立つことも紹介したい。
https://forms.gle/gTP8qNZwPyQyxjTj8
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
須田 颯 氏 (東京科学大学（旧東京工業大学）)
Scaling limits of a tagged soliton in the randomized box-ball system
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
須田 颯 氏 (東京科学大学（旧東京工業大学）)
Scaling limits of a tagged soliton in the randomized box-ball system
[ 講演概要 ]
The box-ball system (BBS) is a cellular automaton that exhibits the solitonic behavior. In recent years, with the rapid progress in the study of the hydrodynamics of integrable systems, there has been a growing interest in BBS with random initial distribution. In this talk, we consider the scaling limits for a tagged soliton in the BBS starting from certain stationary distribution. This talk is based on a joint work with Stefano Olla and Makiko Sasada.
The box-ball system (BBS) is a cellular automaton that exhibits the solitonic behavior. In recent years, with the rapid progress in the study of the hydrodynamics of integrable systems, there has been a growing interest in BBS with random initial distribution. In this talk, we consider the scaling limits for a tagged soliton in the BBS starting from certain stationary distribution. This talk is based on a joint work with Stefano Olla and Makiko Sasada.
2024年12月10日(火)
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) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
若月 駿 氏 (名古屋大学)
Computation of the magnitude homology as a derived functor (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
若月 駿 氏 (名古屋大学)
Computation of the magnitude homology as a derived functor (JAPANESE)
[ 講演概要 ]
Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
[ 参考URL ]Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
作用素環セミナー
15:00-16:30 数理科学研究科棟(駒場) 002号室
時間，部屋が普段と違います．
谷本溶 氏 (Univ. Rome, "Tor Vergata")
Introduction to Lean theorem prover
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
時間，部屋が普段と違います．
谷本溶 氏 (Univ. Rome, "Tor Vergata")
Introduction to Lean theorem prover
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 002号室
部屋が普段と違います．
Maria Stella Adamo 氏 (FAU Erlangen-Nürnberg)
Osterwalder-Schrader axioms for unitary full VOAs
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
部屋が普段と違います．
Maria Stella Adamo 氏 (FAU Erlangen-Nürnberg)
Osterwalder-Schrader axioms for unitary full VOAs
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024年12月11日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
大江亮輔 氏 (東京大学大学院数理科学研究科)
The characteristic cycle of an l-adic sheaf on a smooth variety (Japanese)
大江亮輔 氏 (東京大学大学院数理科学研究科)
The characteristic cycle of an l-adic sheaf on a smooth variety (Japanese)
[ 講演概要 ]
The characteristic cycle of an l-adic sheaf on a smooth variety over a perfect field is defined by Saito as a cycle on the cotangent bundle and the intersection with the zero section computes the Euler number. On the other hand, the characteristic cycle of an l-adic sheaf on a regular scheme in mixed characteristic is not yet defined. In this talk, I define the F-characteristic cycle of a rank one sheaf on an arithmetic surface whose intersection with the zero section computes the Swan conductor of the cohomology of the generic fiber. The definition is based on the computation of the characteristic cycle in equal characteristic by Yatagawa. I explain the rationality and the integrality of the characteristic form of an abelian character, which are necessary for the definition of the F-characteristic cycle.
The characteristic cycle of an l-adic sheaf on a smooth variety over a perfect field is defined by Saito as a cycle on the cotangent bundle and the intersection with the zero section computes the Euler number. On the other hand, the characteristic cycle of an l-adic sheaf on a regular scheme in mixed characteristic is not yet defined. In this talk, I define the F-characteristic cycle of a rank one sheaf on an arithmetic surface whose intersection with the zero section computes the Swan conductor of the cohomology of the generic fiber. The definition is based on the computation of the characteristic cycle in equal characteristic by Yatagawa. I explain the rationality and the integrality of the characteristic form of an abelian character, which are necessary for the definition of the F-characteristic cycle.
2024年12月12日(木)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 128号室
Chenyang Xu 氏 (Princeton University)
Irreducible symplectic varieties with a large second Betti number
Chenyang Xu 氏 (Princeton University)
Irreducible symplectic varieties with a large second Betti number
[ 講演概要 ]
(joint with Yuchen Liu, Zhiyu Liu) We show that the Lagrangian fibration constructed by Iiiev-Manivel using intermediate Jacobians of cubic fivefolds containing a fixed cubic fourfold, admits a compactification as a terminal Q-factorial irreducible symplectic varieties. As far as I know, besides OG10, this is the second family of irreducible symplectic varieties with the second Betti number at least 24.
(joint with Yuchen Liu, Zhiyu Liu) We show that the Lagrangian fibration constructed by Iiiev-Manivel using intermediate Jacobians of cubic fivefolds containing a fixed cubic fourfold, admits a compactification as a terminal Q-factorial irreducible symplectic varieties. As far as I know, besides OG10, this is the second family of irreducible symplectic varieties with the second Betti number at least 24.
2024年12月16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
Laurent Stolovitch 氏 (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
https://forms.gle/gTP8qNZwPyQyxjTj8
Laurent Stolovitch 氏 (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
[ 講演概要 ]
In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
[ 参考URL ]In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024年12月17日(火)
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) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Emmanuel Graff 氏 (東京大学大学院数理科学研究科)
Is there torsion in the homotopy braid group? (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Emmanuel Graff 氏 (東京大学大学院数理科学研究科)
Is there torsion in the homotopy braid group? (ENGLISH)
[ 講演概要 ]
In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
[ 参考URL ]In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 122号室
作用素環賞受賞講演です．
山下真 氏 (Univ. Oslo)
題未定
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
作用素環賞受賞講演です．
山下真 氏 (Univ. Oslo)
題未定
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024年12月18日(水)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 122号室
通常の曜日、教室と異なります。オンラインでも開催されます。
Amy Novick-Cohen 氏 (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
通常の曜日、教室と異なります。オンラインでも開催されます。
Amy Novick-Cohen 氏 (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
[ 講演概要 ]
We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
下記の [参考URL] からZoomミーティングにご参加ください。
ミーティング ID: 833 0620 3126
パスコード: 223203
[ 参考URL ]We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
下記の [参考URL] からZoomミーティングにご参加ください。
ミーティング ID: 833 0620 3126
パスコード: 223203
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
2024年12月19日(木)
東京無限可積分系セミナー
14:00-15:30 数理科学研究科棟(駒場) 002号室
Omar Kidwai 氏 (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
Omar Kidwai 氏 (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
[ 講演概要 ]
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
2024年12月20日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 大講義室号室
小薗英雄 氏 (早稲田大学基幹理工学部 / 東北大学数理科学共創社会センター)
Helmholtz-Weyl分解とその電磁流体力学方程式への応用 (日本語)
https://forms.gle/QNj3fohg3ZRMD8RHA
小薗英雄 氏 (早稲田大学基幹理工学部 / 東北大学数理科学共創社会センター)
Helmholtz-Weyl分解とその電磁流体力学方程式への応用 (日本語)
[ 講演概要 ]
3次元Euclid空間内の滑らかな境界をもつ有界領域における$L^r$-ベクトル場のHelmholtz-Weyl分解について紹介する．コンパクトRiemann多様体上の$p$-次微分形式に対するde Rham-Hodge-小平分解についてはよく知られているが，ベクトル場が滑らかとは限らないLebesgue空間に属する場合には，藤原ー森本等によって比較的最近に得られた．本講演では3次元有界領域の場合に限って，調和ベクトル場の空間を境界に接している場合と，直交している場合の２種類の境界条件によって特徴づけ，$L^r$-ベクトル場の直和分解について解説する．特に，ベクトルポテンシャルの回転によって張られる部分空間の特徴づけに焦点をあてる．応用として，第２Betti数がゼロではない領域上の電磁流体力学方程式の調和ベクトルに附随する平衡解が，漸近安定であることを明らかにする．本講演の内容は，清水扇丈氏（京都大学）と柳澤卓氏（奈良女子大学）との共同研究に基づいている．
[ 参考URL ]3次元Euclid空間内の滑らかな境界をもつ有界領域における$L^r$-ベクトル場のHelmholtz-Weyl分解について紹介する．コンパクトRiemann多様体上の$p$-次微分形式に対するde Rham-Hodge-小平分解についてはよく知られているが，ベクトル場が滑らかとは限らないLebesgue空間に属する場合には，藤原ー森本等によって比較的最近に得られた．本講演では3次元有界領域の場合に限って，調和ベクトル場の空間を境界に接している場合と，直交している場合の２種類の境界条件によって特徴づけ，$L^r$-ベクトル場の直和分解について解説する．特に，ベクトルポテンシャルの回転によって張られる部分空間の特徴づけに焦点をあてる．応用として，第２Betti数がゼロではない領域上の電磁流体力学方程式の調和ベクトルに附随する平衡解が，漸近安定であることを明らかにする．本講演の内容は，清水扇丈氏（京都大学）と柳澤卓氏（奈良女子大学）との共同研究に基づいている．
https://forms.gle/QNj3fohg3ZRMD8RHA
2024年12月23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
野口 潤次郎 氏 (東京大学)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
野口 潤次郎 氏 (東京大学)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
[ 講演概要 ]
We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
[ 参考URL ]We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024年12月24日(火)
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
対面・オンラインハイブリッド開催，場所にご注意ください
筧知之 氏 (筑波大学)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
https://forms.gle/2otzqXYVD6DqM11S8
対面・オンラインハイブリッド開催，場所にご注意ください
筧知之 氏 (筑波大学)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
[ 講演概要 ]
In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
[ 参考URL ]In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
https://forms.gle/2otzqXYVD6DqM11S8
2024年12月26日(木)
離散数理モデリングセミナー
15:00-17:00 数理科学研究科棟(駒場) 002号室
Wookyung KIM 氏 (東京大学大学院数理科学研究科)
Integrable deformation of cluster map associated to finite type Dynkin diagram
Wookyung KIM 氏 (東京大学大学院数理科学研究科)
Integrable deformation of cluster map associated to finite type Dynkin diagram
[ 講演概要 ]
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
