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過去の記録 ～03/16｜本日 03/17 | 今後の予定 03/18～
2026年03月18日(水)
日仏数学拠点FJ-LMIセミナー
13:30-14:15 数理科学研究科棟(駒場) 056号室
Amaury HAYAT 氏 (ENPC, Paris)
Stabilization of PDEs and AI for mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Amaury HAYAT 氏 (ENPC, Paris)
Stabilization of PDEs and AI for mathematics (英語)
[ 講演概要 ]
Control theory consists in asking: if we can act on a system, what can we make it do? One of the main problems is the stabilization problem: how can we act on a system to guarantee the long-term behavior of its solutions? In this presentation, we will examine this problem from several angles. First, we will look at the problem of stabilizing PDEs from an abstract perspective and present a recent approach called F-equivalence (or sometimes Fredholm backstepping). The principle is simple: instead of trying to find a control that makes the system stable, we look at another problem: we try find a control that renders the PDE system dynamically equivalent to a simpler system for which stability is already known. Besides being interesting in itself, this approach has also resulted in new results in control theory, and we will review the progress that has been made in the last three years. In a second part, we will focus on a more concrete problem: the stabilization of hyperbolic equations modeling road traffic. We will show how abstract mathematical concepts, such as entropic solutions, can have tangible impacts in real-world scenarios, and we will discuss their application to traffic regulation and the reduction of traffic jams.
[ 参考URL ]Control theory consists in asking: if we can act on a system, what can we make it do? One of the main problems is the stabilization problem: how can we act on a system to guarantee the long-term behavior of its solutions? In this presentation, we will examine this problem from several angles. First, we will look at the problem of stabilizing PDEs from an abstract perspective and present a recent approach called F-equivalence (or sometimes Fredholm backstepping). The principle is simple: instead of trying to find a control that makes the system stable, we look at another problem: we try find a control that renders the PDE system dynamically equivalent to a simpler system for which stability is already known. Besides being interesting in itself, this approach has also resulted in new results in control theory, and we will review the progress that has been made in the last three years. In a second part, we will focus on a more concrete problem: the stabilization of hyperbolic equations modeling road traffic. We will show how abstract mathematical concepts, such as entropic solutions, can have tangible impacts in real-world scenarios, and we will discuss their application to traffic regulation and the reduction of traffic jams.
https://fj-lmi.cnrs.fr/seminars/
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
Dietmar Hoemberg 氏 (Weierstrass Institute, Berlin)
A phasefield approach to two-scale topology optimization (English)
Dietmar Hoemberg 氏 (Weierstrass Institute, Berlin)
A phasefield approach to two-scale topology optimization (English)
[ 講演概要 ]
Subject of my presentation is a novel approach for optimizing both the macroscopic shape and the porous mesoscopic structure of components. In the first part of my presentation I will introduce the concept of phasefield based topology optimization. The second part of my presentation is devoted to two-scale topology optimization. The key feature here is the introduction of an additional local volume control (LVC), which allows to adjust the desired spatial scales. The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. I will present some analytical results for the resulting optimal control problem and conclude with numerical results showing the versatility of our approach for creating optimal macroscopic designs with tailored mesostructures.
Subject of my presentation is a novel approach for optimizing both the macroscopic shape and the porous mesoscopic structure of components. In the first part of my presentation I will introduce the concept of phasefield based topology optimization. The second part of my presentation is devoted to two-scale topology optimization. The key feature here is the introduction of an additional local volume control (LVC), which allows to adjust the desired spatial scales. The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. I will present some analytical results for the resulting optimal control problem and conclude with numerical results showing the versatility of our approach for creating optimal macroscopic designs with tailored mesostructures.
2026年03月19日(木)
日仏数学拠点FJ-LMIセミナー
13:30-14:15 数理科学研究科棟(駒場) 056号室
Amaury HAYAT 氏 (ENPC, Paris)
How can AI Help Mathematicians? (英語)
https://fj-lmi.cnrs.fr/seminars/
Amaury HAYAT 氏 (ENPC, Paris)
How can AI Help Mathematicians? (英語)
[ 講演概要 ]
The advent of artificial intelligence raises an important question: can AI assist mathematicians in solving open problems in mathematics? This talk explores this question from multiple perspectives. We will explore how different types of AI models can be trained to provide valuable insights into mathematical questions from different areas of mathematics and applied mathematics. We will also present recent works on AI models specifically designed for automated theorem proving.
[ 参考URL ]The advent of artificial intelligence raises an important question: can AI assist mathematicians in solving open problems in mathematics? This talk explores this question from multiple perspectives. We will explore how different types of AI models can be trained to provide valuable insights into mathematical questions from different areas of mathematics and applied mathematics. We will also present recent works on AI models specifically designed for automated theorem proving.
https://fj-lmi.cnrs.fr/seminars/
2026年03月27日(金)
談話会・数理科学講演会
16:00-17:00 数理科学研究科棟(駒場) NISSAY Lecture Hall(大講義室)号室
吉田朋広 氏 (東京大学大学院数理科学研究科)
偶然と無作為の研究：選択バイアスがある私的小史 (日本語)
吉田朋広 氏 (東京大学大学院数理科学研究科)
偶然と無作為の研究：選択バイアスがある私的小史 (日本語)
[ 講演概要 ]
確率統計学を学んできましたが、方針が半ば無作為ながらも多くの偶然に導かれてまいりました。
話題の選択と成り行きの評価にバイアスがあることを承知の上で、今に至った経緯を振り返りたいと思います。
確率統計学を学んできましたが、方針が半ば無作為ながらも多くの偶然に導かれてまいりました。
話題の選択と成り行きの評価にバイアスがあることを承知の上で、今に至った経緯を振り返りたいと思います。
2026年04月10日(金)
幾何解析セミナー
16:00-17:00 数理科学研究科棟(駒場) 号室
松尾信一郎 氏 (名古屋大学)
Dirac作用素の指数の離散化と格子ゲージ理論 (日本語)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
松尾信一郎 氏 (名古屋大学)
Dirac作用素の指数の離散化と格子ゲージ理論 (日本語)
[ 講演概要 ]
講演者の真の目的はSeiberg-Witten理論の離散化であり，四次元におけるPL=DIFFを念頭にPL的SW理論の構築を目論んでいる．
その第一歩として，Dirac作用素の指数を離散化した．
ただし，Fredholm指数とは無限次元的なものであり，Dirac作用素を単純に離散化してもその指数は自明になってしまう．
そこで，格子ゲージ理論のアイデアを活用する．
本講演は，物理学者四人と数学者三人の共同研究である次の二本の論文に基づく．
https://arxiv.org/abs/2602.12576
https://arxiv.org/abs/2407.17708
[ 参考URL ]講演者の真の目的はSeiberg-Witten理論の離散化であり，四次元におけるPL=DIFFを念頭にPL的SW理論の構築を目論んでいる．
その第一歩として，Dirac作用素の指数を離散化した．
ただし，Fredholm指数とは無限次元的なものであり，Dirac作用素を単純に離散化してもその指数は自明になってしまう．
そこで，格子ゲージ理論のアイデアを活用する．
本講演は，物理学者四人と数学者三人の共同研究である次の二本の論文に基づく．
https://arxiv.org/abs/2602.12576
https://arxiv.org/abs/2407.17708
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
