2022 May

Professor Yoshikazu Giga is one of the world-leading mathematical analysts known for his seminal works on several important PDEs including the Navier-Stokes equations, blow-up phenomena for semilinear heat equations, a level-set method for the mean curvature flow equation, and singular diffusion equations. He received his degree from the University of Tokyo and spent at several institutions including Nagoya University, the Courant Institute, University of Maryland, and IMA before he moved to Hokkaido University in 1986. He worked there as a full professor from 1991 until he moved to the University of Tokyo in 2004. He was invited to ICM in 2018 and to ICIAM in 2003. He received several prizes including the Medal with Purple Ribbon from the Japanese government for a distinguished scientist.

Title : 

The level-set mean curvature flow equation versus the total variation flow equation

Abstract: The level-set mean curvature flow equation has been introduced to track an evolving hypersurface by its mean curvature after it develops singularities. A level-set of a solution of the level-set mean curvature flow equation moves its mean curvature. The total variation flow equation is often used to remove noise from images. Although these two equations look similar, analytic properties are quite different; the former equation is a local equation while the latter is a nonlocal equation. In this talk, we compare these two equations as well as a few applications. 

Discussion Theme (for the 2nd part of the event) : 

How to collaborate with researchers other than mathematicians 

数学研究者以外の研究者とどのように共同研究するか

Feedback for Breakout  Room  Discussion from participants : 

・       The thoughts of the speaker about working with non-mathematicians were very inspiring. The fact that the talk was concise was very appreciated because there was less time pressure on the BR discussions and things were more relaxed. I think it was also easy to follow for non-japanese speakers because the speaker’s speech was very close to his written slides in English.

・       他分野の方と話をするときに、お互いの知識のすり合わせに時間がかかる場合が多いかと思うが、そのような場合にも粘り強く、交流を続けていくことで、新たな知見が得られる場合があるのではないかと感じた。

・       私たちのグループでは、産業界との共同研究について、儀我先生に直接お話をお聞きすることができました。 海外では企業が高待遇で数学者をヘッド・ハンティングしており、数学の価値が産業界で高まっている一方で、日本においては ・産業界の数学人材が圧倒的に足りていない ・プロジェクトをまとめる人間が数学の価値を正しく認識していない といった問題が根深いというお話がとても印象的でした。 数学の専門性を理解し、産業界のニーズに人材をマッチングさせるコンサルティングのような役割が求められている、と改めて感じました。 また、儀我先生が最後におっしゃっていた、数学の人なら相手の言わんとしている本質的な部分をうまく見抜くことができるはず、というお話は、これまであまり意識して来なかったことだったので大変心に残りました。

・       話題にもよりますが若干時間が短いようにおもいました。

・       The were members of our group that had experience in communication between mathematics and physics, from either side. We discussed how there can initially be a long period of time needed to find common ground in projects across disciplines, and so making such a commitment is not easy. In particular, it is not always clear what skills people on the other side have to offer (and vice versa), and understanding different points of view can take a great effort. There was some experience in the group with top-down initiatives for interdisciplinary collaboration, but the general feeling was that the success of such projects ultimately depends on individuals being prepared to spend time genuinely trying to listen and understand each other - in the end, it was expressed that “it has to come from the heart”!

・       参加したブレイクアウトルームでは、率直なところ、産業界や他分野との共同研究にあまり興味が持てない、興味はあるが時間がない、という方もいました。異分野との共同研究に興味を持つようになったきっかけや、共同研究とそうでない研究の時間配分、いくつもの研究テーマを並行して行うための工夫、などについても機会があればいろいろな方にお聞きしてみたいと思いました。