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PDE実解析研究会
過去の記録 ～03/19｜次回の予定｜今後の予定 03/20～
| 開催情報 | 火曜日 10:30～11:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 儀我美一、石毛和弘、三竹大寿、米田剛 |
| セミナーURL | https://www.math.sci.hokudai.ac.jp/coe/sympo/pde_ra/ |
| 目的 | 首都圏の偏微分方程式、実解析の研究をさらに活発にするために本研究会を東大で開催いたします。 偏微分方程式研究者と実解析研究者の討論がより日常的になることを目指しています。 そのため、講演がその分野の概観をもわかるような形になるよう配慮いたします。 また講演者との1対1の討論がしやすいように講演は火曜の午前とし、午後に討論用の場所を用意いたします。 この研究会を通して皆様に気楽に東大を訪問していただければ幸いです。 北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)の情報が掲載されております。 |
2019年11月19日(火)
10:30-11:30 数理科学研究科棟(駒場) 056号室
Peter Topping 氏 (University of Warwick)
Starting Ricci flow with rough initial data (English)
Peter Topping 氏 (University of Warwick)
Starting Ricci flow with rough initial data (English)
[ 講演概要 ]
Ricci flow is a nonlinear PDE that is traditionally used to deform a manifold we would like to understand into a manifold we already understand. For example, Hamilton showed that a simply connected closed 3-manifold with positive Ricci curvature is deformed into a manifold of constant sectional curvature, thus allowing us to identify it as topologically a sphere.
In this talk we take a look at a different use of Ricci flow. We would like to exploit the regularising effect of parabolic PDE to turn a rough space into a smooth space by running the Ricci flow. In practice, this revolves around proving good a priori estimates on solutions, and taking unorthodox approaches to solving parabolic PDE. We will see some theory, first in 2D, then in higher dimension, and some applications.
Ricci flow is a nonlinear PDE that is traditionally used to deform a manifold we would like to understand into a manifold we already understand. For example, Hamilton showed that a simply connected closed 3-manifold with positive Ricci curvature is deformed into a manifold of constant sectional curvature, thus allowing us to identify it as topologically a sphere.
In this talk we take a look at a different use of Ricci flow. We would like to exploit the regularising effect of parabolic PDE to turn a rough space into a smooth space by running the Ricci flow. In practice, this revolves around proving good a priori estimates on solutions, and taking unorthodox approaches to solving parabolic PDE. We will see some theory, first in 2D, then in higher dimension, and some applications.
