今後の予定

過去の記録 ~03/18本日 03/19 | 今後の予定 03/20~

2024年03月21日(木)

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
Mostafa Fazly 氏 (University of Texas at San Antonio)
Symmetry Results for Nonlinear PDEs (English)
[ 講演概要 ]
The study of qualitative behavior of solutions of Partial Differential Equations (PDEs) started roughly in mid-18th century. Since then scientists and mathematicians from different fields have put in a great effort to expand the theory of nonlinear PDEs. PDEs can be divided into two kinds: (a) the linear ones, which are relatively easy to analyze and can often be solved completely, and (b) the nonlinear ones, which are much harder to analyze and can almost never be solved completely.
We begin this talk by an introduction on foundational ideas behind the De Giorgi’s conjecture (1978) for the Allen-Cahn equation that is inspired by the Bernstein’s problem (1910). This conjecture brings together three groups of mathematicians: (a) a group specializing in nonlinear partial differential equations, (b) a group in differential geometry, and more specially on minimal surfaces and constant mean curvature surfaces, and (c) a group in mathematical physics on phase transitions. We then present natural generalizations and counterparts of the problem. These generalizations lead us to introduce certain novel concepts, and we illustrate why these novel concepts seem to be the right concepts in the context and how they can be used to study particular systems and models arising in Sciences. We give a survey of recent results.

2024年04月10日(水)

日仏数学拠点FJ-LMIセミナー

16:00-17:00   数理科学研究科棟(駒場) 056号室
Séverin PHILIP 氏 (京都大学 数理解析研究所, RIMS, Kyoto University)
Galois outer representation and the problem of Oda
(英語)
[ 講演概要 ]
Oda’s problem stems from considering the pro-l outer Galois actions on the moduli spaces of hyperbolic curves. These actions come from a generalization by Oda of the standard étale homotopy exact sequence for algebraic varieties over the rationals. We will introduce these geometric Galois actions and present some of the mathematics that they have stimulated over the past 30 years along with the classical problem of Oda. In the second and last part of this talk, we will see how a cyclic special loci version of this problem can be formulated and resolved in the case of simple cyclic groups using the maximal degeneration method of Ihara and Nakamura adapted to this setting.
[ 参考URL ]
https://fj-lmi.cnrs.fr/seminars/

2024年04月26日(金)

代数幾何学セミナー

13:30-15:00   数理科学研究科棟(駒場) 056号室
河上 龍郎 氏 (京都大学)
Frobenius stable Grauert-Riemenschneider vanishing fails (日本語)
[ 講演概要 ]
We show that the Frobenius stable version of Grauert-Riemenschneider vanishing fails for a terminal 3-fold in characteristic 2. To prove this, we introduce the notion of $F_p$-rationality for singularities in positive characteristic, and prove that 3-dimensional klt singularities are $\mathbb F_p$-rational. I will also talk about the vanishing of $F_p$-cohomologies of log Fano threefolds. This is joint work with Jefferson Baudin and Fabio Bernasconi.