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今週のセミナー
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2025.10.7（火） | セミナー
幾何セミナー(15:00--15:45 【会場：数学棟305号室】)
発表者：村上 怜 氏（東北大学）
題目：Griffiths予想への解析的アプローチ
概要：
Griffiths予想は，正則ベクトル束の豊富性と，曲率がGriffiths正値となる計量の存在が同値であると主張する予想である．直線束の場合は小平の埋め込み定理により，また1次元の場合についても既に解決されている．近年，J.-P. Demaillyはこの予想に対し，偏微分方程式系を用いた解析的アプローチを提示した．本講演ではこのアプローチを用いた1次元Griffiths予想の再証明を与える．
幾何セミナーHP
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2025.10.9（木） | セミナー
応用数理解析セミナー(16:30--18:00【会場：合同A棟8階 801室】)
発表者：Luca Scarpa 氏 (Politecnico di Milano)
題目：The effect of noise on doubly nonlinear evolution equations
概要：
We give an overview of some recent results for doubly nonlinear stochastic evolution equations in Hilbert spaces. In the first part of the talk we introduce the prototypes of the problems in consideration and we discuss the main existence results. Secondly, we focus on the direction of uniqueness by noise for doubly nonlinear evolutions by means of the associated Kolmogorov equations, highlighting some recent contributions and open problems. The works presented in the talk are based on joint collaborations with Prof. Ulisse Stefanelli (University of Vienna, Austria) and Prof. Carlo Orrieri (University of Pavia, Italy).
応用数理解析セミナーHP
来週以降のセミナー
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2025.10.16（木） | セミナー
応用数理解析セミナー(16:30--18:00【会場：合同A棟8階 801室】)
発表者：Philippe Souplet 氏 (Université Sorbonne Paris Nord)
題目：Diffusive Hamilton-Jacobi equations: gradient blow-up singularities, Liouville-type theorems and continuation after blow-up
概要：
We consider the diffusive Hamilton-Jacobi equation $u_t-\Delta u=|\nabla u|^p$ with homogeneous Dirichlet boundary conditions, which plays an important role in stochastic optimal control theory and in certain models of surface growth (KPZ). Despite its simplicity, it displays a variety of interesting and surprising behaviors and significant progress has been made in the past ten years.
We will discuss the following issues:
- Gradient blow-up (GBU) on the boundary: time rate, single-point GBU, space and time-space profiles;
- Liouville type theorems and their applications;
- Continuation after GBU as a global viscosity solution with loss and recovery of boundary conditions.
応用数理解析セミナーHP
