中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
动力系统研讨班
Speaker: Antonio Siconolfi (University of Roma, la Sapienza)
Inviter: 张建路
Language: English
Title: Dynamical mini courses——Optimal transport, Hamilton-Jacobi equations and Mean field games
Time & Venue: 2026年4月14日（星期二）4月16日（星期四）4月21日（星期二）14：00-16：30 & 南楼N913
Abstract: This is a short course supply a preliminary introduction of the following topics,
– Optimal transport and the Kantorovich duality theorem in the discrete setting.
– Existence of optimal transport plans in the continuous setting.
– Wasserstein distances.
– Lagrangian cost functions.
– The dynamical formulation of Benamou–Brenier.
– Time-dependent Hamilton–Jacobi equations with non-autonomous Hamiltonians
and the Lax–Oleinik formula.
– Kantorovich duality in the continuous setting.
– g0-optimal curves and measures.
– g0-optimal measures and their relation to optimal transport.
– Borel vector fields associated with Lax–Oleinik solutions.
– g0-optimal measures as solutions to continuity equations.
– First-order time-dependent Mean Field Game (MFG) models.
– A fixed-point theorem for MFG.
– General existence results for MFG solutions.
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