Antonio Siconolfi：Dynamical mini courses——Optimal transport, Hamilton-Jacobi equations and Mean field games
Speaker: Antonio Siconolfi，University of Roma, la Sapienza
Inviter: 张建路
Title: Dynamical mini courses——Optimal transport, Hamilton-Jacobi equations and Mean field games
Language: English
Time & Venue: 2026.04.14 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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修改:vinbo FROM 202.120.11.*
FROM 202.120.11.*