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: 2026.04.21   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.