PIMS Network-Wide Colloquium

Thu., Jan. 25, 2024 3:30 p.m.

Location: By Zoom

Speaker: Wilford Gangbo (UCLA)

Title: Hamilton-Jacobi equations on the Wasserstein space on graphs.

Registration in advance and details at: https://www.pims.math.ca/scientific-event/240125-pnwcwg

Abstract:

We consider metric tensors on undirected weighted graphs G, which allows us to treat P(G), the set of probability vectors on G, as a length space. On defines a divergence operator div_\mu(G) for mu in P(G), in such a way that we can use control vectors m to define paths s:[0,T] \to P(G), satisfying the system of ODEs: d\sigma/dt + div_G(m) + \hbar div_\sigma(\nabla_G log \sigma)=0. These paths serve as characteristics for Hamilton-Jacobi equations involving graph-individual noise operators. We propose a well posedness theory on P(G).(This talk is based on a joint work with C. Mou and A. Swiech).