Ideas

This page contains preliminary research ideas, open questions, and possible directions for future work.

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Gradient Flows on Spaces of Invariant Measures

Status: Preliminary idea
Last updated: August 2026

I am interested in whether Wasserstein geometry can be used to define meaningful gradient flows on spaces of invariant probability measures.

The broad objective is to identify functionals whose gradient flows may help characterize distinguished invariant measures, such as Gibbs or SRB measures.

Open Questions

1. What is the appropriate tangent structure on a space of invariant measures?
2. When does a Wasserstein gradient flow preserve invariance?
3. Can entropy or pressure be incorporated into a useful variational functional?