# Analysis, Geometry, and Dynamical Systems Seminar

## Past sessions

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### Random Construction of Riemann Surfaces

What are the geometric properties of a typical Riemann surface of large genus? In a joint work with Robert Brooks we address this problem by constructing compact Riemann surfaces from random cubic graphs. The resulting surfaces form a dense set in the set of all Riemann surfaces. This construction enables us to investigate the geometry of Riemann surfaces using the geometry of random graphs. The resulting picture is an interesting mix of techniques from Riemannian geometry, complex analysis, and probability theory, and contains some surprising answers.

### Homoclinic and Heteroclinic solutions of a Singular Hamiltonian System

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