Λέσχη Μαθηματικών

The Riemann mapping theorem and a probabilistic solution to the Dirichlet problem

Ορέστης Πλευράκης (Princeton)

Abstract: The Riemann mapping theorem is one of the most central results of complex analysis. However, the standard proof lacks intuition. We will see an intuitive proof using ideas from topology and probability theory. Along the way we will solve the Dirichlet problem for Laplace equation using random walks.

Προαπαιτούμενα:

1. Μιγαδική ανάλυση (σε προπτυχιακό επίπεδο)
2. Πιθανότητες (σε προπτυχιακό επίπεδο)

Βιβλιογραφία:

1. The Riemann Mapping Theorem from Riemann's Viewpoint, by Robert Greene and Kang-Tae Kim.
2. Probability: Theory and Examples, by Rick Durrett. Chapters 7 and 9.5.