The Loewner energy is a functional on Jordan curves that is the large-deviations rate function for Schramm-Loewner Evolutions (SLE's).  Recent work has shown it also has surprising connections to other areas of probability, complex analysis, geometric measure theory, hyperbolic geometry, and even Teichmuller theory.  In the first part of this talk we survey some of these connections, providing an "appetizer" for Yilin Wang's upcoming summer school.

In the second part of the talk we show that Loewner-energy minimizers give insight into the regularity of the inverse Loewner transform (the map taking a driving function to its associated curve).  In particular, we use energy minimizers to exhibit curves of differing regularity that have driving functions of the same regularity, thus showing a theorem of Carto Wong is sharp.  This portion of the talk will be deterministic in nature.

Bio:Tim Mesikepp studied complex analysis under Steffen Rohde at the University of Washington and began his postdoc at BICMR last fall.  He is investigating analogies between probability and dynamical systems and is also interested in the Loewner energy, SLE, and deterministic aspects of the Loewner transform.