SLE and Its Partition Function in Multiply Connected Domains

This talk explores Schramm-Loewner Evolution (SLE_κ) in multiply connected domains, examining the unique challenges that arise beyond simply connected domains. Learn how the conformal invariance and Markov property that uniquely determine SLE_κ in simply connected domains are insufficient in multiply connected settings, where additional degrees of freedom exist. Discover Lawler's suggested approach of imposing the restriction property as a non-constructive characterization method. The 26-minute presentation reviews two explicit constructions of SLE_κ across different κ values and topological cases, demonstrating how the partition function can be determined and proven finite. The talk is based on joint research with J. Aru and is presented at the Hausdorff Center for Mathematics.