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Title: The extremal length systole of the Bolza surface
Abstract: The extremal length of a curve on a Riemann surface is a conformal invariant that has a nice geometric description but is not so simple to compute in practice. The extremal length systole is defined as the infimum of the extremal lengths of all non-contractible closed curves. I will discuss joint work with Didac Martinez-Granado and Franco Vargas Pallete in which we compute the extremal length systole of the Bolza surface, the most symmetric surface of genus two. The calculation involves certain identities for elliptic integrals called the Landen transformations. We also prove that the Bolza surface is a local maximizer for the extremal length systole and conjecture that it is the unique global maximizer.