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SUMMARY:Eveliina Peltola (Bonn)
DTSTART:20210305T173000Z
DTEND:20210305T183000Z
DTSTAMP:20260423T004911Z
UID:PatC/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/32/">On
  large deviations of SLEs\, real rational functions\, and zeta-regularized
  determinants of Laplacians</a>\nby Eveliina Peltola (Bonn) as part of Pro
 bability and the City Seminar\n\n\nAbstract\nThe talk concerns a large dev
 iation principle (LDP) for (multiple) Schramm-Loewner evolution (SLE) curv
 es for the Hausdorff metric.\nWhen studying the LDP\, we introduced a ''Lo
 ewner potential'' that describes the rate function.\nThis object turned ou
 t to have several intrinsic\, and perhaps surprising\, connections to vari
 ous fields.\nFor instance\, it has a simple expression in terms of zeta-re
 gularized determinants of Laplace-Beltrami operators.\nOn the other hand\,
  minima of the Loewner potential solve a nonlinear first order PDE that ar
 ises\nin a semiclassical limit of certain correlation functions in conform
 al field theory (arguably also related to isomonodromic systems).\nFinally
 \, the Loewner potential minimizers classify rational functions with real 
 critical points\, thereby providing a novel proof for\na version of the no
 w well-known Shapiro-Shapiro conjecture in real enumerative geometry. This
  talk is based on joint work with Yilin Wang (MIT).\n
LOCATION:https://researchseminars.org/talk/PatC/32/
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