BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Simon Bortz (University of Alabama) DTSTART:20220614T160000Z DTEND:20220614T170000Z DTSTAMP:20260423T021105Z UID:OSGA/115 DESCRIPTION:Title: C aloric Measure and Parabolic Uniform Rectifiability\nby Simon Bortz (U niversity of Alabama) as part of Online Seminar "Geometric Analysis"\n\n\n Abstract\nIn the late 70's Dahlberg showed that harmonic measure and surfa ce measure are mutually absolutely continuous in Lipschitz domains in $\\m athbb{R}^d$ (this was a long standing conjecture). In fact\, he showed a s tronger quantitative version of mutual absolute continuity \, $A_\\infty$\ , which is equivalent to certain $L^p$ estimates on solutions. It was conj ectured by Hunt that the same is true in the parabolic setting\, that is\, for parabolic Lipschitz graph domains\; however\, this turned out to be f alse as a counterexample was produced by Kaufman and Wu. On the other hand \, it was later shown by Lewis and Murray that if the graphs had a little more time-regularity then Dahlberg's theorem holds.\n\nTogether with my co -authors\, we have shown the work of Lewis and Murray is sharp. In particu lar\, if a domain is given by the region above a parabolic Lipschitz graph the $A_\\infty$ property of caloric measure is equivalent to this extra t ime regularity. These `regular' parabolic Lipschitz graphs are the prototy pical parabolic uniformly rectifiable (P-UR) sets and this project is part of a larger program to characterize P-UR sets by properties of caloric fu nctions/measure.\n LOCATION:https://researchseminars.org/talk/OSGA/115/ END:VEVENT END:VCALENDAR