BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Max Engelstein (University of Minnesota) DTSTART:20210119T170000Z DTEND:20210119T175000Z DTSTAMP:20260423T024839Z UID:anpdews/46 DESCRIPTION:Title: Lojasiewicz Inequalities and the Zero Sets of Harmonic Functions\nby Max Engelstein (University of Minnesota) as part of HA-GMT-PDE Seminar\n\n \nAbstract\nWhereas $C^\\infty$ functions can vanish (almost) arbitrarily often to arbitrarily high order (e\,g\, $f(x) = e^{-1/x}$ vanishes to infi nite order at zero)\, the zero sets of analytic functions have a lot more structure. For example\, you learn in intro to complex analysis that the z eroes of a Holomorphic function are isolated.\n\nThe Lojasiewicz inequalit ies (partially) quantify this extra structure possessed by analytic functi ons. Developed originally by algebraic geometers\, Lojasiewicz inequalitie s have been used with great success to study geometric flows. In this talk \, I will give a brief introduction to these inequalities and then discuss some joint work (and maybe some work in progress) with Matthew Badger (UC onn) and Tatiana Toro (U Washington)\, in which we use Lojasiewicz inequal ities to study the zero sets of harmonic functions and\, more interestingl y\, sets which are infinitesimally approximated by the zero sets of harmon ic functions.\n LOCATION:https://researchseminars.org/talk/anpdews/46/ END:VEVENT END:VCALENDAR