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SUMMARY:Cole Jeznach (University of Minnesota)
DTSTART:20210510T160000Z
DTEND:20210510T165000Z
DTSTAMP:20260423T010012Z
UID:anpdews/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/61/"
 >Regularized Distances and Geometry of Measures</a>\nby Cole Jeznach (Univ
 ersity of Minnesota) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nI will p
 resent joint work with Max Engelstein and Svitlana Mayboroda where we gene
 ralize the notion of the regularized distance function \n$$\nD_{\\mu\,\\al
 pha}(x)= \\left(\\int |x-y|^{d-\\alpha}\\\, d\\mu(y)\\right)^{1/\\alpha}\,
 \n$$\n \n\nto functions with more general integrands. We provide a large c
 lass of integrands for which the corresponding distance functions contain 
 geometric information about $\\mu$. In particular\, we produce examples th
 at are in some sense far from the original kernel $|x-y|^{d-\\alpha}$ but 
 still characterize the geometry of $\\mu$  since they have nice symmetries
  with respect to flat sets. In co-dimension 1\, these examples are explici
 t\, but in higher co-dimensions\, our proof of existence of such examples 
 is non-constructive\, and thus we have no additional information about the
 ir structure.\n
LOCATION:https://researchseminars.org/talk/anpdews/61/
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