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DTSTAMP:20260105T145425
DTSTART;TZID=America/Detroit:20260123T143000
DTEND;TZID=America/Detroit:20260123T153000
SUMMARY:Workshop / Seminar:A reflection principle for nonintersecting paths and lozenge tilings with free boundaries (Combinatorics seminar)
DESCRIPTION:Okada and Stembridge's Pfaffian formula for the enumeration of families of nonintersecting paths with fixed starting points and unfixed ending points has been widely used to resolve many challenging problems in enumerative combinatorics. In this talk\, we present a new formula that complements Okada and Stembridge's Pfaffian formula. The combinatorial interpretation of the new formula gives a reflection principle for nonintersecting paths. It implies that the enumeration of families of nonintersecting paths with unfixed ending points can be resolved by enumerating families of nonintersecting paths with fixed ending points instead. Using this formula\, we also show that the enumeration of lozenge tilings of a large family of regions with free boundaries can be deduced from those without free boundaries and present several applications of this result.
UID:139210-21885089@events.umich.edu
URL:https://events.umich.edu/event/139210
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 3866
CONTACT:
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DTSTAMP:20260113T104609
DTSTART;TZID=America/Detroit:20260123T150000
DTEND;TZID=America/Detroit:20260123T160000
SUMMARY:Lecture / Discussion:AIM Seminar:  Relativistic Initial Data Sets with Prescribed Asymptotics
DESCRIPTION:Abstract:  In General Relativity\, Einstein's equation may be viewed as a second-order system of nonlinear PDE's for the Lorentzian metric on (n+1)-dimensional spacetime that admits an initial value formulation. The required initial data is comprised of a (usually complete) n-dimensional Riemannian manifold equipped with a symmetric (0\,2)-tensor\, respectively representing a spatially global \"instant in time\" and the \"initial velocity\" of the metric. The Gauss-Codazzi equations imply that not every such pair is admissible\, however\, and a working initial data set must satisfy certain nonlinear elliptic PDE’s dubbed the constraint equations. In this talk\, I will discuss recent work with several collaborators on the construction of working asymptotically flat initial data sets in which various asymptotic features of physical interest can be prescribed.\n\nContact:  AIM Seminar Organizers
UID:141894-21889609@events.umich.edu
URL:https://events.umich.edu/event/141894
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1084
CONTACT:
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