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UID:DSC-22959
DTSTART;TZID=Europe/Berlin:20260615T100000
SEQUENCE:1780983509
TRANSP:OPAQUE
DTEND;TZID=Europe/Berlin:20260615T120000
URL:https://www.dresden-science-calendar.de/calendar/en/detail/22959
LOCATION:MPI-CBG\, Pfotenhauerstraße 10801307 Dresden
SUMMARY:Melczer: P-Recursive Positivity and Numeric Analytic Continuation: 
 An Application to the Uniqueness of Biomembranes
CLASS:PUBLIC
DESCRIPTION:Speaker: Stephen Melczer\nInstitute of Speaker: University of W
 aterloo\nTopics:\n\n Location:\n  Name: MPI-CBG (MPI-CBG CSBD SR Top Floor
  (VC))\n  Street: Pfotenhauerstraße 108\n  City: 01307 Dresden\n  Phone: 
 +49 351 210-0\n  Fax: +49 351 210-2000\nDescription: Since the invention o
 f the compound microscope in the early seventeenth century\, scientists ha
 ve marvelled over red blood cells and their surprising shape. An influenti
 al model of Canham predicts the shapes of blood cells and similar biomembr
 anes come from a variational problem minimizing the “bending energy” o
 f these surfaces. Because observed cells have the same shape in humans\, i
 t is natural to ask whether the model admits a unique solution. Yu and Che
 n reduced solution uniqueness for the genus one Canham problem (for a rang
 e of isoperimetric ratios) to proving positivity of a P-recursive sequence
  defined by an explicit linear recurrence relation with polynomial coeffic
 ients. In this talk we discuss a method of proving this positivity propert
 y\, joint with Marc Mezzarobba\, and its generalization\, with Mezzarobba 
 and Ruiwen Dong\, to a wide range of P-recursive sequences. We combine rig
 orous numeric analytic continuation of D-finite functions with classic bou
 nds from singularity analysis to derive an effective index where the asymp
 totic behaviour of the sequence\, which is positive\, dominates the sequen
 ce behaviour. Positivity of the finite number of remaining terms can then 
 be checked computationally. Our work has been incorporated into the SageMa
 th ore_algebra package\, and can be used by researchers to automatically p
 rove positivity for “generic” positive P-recursive sequences.
DTSTAMP:20260609T202547Z
CREATED:20260604T053747Z
LAST-MODIFIED:20260609T053829Z
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