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SUMMARY:Antonio Rieser (CIMAT - Mexico)
DTSTART:20211119T160000Z
DTEND:20211119T170000Z
DTSTAMP:20260423T022927Z
UID:GEOTOP-A/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/8/"
 >Applied topology from the classical point of view</a>\nby Antonio Rieser 
 (CIMAT - Mexico) as part of GEOTOP-A seminar\n\n\nAbstract\nWe generalize 
 several basic notions in algebraic topology to categories which contain bo
 th topological spaces classically treated by classical homotopy theory as 
 well as more discrete and combinatorial spaces of interest in applications
 \, such as graphs and point clouds. The advantage of doing so is that ther
 e are now non-trivial 'continuous' maps from paracompact Hausdorff spaces 
 to finite spaces (given the appropriate structure)\, and one may then comp
 are the resulting topological invariants on each side functorially. We fin
 d that there are a number of possible such categories\, each with its own 
 particular homotopy theory and associated homologies\, and\, additionally\
 , that there is a generalization of the coarse category which allows finit
 e sets to be non-trivial (i.e. not 'coarsely' equivalent to a point). We w
 ill give an overview of these theories and several applications\, show how
  they are related to familiar objects in applied topology\, such as the Vi
 etoris-Rips homology\, and discuss the advantages and disadvantages of eac
 h. We finish by describing a recent construction of sheaf theory in the ca
 tegory of Cech closure spaces\, a strict generalization of the category of
  topological spaces.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/8/
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