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SUMMARY:Atabey Kaygun (Istanbul Technical University)
DTSTART:20210405T103000Z
DTEND:20210405T113000Z
DTSTAMP:20260422T140031Z
UID:BilTop/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilTop/18/">
 From filtered complexes to matroids to cobordisms: an unlikely story in th
 ree parts</a>\nby Atabey Kaygun (Istanbul Technical University) as part of
  Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nOur stor
 y starts with a question in data analysis and computational topology/geome
 try. Given a finite sample of points from an unknown manifold embedded in 
 an affine space\, how can we extract information about topological invaria
 nts of the said manifold? Even though the answer is known for a long time\
 , the connections of the question with computational geometry and data ana
 lysis have only recently been made. We will review these connections\, and
  then move on to the "representation problem" of homology of filtered comp
 lexes. Specifically\, we will explain why "bar-codes" are enough for filte
 red complexes over reals\, but why there is no such hope for other seeming
 ly nice posets. Then we will talk about why matroids and cobordisms (of sp
 heres) might naturally provide us the necessary tools for devising a solut
 ion for this problem.\n
LOCATION:https://researchseminars.org/talk/BilTop/18/
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