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SUMMARY:Magnus Botnan (Vrije Universiteit Amsterdam)
DTSTART:20201110T091000Z
DTEND:20201110T100000Z
DTSTAMP:20260419T112030Z
UID:icra2020/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/icra2020/4/"
 >Quiver Representations in Topological Data Analysis I</a>\nby Magnus Botn
 an (Vrije Universiteit Amsterdam) as part of ICRA 2020\n\n\nAbstract\nThe 
 goal of these three lectures is to highlight the role of quiver representa
 tions in the field of topological data analysis (TDA). Emphasis will be pu
 t on the interplay between the pure and applied. Familiarity with simplici
 al (co-)homology will be assumed.\n\nLecture 1: Persistent homology in a s
 ingle parameter\n\nPersistent homology is a central topic in the burgeonin
 g field of topological data analysis. The key idea is to study topological
  spaces constructed from data and infer the ‘‘shape’’ of the data 
 from topological invariants. The term ‘’persistent’’ refers to the
  fact that the construction of these spaces usually depends on one or more
  parameters\, and in order to obtain information about the data in a stabl
 e and robust way\, it is crucial to consider how the family of resulting i
 nvariants relate across scales. This naturally leads to a representation o
 f a totally ordered set.\n\nIn this first lecture I will motivative persis
 tent homology in a single parameter\, introduce the necessary terminology\
 , and state foundational results.\n\nLecture 2: Multiparameter persistent 
 homology part 1\n\nMultiparameter persistent homology is a vibrant subfiel
 d of topological data analysis which has attracted much attention in recen
 t years. It has become evident that the transition from a single to multip
 le parameters comes with significant computational and mathematical challe
 nges. At the level of representation theory\, this can be understood by th
 e fact that one is studying representations of a partially ordered set of 
 wild representation type.\n\nIn this lecture we shall identify settings fo
 r which the theory in the first lecture generalizes to more general posets
 . Of particular interest is level-set zigzag persistent homology.\n\nLectu
 re 3: Multiparameter persistent homology part 2\n\nIn this lecture we will
  consider models for constructing representations of posets for which most
  of the theory developed in the first lecture does not generalize in a rea
 sonable way. However\, we shall see that we still can extract useful invar
 iants for the purpose of data analysis. Our primary motivation will come f
 rom clustering (in the data-scientific sense).\n
LOCATION:https://researchseminars.org/talk/icra2020/4/
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