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SUMMARY:Magnus Botnan (Vrije Universiteit Amsterdam)
DTSTART:20201111T091000Z
DTEND:20201111T100000Z
DTSTAMP:20260419T112039Z
UID:icra2020/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/icra2020/6/"
 >Quiver Representations in Topological Data Analysis II</a>\nby Magnus Bot
 nan (Vrije Universiteit Amsterdam) as part of ICRA 2020\n\n\nAbstract\nThe
  goal of these three lectures is to highlight the role of quiver represent
 ations in the field of topological data analysis (TDA). Emphasis will be p
 ut on the interplay between the pure and applied. Familiarity with simplic
 ial (co-)homology will be assumed.\n\nLecture 1: Persistent homology in a 
 single parameter\n\nPersistent homology is a central topic in the burgeoni
 ng field of topological data analysis. The key idea is to study topologica
 l spaces constructed from data and infer the ‘‘shape’’ of the data
  from topological invariants. The term ‘’persistent’’ refers to th
 e fact that the construction of these spaces usually depends on one or mor
 e parameters\, and in order to obtain information about the data in a stab
 le and robust way\, it is crucial to consider how the family of resulting 
 invariants relate across scales. This naturally leads to a representation 
 of a totally ordered set.\n\nIn this first lecture I will motivative persi
 stent 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 subfie
 ld of topological data analysis which has attracted much attention in rece
 nt years. It has become evident that the transition from a single to multi
 ple parameters comes with significant computational and mathematical chall
 enges. At the level of representation theory\, this can be understood by t
 he fact that one is studying representations of a partially ordered set of
  wild representation type.\n\nIn this lecture we shall identify settings f
 or which the theory in the first lecture generalizes to more general poset
 s. Of particular interest is level-set zigzag persistent homology.\n\nLect
 ure 3: Multiparameter persistent homology part 2\n\nIn this lecture we wil
 l consider models for constructing representations of posets for which mos
 t of the theory developed in the first lecture does not generalize in a re
 asonable way. However\, we shall see that we still can extract useful inva
 riants for the purpose of data analysis. Our primary motivation will come 
 from clustering (in the data-scientific sense).\n
LOCATION:https://researchseminars.org/talk/icra2020/6/
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