BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Magnus Botnan (Vrije Universiteit Amsterdam) DTSTART:20201113T091000Z DTEND:20201113T100000Z DTSTAMP:20260419T112036Z UID:icra2020/8 DESCRIPTION:Title: Quiver Representations in Topological Data Analysis III\nby Magnus Bo tnan (Vrije Universiteit Amsterdam) as part of ICRA 2020\n\n\nAbstract\nTh e goal of these three lectures is to highlight the role of quiver represen tations in the field of topological data analysis (TDA). Emphasis will be put on the interplay between the pure and applied. Familiarity with simpli cial (co-)homology will be assumed.\n\nLecture 1: Persistent homology in a single parameter\n\nPersistent homology is a central topic in the burgeon ing field of topological data analysis. The key idea is to study topologic al spaces constructed from data and infer the ‘‘shape’’ of the dat a from topological invariants. The term ‘’persistent’’ refers to t he fact that the construction of these spaces usually depends on one or mo re parameters\, and in order to obtain information about the data in a sta ble 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 pers istent homology in a single parameter\, introduce the necessary terminolog y\, and state foundational results.\n\nLecture 2: Multiparameter persisten t homology part 1\n\nMultiparameter persistent homology is a vibrant subfi eld of topological data analysis which has attracted much attention in rec ent years. It has become evident that the transition from a single to mult iple parameters comes with significant computational and mathematical chal lenges. At the level of representation theory\, this can be understood by the fact that one is studying representations of a partially ordered set o f wild representation type.\n\nIn this lecture we shall identify settings for which the theory in the first lecture generalizes to more general pose ts. Of particular interest is level-set zigzag persistent homology.\n\nLec ture 3: Multiparameter persistent homology part 2\n\nIn this lecture we wi ll consider models for constructing representations of posets for which mo st of the theory developed in the first lecture does not generalize in a r easonable way. However\, we shall see that we still can extract useful inv ariants for the purpose of data analysis. Our primary motivation will come from clustering (in the data-scientific sense).\n LOCATION:https://researchseminars.org/talk/icra2020/8/ END:VEVENT END:VCALENDAR