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DTSTART:20260329T030000
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UID:1779195600@ist.ac.at
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DESCRIPTION:Speaker: Nati Linial\nhosted by Matthew Kwan and Uli Wagner\nAb
 stract: Abstract: Let X=[n] be a finite set of points. An (x\,y)-path 
 is a sequence of distinct points that starts with x and ends with y. A 
 path system Π on X is a collection of paths with exactly one (x\,y)-
 path for every two distinct points x\,y∈X. Think of this path Px\,y a
 s the chosen path between these two points. We always assume that Py\,x 
 coincides with Px\,y read in reverse. We say that the path system Π i
 s consistent if the following holds: For every point z on the path Px\,
 y\, this path is the concatenation of the paths Px\,z and Pz\,y. It is 
 easy to construct metric consistent path systems: Assign a positive distan
 ce w(u\,v) with every pair of points u\,v∈X and let Px\,y be a w-
 shortest (x\,y) path Q\; Is every consistent path system necessarily me
 tric? The answer is negative and we give various quantitative manifestatio
 ns of this statement. Skipping the necessary definitions we ask if every c
 onsistent path system is approximately metric. A: there exist consistent p
 ath systems with metric distortion Ω(√n). The best result of this form
  is still unknown. I will briefly survey some of the many results that we 
 already have in this general domain. Every path system gives rise to a gra
 ph (X\,E) where xy is an edge whenever the path Px\,y=x\,y. Indeed\, 
 many of our results are graph-theoretic. All the papers in this domain are
  joint with my student Daniel Cizma\, some are also with Maria Chudnovsky\
 , if time allows I will also mention a recent result with my students Itai
  Goldflam.
LOCATION:Raiffeisen Lecture Hall\, Central Building\, ISTA
ORGANIZER:Stephanie.Dolot@ist.ac.at
SUMMARY:Nati Linial: Path Geometry
URL:https://talks-calendar.ista.ac.at/events/6468
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