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UID:5dfa04553409b732765736@ist.ac.at
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DESCRIPTION:Speaker: Tamas Titkos\nhosted by Laszlo Erdös / Dániel Virosz
 tek\nAbstract: Due to its nice theoretical properties and an astonishing n
 umber of applications via optimal transport problems\, probably the most i
 ntensively studied metric nowadays is the p-Wasserstein metric.  Given a 
 complete and separable metric space X and a real number p belonging to [1\
 ,∞)\, one defines the p-Wassersteinspace W_p(X) as the collection of Bor
 el probability measures with finite p-th moment\, endowed with a distance 
 which is calculated by means of transport plans. The main aim of our resea
 rch project is to reveal the structure of the isometry group Isom(W_p(X)).
  Although  Isom(X) embeds naturally into Isom(W_p(X)) by push-forward\, a
 nd this embedding turned out to be surjective in many cases (see e.g. [1])
 \, these two groups are not isomorphic in general. Kloeckner computed in [
 2] the isometry group of the quadratic Wasserstein space over the real lin
 e. It turned out that this group is extremely rich: it contains a flow of 
 wild behaving isometries that distort the shape of measures. Following thi
 s line of investigation\, we computed Isom(W_p(R)) and Isom(W_p([0\,1]) fo
 r all p in [1\,∞). In this talk\, I will survey first some of the earlie
 r results in the subject\, and then I will present the key results of our 
 recent manuscript [3]. Joint work with György Pál Gehér (University of 
 Reading) and Dániel Virosztek (IST Austria).[1] J. Bertrand and B. Kloeck
 ner\,  A geometric study of Wasserstein spaces: isometric rigidity in neg
 ative curvature\, International Mathematics Research Notices\, 2016 (5)\, 
 1368-1386.[2] B. Kloeckner\,  A geometric study of Wasserstein spaces: Eu
 clidean spaces\, Annali della Scuola Normale Superiore di Pisa - Classe di
  Scienze\, Serie 5\, Tome 9 (2010) no.  2\, 297-323.[3] Gy.  P. Gehér\,
  T. Titkos\, D. Virosztek\, Isometric study of Wasserstein spaces – the 
 real line\, accepted for publication in Trans. Amer. Math. Soc. Available 
 at https://research-explorer.app.ist.ac.at/record/7389 
LOCATION:Heinzel Seminar Room / Office Bldg West (I21.EG.101)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Tamas Titkos: Isometries of Wasserstein spaces
URL:https://talks-calendar.ista.ac.at/events/2456
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