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UID:6419b3301c3b602e6aee7f4ba3aef810
CATEGORIES:Topology/Geometry Seminar
CREATED:20250210T093517
SUMMARY:Gromov-like distances between spheres
LOCATION:Hill 705
DESCRIPTION:Notions of distances between metric (measure) spaces such as the Gromov-Hau
 sdorff distance and its Optimal Transport variants are nowadays often invok
 ed in applications related to data classification. Interestingly, the preci
 se value of these distances on pairs of canonical shapes is known only in v
 ery limited cases. In this talk, I will describe lower bounds for the Gromo
 v-Hausdorff distance between spheres (endowed with their geodesic distances
 ) which we prove to be tight in some cases via the construction of optimal 
 correspondences.  These lower bounds arise from applying a certain version 
 of the Borsuk-Ulam theorem for discontinuous functions. \n
X-ALT-DESC;FMTTYPE=text/html:<p>Notions of distances between metric (measure) spaces such as the Gromov-
 Hausdorff&nbsp;distance and its Optimal Transport variants are nowadays oft
 en invoked in applications related to data classification. Interestingly, t
 he precise value of these distances&nbsp;on pairs of canonical shapes is kn
 own only in very limited cases. In this talk, I will describe lower bounds 
 for the Gromov-Hausdorff&nbsp;distance between spheres&nbsp;(endowed with t
 heir geodesic distances) which we prove to be tight in some cases via the c
 onstruction of optimal correspondences.&nbsp; These lower bounds arise&nbsp
 ;from&nbsp;applying a certain version of the Borsuk-Ulam theorem for discon
 tinuous functions.&nbsp;</p>
CONTACT:Facundo Memoli Techera, Rutgers
DTSTAMP:20260829T062137
DTSTART;TZID=America/New_York:20250225T160000
DTEND;TZID=America/New_York:20250225T170000
SEQUENCE:0
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