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SUMMARY:Hadamard ranks of algebraic varieties
DTSTART:20261001T120000Z
DTEND:20261001T140000Z
DTSTAMP:20261011T094000Z
UID:indico-event-17003@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alessandro Oneto (Università di Genova)\n\nThe addi
 tive notion of rank with respect of an embedded algebraic variety is a cla
 ssical notion that employs the language of secant varieties to give a gene
 ral framework for matrix rank\, tensor rank\, and other similar notions. I
 n the last decade\, motivated by the study of particular algebraic statist
 ical models called Restricted Boltzmann Machines\, it has been introduced 
 the notion of Hadamard product of two algebraic varieties\, namely\, the Z
 ariski closure of the coordinate-wise product of all possible pairs of poi
 nts in the Cartesian product. This definition can be used to construct Had
 amard powers of algebraic varieties and define Hadamard ranks\, which can 
 be regarded as a multiplicative version of secant varieties and the classi
 cal notion of rank. The multiplicative nature of the construction allows m
 ethods from tropical geometry to be successfully applied to these problems
 . In this talk\, I will introduce these notions and present recent results
  and open problems. This is based on joint works with Dario Antolini\, Edo
 ardo Ballico\, Guido Montufar and Nick Vannieuwenhoven.\n\nhttps://indico.
 math.cnrs.fr/event/17003/
URL:https://indico.math.cnrs.fr/event/17003/
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