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SUMMARY:Giorgio Ottaviani (Università di Firenze)
DTSTART:20201112T140000Z
DTEND:20201112T150000Z
DTSTAMP:20260423T024507Z
UID:GeoSem/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GeoSem/10/">
 Singular t-ples of tensors and their geometry</a>\nby Giorgio Ottaviani (U
 niversità di Firenze) as part of Geometry Seminar - University of Florenc
 e\n\n\nAbstract\nThere is a natural invariant metric on the space of tenso
 rs\, called Frobenius metric. In optimization setting one considers the (c
 omplex) critical points on the Segre variety of the distance function from
  a given tensor\, they are called singular t-ples\, among them there is th
 e best rank one approximation. Their number is the EDdegree of the Segre v
 ariety. The geometry of the critical points is appealing\, since they lie 
 in a linear space called critical space\, which has dimension smaller than
  the number of critical points\, in other words the critical points are li
 nearly dependent\, unless the matrix case. We expose some properties of si
 ngular t-ples. In a following talk Emanuele Ventura will lecture about the
  asymptotic behaviour of EDdegree and other more advanced properties.\n\nA
 pplied Algebraic Geometry 2020-2021:\nhttp://web.math.unifi.it/gruppi/alge
 braic-geometry/AppliedAlgebraicGeometry20202021.html\n
LOCATION:https://researchseminars.org/talk/GeoSem/10/
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