BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//TYPO3/NONSGML Calendarize//EN
BEGIN:VEVENT
UID:calendarize-the-wonderful-geometry-of-the-vandermonde-map-symmetry-at-
infinity-and-applications
DTSTAMP:20241107T162141Z
DTSTART:20231214T160000Z
DTEND:20231213T230000Z
SUMMARY: The wonderful geometry of the Vandermonde map: Symmetry at infi
nity and applications. Prof. Dr. Cordian Riener
DESCRIPTION:The Vandermonde map is given by $d$ power sum polynomials in $
n$ variables. We study in detail the image of the probability simplex $\\D
elta_n$ under this map. We will see that this image possesses a combinator
ial structure resembling a cyclic polytope. After analyzing the image in f
initely many variables\, we concentrate on the limit as the number of vari
ables approaches infinity. We explain how the geometry of the limit plays
a crucial role in undecidability results in nonnegativity of symmetric pol
ynomials\, deciding validity of trace inequalities in linear algebra\, and
extremal combinatorics.
X-ALT-DESC;FMTTYPE=text/html:The Vandermonde map is given by $d$ power
sum polynomials in $n$ variables. We study in detail the image of the prob
ability simplex $\\Delta_n$ under this map. We will see that this image po
ssesses a combinatorial structure resembling a cyclic polytope. After anal
yzing the image in finitely many variables\, we concentrate on the limit a
s the number of variables approaches infinity. We explain how the geometry
of the limit plays a crucial role in undecidability results in nonnegativ
ity of symmetric polynomials\, deciding validity of trace inequalities in
linear algebra\, and extremal combinatorics.

LOCATION:G201
END:VEVENT
END:VCALENDAR