BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jurij Volčič (Texas A&M)
DTSTART:20201116T171500Z
DTEND:20201116T181500Z
DTSTAMP:20260423T021650Z
UID:GASC/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GASC/7/">Pos
 itive polynomials in matrix variables</a>\nby Jurij Volčič (Texas A&M) a
 s part of Geometry\, Algebra\, Singularities\, and Combinatorics\n\n\nAbst
 ract\nHilbert's 17th problem asked whether every positive polynomial can b
 e\nwritten as a quotient of sums of squares of polynomials. As many others
 \non Hilbert's famous list\, this problem and its affirmative resolution b
 y\nEmil Artin started a thriving mathematical discipline\, known as real\n
 algebraic geometry. At its core\, it studies the interplay between\npolyno
 mial inequalities and positivity (geometry) and sums of squares\ncertifyin
 g such positivity (algebra). Apart from its pure mathematics\nappeal\, thi
 s theory is the pillar of polynomial optimization\, since sums\nof squares
  can be efficiently traced via semidefinite programming.\n\nThis talk revi
 ews old and new results on positivity of noncommutative\npolynomials and t
 heir traces\, in terms of their matrix evaluations.\nThere are two natural
  setups to consider: positivity in matrix variables\nof a given fixed size
 \, and positivity in matrix variables of arbitrary\nsize. This talk compar
 es the sums-of-squares certificates of positivity\nacross these two setups
 \, their shortcomings and open ends.\n
LOCATION:https://researchseminars.org/talk/GASC/7/
END:VEVENT
END:VCALENDAR