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SUMMARY:Davit Harutyunyan (University of California Santa Barbara)
DTSTART:20220218T150000Z
DTEND:20220218T160000Z
DTSTAMP:20260423T021215Z
UID:YMC/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/YMC/31/">On 
 the extreme rays of the cone of 3 times 3 quasiconvex quadratic forms: Ext
 remal determinants vs extremal and polyconvex forms.</a>\nby Davit Harutyu
 nyan (University of California Santa Barbara) as part of Yerevan Mathemati
 cal Colloquium\n\n\nAbstract\nQuasiconvexity is a central notion in the Ca
 lculus of Variations and is tied with lower-semicontinuity and existence o
 f minimizers of integral functionals. This talk is concerned with characte
 rization of all 3 by 3 quasiconvex quadratic forms. The problem has a long
  story and arises naturally in several questions in Materials Science. We 
 study the extreme rays of the convex cone of 3 by 3 quasiconvex quadratic 
 forms by providing a link between the extremality of a form and the extrem
 ality of its acoustic tensor determinant. The problem is also closely rela
 ted to the problem of "Sums of Squares" in Real Algebraic Geometry\, where
  in the language of positive biquadratic forms\, quasiconvex quadratic for
 ms correspond to nonnegative biquadratic forms. Our results recover all pr
 eviously known results (to our best knowledge) on examples of extreme rays
  of the cone. The proofs are all established by means of several classical
  results from Linear Algebra\, Convex Geometry\, Real Algebraic Geometry\,
  and the Calculus of Variations.\n\nThis is joint work with Narek Hovsepya
 n\n\nThe talk will be chaired by Hayk Mikayelyan (Univ. Nottingham Ningbo\
 , China)\n
LOCATION:https://researchseminars.org/talk/YMC/31/
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