2 citations · 3 across the 3 of their papers we have counts for
5 papers
Weak and Strong Extremal Biquadratics
Grigoriy Blekherman, Bogdan Raiţă, Isabelle Shankar +1
We study quasiconvex quadratic forms on matrices which correspond to nonnegative biquadratic forms in variables. We disprove a conjecture stated by Harutyunyan…
Intersection Bodies of Polytopes
Katalin Berlow, Marie-Charlotte Brandenburg, Chiara Meroni +1
We investigate the intersection body of a convex polytope using tools from combinatorics and real algebraic geometry. In particular, we show that the intersection body of a polytop…
The degree of the central curve in semidefinite, linear, and quadratic programming
Serkan Hoşten, Isabelle Shankar, Angélica Torres
The Zariski closure of the central path which interior point algorithms track in convex optimization problems such as linear, quadratic, and semidefinite programs is an algebraic c…
Symmetry Adapted Gram Spectrahedra
Alexander Heaton, Serkan Hoşten, Isabelle Shankar
This paper explores the geometric structure of the spectrahedral cone, called the symmetry adapted PSD cone, and the symmetry adapted Gram spectrahedron of a symmetric polynomial.…
An SOS counterexample to an inequality of symmetric functions
Alexander Heaton, Isabelle Shankar
It is known that differences of symmetric functions corresponding to various bases are nonnegative on the nonnegative orthant exactly when the partitions defining them are comparab…