1 citations · 2 across the 14 of their papers we have counts for
21 papers
ON THE DISTANCE TO DISCRIMINANTS AND OSCULATING VARIETIES
Khazhgali Kozhasov, Bernard Mourrain, Adam Parusi{ń}ski
We study the problem of finding the closest singular hypersurface to a given nonsingular one from algebro-geometric point of view. The set of singular hypersurfaces of a given…
Stubborn Polynomials
Lorenzo Baldi, Grigoriy Blekherman, Khazhgali Kozhasov +3
The relationship between nonnegative polynomials and sums of squares is a classical topic in real algebraic geometry. We study \emph{stubborn polynomials} on a real variety …
Certificates for nonnegativity of multivariate integer polynomials under perturbations
Matías R Bender, Khazhgali Kozhasov, Elias Tsigaridas +1
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their…
On odd powers of nonnegative polynomials that are not sums of squares
Grigoriy Blekherman, Khazhgali Kozhasov, Bruce Reznick
We initiate a systematic study of nonnegative polynomials such that is not a sum of squares for any odd , calling such \emph{stubborn}. We develop a new inva…
On the minimal algebraic complexity of the rank-one approximation problem for general inner products
Khazhgali Kozhasov, Alan Muniz, Yang Qi +1
We study the algebraic complexity of Euclidean distance minimization from a generic tensor to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Verones…
Non-negative forms, volumes of sublevel sets, complete monotonicity and moment matrices
Khazhgali Kozhasov, Jean B. Lasserre
Let be the convex cone consisting of real -variate degree forms that are strictly positive on . We prove that the L…
Probabilistic bounds on best rank-one approximation ratio
Khazhgali Kozhasov, Josué Tonelli-Cueto
We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors…
On eigenvalues of symmetric matrices with PSD principal submatrices
Khazhgali Kozhasov
We investigate convexity properties of the set of eigenvalue tuples of real symmetric matrices, whose all (where is fixed) minors are positive sem…
Nodes on quintic spectrahedra
Taylor Brysiewicz, Khazhgali Kozhasov, Mario Kummer
We classify transversal quintic spectrahedra by the location of 20 nodes on the respective real determinantal surface of degree 5. We identify 65 classes of such surfaces and find…
Minimality of tensors of fixed multilinear rank
Alexander Heaton, Khazhgali Kozhasov, Lorenzo Venturello
We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of fixed multilinear rank form a minimal submanif…
Rational functions with only real periodic points
Khazhgali Kozhasov, Mario Kummer
We study self-morphisms of smooth real projective algebraic curves that have only real periodic points. In the case of the projective line we provide a convenient characterization…
On minimality of determinantal varieties
Khazhgali Kozhasov
We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribe…
Nonnegative forms with sublevel sets of minimal volume
Khazhgali Kozhasov, Jean-Bernard Lasserre
We show that the Euclidean ball has the smallest volume among sublevel sets of nonnegative forms of bounded Bombieri norm as well as among sublevel sets of sum of squares forms who…
Positivity Certificates via Integral Representations
Khazhgali Kozhasov, Mateusz Michałek, Bernd Sturmfels
Complete monotonicity is a strong positivity property for real-valued functions on convex cones. It is certified by the kernel of the inverse Laplace transform. We study this for n…
Chebyshev polynomials and best rank-one approximation ratio
Andrei Agrachev, Khazhgali Kozhasov, André Uschmajew
We establish a new extremal property of the classical Chebyshev polynomials in the context of best rank-one approximation of tensors. We also give some necessary conditions for a t…
On the geometry of the set of symmetric matrices with repeated eigenvalues
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
We investigate some geometric properties of the real algebraic variety of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection wit…
The real polynomial eigenvalue problem is well conditioned on the average
Carlos Beltran, Khazhgali Kozhasov
We study the average condition number for polynomial eigenvalues of collections of matrices drawn from various random matrix ensembles. In particular, we prove that polynomial eige…
Random spectrahedra
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
Spectrahedra are affine-linear sections of the cone of positive semidefinite symmetric -matrices. We consider random spectrahedra that are obtained by in…
On fully real eigenconfigurations of tensors
Khazhgali Kozhasov
We construct generic real symmetric tensors with only real eigenvectors or, equivalently, real homogeneous polynomials with the maximum possible finite number of critical points on…
On the number of flats tangent to convex hypersurfaces in random position
Khazhgali Kozhasov, Antonio Lerario
We investigate the problem of the number of flats simultaneously tangent to several convex hypersurfaces in real projective space from a random point of view. More precisely, we sa…
Geometric flow of -structures on
Khazhgali Kozhasov
We introduce a first order flow of -structures and construct its explicit solution in case of a cone over . Also we prove for this situation that starting…