Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Sinn, Rainer"'
We study spurious second-order stationary points and local minima in a nonconvex low-rank formulation of sum-of-squares optimization on a real variety $X$. We reformulate the problem of finding a spurious local minimum in terms of syzygies of the und
Externí odkaz:
http://arxiv.org/abs/2411.02208
We study the Pythagoras numbers $py(3,2d)$ of real ternary forms, defined for each degree $2d$ as the minimal number $r$ such that every degree $2d$ ternary form which is a sum of squares can be written as the sum of at most $r$ squares of degree $d$
Externí odkaz:
http://arxiv.org/abs/2410.17123
We introduce tools for transferring nonnegativity certificates for global sections between line bundles on real algebraic surfaces. As applications, we improve Hilbert's degree bounds on sum-of-squares multipliers for nonnegative ternary forms, give
Externí odkaz:
http://arxiv.org/abs/2409.08834
Every polygon with n vertices in the complex projective plane is naturally associated with its adjoint curve of degree n-3. Hence the adjoint of a heptagon is a plane quartic. We prove that a general plane quartic is the adjoint of exactly 864 distin
Externí odkaz:
http://arxiv.org/abs/2408.15759
The cone of nonnegative polynomials is of fundamental importance in real algebraic geometry, but its facial structure is understood in very few cases. We initiate a systematic study of the facial structure of the cone of nonnegative polynomials $\pos
Externí odkaz:
http://arxiv.org/abs/2407.06017
Publikováno v:
Mathematica Scandinavica, 130(3), 433-466 (2024)
We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our main result states that tree amplituhedra in ${\rm Gr}(2,4)$ are pos
Externí odkaz:
http://arxiv.org/abs/2402.06527
Autor:
Sinn, Rainer, Ziegler, Günter M.
In his first mathematical paper, published in 1895 when he was 18, Edmund Landau suggested a new way to determine the winner of a chess tournament by not simply adding for each player the fixed number of points they would get for each win or draw, bu
Externí odkaz:
http://arxiv.org/abs/2210.17300
This is a case study of the algebraic boundary of convex hulls of varieties. We focus on surfaces in fourspace to showcase new geometric phenomena that neither curves nor hypersurfaces do. Our method is a detailed analysis of a general purpose formul
Externí odkaz:
http://arxiv.org/abs/2209.01151
We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we develop criteria for characterizing their positive part. We focus on the
Externí odkaz:
http://arxiv.org/abs/2205.14972
We study quasiconvex quadratic forms on $n \times m$ matrices which correspond to nonnegative biquadratic forms in $(n,m)$ variables. We disprove a conjecture stated by Harutyunyan--Milton (Comm. Pure Appl. Math. 70(11), 2017) as well as Harutyunyan-
Externí odkaz:
http://arxiv.org/abs/2204.10625