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Automatic Generation of Explicit Quadratic Programming Solvers
Maximilian Schaller, Daniel Arnstr\"om, Alberto Bemporad, Stephen Boyd
https://arxiv.org/abs/2506.11513

Automatic Generation of Explicit Quadratic Programming Solvers
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a so…

K3 surfaces over small number fields and Kummer constructions in families
Stefan Schr\"oer
https://arxiv.org/abs/2506.14732 https://

K3 surfaces over small number fields and Kummer constructions in families
We construct K3 surfaces over number fields that have good reduction everywhere. These do not exists over the rational numbers, by results of Abrashkin and Fontaine. Our surfaces exist for three quadratic number fields, and an infinite family of $S_3$-number fields. To this end we develop a theory of Kummer constructions in families, based on Romagny's notion of the effective models, here applied to sign involutions. This includes quotients of non-normal surfaces by infinitesimal group schemes …

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This https://arxiv.org/abs/2503.13965 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

First-Order Projected Algorithms With the Same Linear Convergence Rate Bounds as Their Unconstrained Counterparts
In this paper, we propose a systematic approach for constructing first-order projected algorithms for optimization problems with general set constraints, building upon their unconstrained counterparts. We show that these projected algorithms retain the same linear convergence rate bounds, when the latter are obtained for the unconstrained algorithms via quadratic Lyapunov functions arising from integral quadratic constraint (IQC) characterizations. The projected algorithms are constructed by ap…

Spin-dependent transport through edge states in 2D semi-Dirac materials with Rashba spin-orbit coupling and band inversion
Marta Garc\'ia-Olmos, Yuriko Baba, Alexander L\'opez, Mario Amado, Rafael A. Molina
https://arxiv.org/abs/2505.24745

Spin-dependent transport through edge states in 2D semi-Dirac materials with Rashba spin-orbit coupling and band inversion
We investigate the bulk-boundary correspondence in two-dimensional type-I semi-Dirac materials with band inversion and Rashba spin-orbit coupling. Employing a dimensional reduction framework, we identify the Zak phase along the quadratically dispersing direction as a topological invariant that captures the presence of edge states. In the non-trivial topological regime, systems with finite width exhibit energy-dependent edge states that are topologically protected only at specific momenta. At kx…

This https://arxiv.org/abs/2210.04851 has been replaced.
link: https://scholar.google.com/scholar?q=a

Pfister's local-global principle for Azumaya algebras with involution
We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion. Our proof relies on a hermitian version of Sylvester's law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms.