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Rouquier dimension is Krull dimension for normal toric varieties
We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull...
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Filtered deformations of commutative algebras of Krull dimension two
Let F be an algebraically closed field of positive characteristic and let R be a finitely generated F -algebra with a filtration with the property...
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Dimension-free bounds and structural results in communication complexity
The purpose of this article is to initiate a systematic study of dimension-free relations between basic communication and query complexity measures...
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The numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension
We prove the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, and also in some related cases.
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Boundary Feedback Controller over a Bluff Body for Prescribed Drag and Lift Coefficients
This chapter presents an improved boundary feedback controller for the two- and three-dimensional Navier–Stokes equations, in a bounded domain Ω, for...
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Examples of Ricci limit spaces with non-integer Hausdorff dimension
We give the first examples of collapsing Ricci limit spaces on which the Hausdorff dimension of the singular set exceeds that of the regular set;...
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Stable homotopy groups of spheres: from dimension 0 to 90
Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic...
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On the Singularities of Complete Holomorphic Vector Fields in Dimension Two
For a germ of singular holomorphic vector field on a complex manifold to be the local model of a complete one, it is necessary for its solutions to...
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Approximate subgroups with bounded VC-dimension
We combine the fundamental results of Breuillard, Green, and Tao (Publ Math Inst Hautes Études Sci 116:115–221,
2012 ) on the structure of approximate... -
On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions
We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of...
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Dimension Theory in Iterated Local Skew Power Series Rings
Many well-known local rings, including soluble Iwasawa algebras and certain completed quantum algebras, arise naturally as iterated skew power series...
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Calibrations for the Volume of Unit Vector Fields in Dimension 2
We use the theory of calibrations to write an equation of a minimal volume vector field on a given Riemann surface.
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A combinatorial cut-and-lift procedure with an application to 0–1 second-order conic programming
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new...
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On the dimension of the algebras of local infinitesimal isometries of 3-dimensional special sub-Riemannian manifolds
Suppose that we are given a contact sub-Riemannian manifold ( M , H , g ) of dimension 3 such that the Reeb vector field is an infinitesimal isometry...