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作者：Sato, Yasuhiko; White, Stuart; Winter, Wilhelm
作者单位：Kyoto University; University of Glasgow; University of Munster
摘要：Simple, separable, unital, monotracial and nuclear C*-algebras are shown to have finite nuclear dimension whenever they absorb the Jiang-Su algebra Z tensorially. This completes the proof of the Toms-Winter conjecture in the unique trace case. The structure theory of simple nuclear C*-algebras is currently undergoing revolutionary progress, driven by the discovery of regularity properties of various flavours: topological, functional analytic and algebraic. Despite the diverse nature of these r...
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作者：Hsu, Tim; Wise, Daniel T.
作者单位：California State University System; San Jose State University; McGill University
摘要：Let be a group splitting as a graph of groups where each vertex group acts properly on a CAT(0) cube complex. When is hyperbolic relative to virtually abelian subgroups, we examine conditions producing a proper action of on a CAT(0) cube complex. When is hyperbolic this action is also cocompact.
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作者：Pera, Keerthi Madapusi
作者单位：Harvard University
摘要：We show that the classical Kuga-Satake construction gives rise, away from characteristic , to an open immersion from the moduli of primitively polarized K3 surfaces (of any fixed degree) to a certain regular integral model for a Shimura variety of orthogonal type. This allows us to attach to every polarized K3 surface in odd characteristic an abelian variety such that divisors on the surface can be identified with certain endomorphisms of the attached abelian variety. In turn, this reduces the...
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作者：Matheus, Carlos; Moeller, Martin; Yoccoz, Jean-Christophe
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Goethe University Frankfurt; Universite PSL; College de France
摘要：We present a Galois-theoretical criterion for the simplicity of the Lyapunov spectrum of the Kontsevich-Zorich cocycle over the Teichmuller flow on the -orbit of a square-tiled surface. The simplicity of the Lyapunov spectrum has been proved by A. Avila and M. Viana with respect to the so-called Masur-Veech measures associated to connected components of moduli spaces of translation surfaces, but is not always true for square-tiled surfaces of genus . We apply our criterion to square-tiled surf...
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作者：Cristofaro-Gardiner, Daniel; Hutchings, Michael; Ramos, Vinicius Gripp Barros
作者单位：Institute for Advanced Study - USA; University of California System; University of California Berkeley; Nantes Universite
摘要：In a previous paper, the second author used embedded contact homology (ECH) of contact three-manifolds to define ECH capacities of four-dimensional symplectic manifolds. In the present paper we prove that for a four-dimensional Liouville domain with all ECH capacities finite, the asymptotics of the ECH capacities recover the symplectic volume. This follows from a more general theorem relating the volume of a contact three-manifold to the asymptotics of the amount of symplectic action needed to...
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作者：Saxton, David; Thomason, Andrew
作者单位：University of Cambridge
摘要：We develop a notion of containment for independent sets in hypergraphs. For every -uniform hypergraph , we find a relatively small collection of vertex subsets, such that every independent set of is contained within a member of , and no member of is large; the collection, which is in various respects optimal, reveals an underlying structure to the independent sets. The containers offer a straightforward and unified approach to many combinatorial questions concerned (usually implicitly) with in...
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作者：Markovic, Vladimir
作者单位：California Institute of Technology
摘要：We prove that a quasiconformal map of the sphere S-2 admits a harmonic quasi-isometric extension to the hyperbolic space H-3, thus confirming the well known Schoen Conjecture in dimension 3.
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作者：Stix, Jakob
作者单位：Goethe University Frankfurt
摘要：A birationally liftable Galois section of a hyperbolic curve over a number field yields an adelic point of the smooth completion . We show that is -integral outside a set of places of Dirichlet density , or is cuspidal. The proof relies on -quotients of for some open . If is totally real or imaginary quadratic, we prove that all birationally adelic, non-cuspidal Galois sections come from rational points as predicted by the section conjecture of anabelian geometry. As an aside we also obtain a ...
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作者：Eldan, Ronen
作者单位：University of Washington; University of Washington Seattle
摘要：The Gaussian noise-stability of a set is defined by where are standard jointly Gaussian vectors satisfying . Borell's inequality states that for all , among all sets with a given Gaussian measure, the quantity is maximized when is a half-space. We give a novel short proof of this fact, based on stochastic calculus. Moreover, we prove an almost tight, two-sided, dimension-free robustness estimate for this inequality: by introducing a new metric to measure the distance between the set and its co...
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作者：Escobedo, M.; Velazquez, J. J. L.
作者单位：University of Basque Country; Basque Center for Applied Mathematics (BCAM); University of Bonn
摘要：The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of classical solutions of the homogeneous bosonic Nordheim equation that blow up in finite time. We also prove finite time condensation for a class of weak solutions of the kinetic equation.
