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作者：Borman, Matthew Strom; Eliashberg, Yakov; Murphy, Emmy
作者单位：Stanford University; Massachusetts Institute of Technology (MIT)
摘要：We establish a parametric extension h-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from [12]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.
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作者：Aptekarev, Alexander I.; Yattselev, Maxim L.
作者单位：Russian Academy of Sciences; Keldysh Institute of Applied Mathematics; Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, , . J. Nuttall has put forward the important relation between the maximal domain of f where the function has a single-valued branch and the domain of convergence of the diagonal Pad, approximants for f. The Pad, approximants, which are rational functions and thus single-valued, approximate a holomorphic branch of f in the domain of their...
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作者：Drasin, David; Pankka, Pekka
作者单位：Purdue University System; Purdue University; University of Helsinki; University of Jyvaskyla
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作者：Achar, Pramod N.; Rider, Laura
作者单位：Louisiana State University System; Louisiana State University; Massachusetts Institute of Technology (MIT)
摘要：We prove the Mirkovic-Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau-Mautner-Williamson theory ...
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作者：Pulita, Andrea
作者单位：Universite de Montpellier
摘要：We prove that the radii of convergence of the solutions of a p-adic differential equation over an affinoid domain X of the Berkovich affine line are continuous functions on X that factorize through the retraction of of X onto a finite graph . We also prove their super-harmonicity properties. This finiteness result means that the behavior of the radii as functions on X is controlled by a finite family of data.
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作者：Gogolev, Andrey; Ontaneda, Pedro; Hertz, Federico Rodriguez
作者单位：State University of New York (SUNY) System; Binghamton University, SUNY; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms. Laying aside many surgery constructions of 3-dimensional Anosov flows, these are the first new examples of manifolds which admit partially hyperbolic diffeomorphisms in the past forty years.
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作者：Poineau, Jerome; Pulita, Andrea
作者单位：Universite de Caen Normandie; Universite de Montpellier
摘要：We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic zero. Relying on work of the second author who investigated its properties on affinoid domains of the affine line, we prove that its slopes give rise to continuous functions that factorise by the retraction through a locally finite subgraph of the curve.
