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作者：Dumas, David
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We show that Thurston's skinning maps of Teichmuller space have finite fibers. The proof centers around a study of two subvarieties of the character variety of a surface-one associated with complex projective structures, and the other associated with a 3-manifold. Using the Morgan-Shalen compactification of the character variety and author's results on holonomy limits of complex projective structures, we show that these subvarieties have only a discrete set of intersections. Along the way, we ...
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作者：Avila, Artur
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study Schrodinger operators with a one-frequency analytic potential, focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials. From the dynamical point of view, the transition signals the emergence of non-uniform hyperbolicity, so the dependence of the Lyapunov exponent with respect to parameters plays a central role in the analysis. Though often ill-behaved by conventional measures, we show that the Lyapunov exponent is in ...
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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：Hesselholt, Lars
作者单位：Nagoya University; University of Copenhagen
摘要：This paper gives a new and direct construction of the multi-prime big de Rham-Witt complex, which is defined for every commutative and unital ring; the original construction by Madsen and myself relied on the adjoint functor theorem and accordingly was very indirect. The construction given here also corrects the 2-torsion which was not quite correct in the original version. The new construction is based on the theory of modules and derivations over a lambda-ring which is developed first. The m...
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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：Enciso, Alberto; Peralta-Salas, Daniel
作者单位：Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT)
摘要：We prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible Euler equation in . More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in , we show that they can be transformed with a C (m) -small diffeomorphism into a set of vortex tubes of a Beltrami field that tends to zero at infinity. The structure of the vortex lines in the tubes is extremely rich, presenting a positive-measure set of invariant tori and...
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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：Verbitsky, Misha
作者单位：HSE University (National Research University Higher School of Economics); University of Tokyo
摘要：Let M be a compact complex manifold. The corresponding Teichmuller space Teich is the space of all complex structures on M up to the action of the group of isotopies. The mapping class group acts on Teich in a natural way. An ergodic complex structure is a complex structure with a -orbit dense in Teich. Let M be a complex torus of complex dimension or a hyperkahler manifold with . We prove that M is ergodic, unless M has maximal Picard rank (there are countably many such M). This is used to sh...
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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.
