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current issue
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Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters J. Am. Math. Soc. (IF 5.413) Pub Date : 2020-06-16 Dzmitry Dudko; Mikhail Lyubich; Nikita Selinger
Abstract:In the 1980s Branner and Douady discovered a surgery relating various limbs of the Mandelbrot set. We put this surgery in the framework of ``Pacman Renormalization Theory'' that combines features of quadratic-like and Siegel renormalizations. We show that Siegel renormalization periodic points (constructed by McMullen in the 1990s) can be promoted to pacman renormalization periodic points
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The 4-dimensional light bulb theorem J. Am. Math. Soc. (IF 5.413) Pub Date : 2020-06-15 David Gabai
Abstract:For embedded 2-spheres in a 4-manifold sharing the same embedded transverse sphere homotopy implies isotopy, provided the ambient 4-manifold has no -torsion in the fundamental group. This gives a generalization of the classical light bulb trick to 4-dimensions, the uniqueness of spanning discs for a simple closed curve in and . In manifolds with -torsion, one surface can be put into a normal
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Geometric stabilisation via 𝑝-adic integration J. Am. Math. Soc. (IF 5.413) Pub Date : 2020-06-15 Michael Groechenig; Dimitri Wyss; Paul Ziegler
Abstract:In this article we give a new proof of Ngô's geometric stabilisation theorem, which implies the fundamental lemma. This is a statement which relates the cohomology of Hitchin fibres for a quasi-split reductive group scheme to the cohomology of Hitchin fibres for the endoscopy groups . Our proof avoids the decomposition and support theorem, instead the argument is based on results for -adic
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Symplectic topology of 𝐾3 surfaces via mirror symmetry J. Am. Math. Soc. (IF 5.413) Pub Date : 2020-06-09 Nick Sheridan; Ivan Smith
Abstract:We study the symplectic topology of certain surfaces (including the ``mirror quartic'' and ``mirror double plane''), equipped with certain Kähler forms. In particular, we prove that the symplectic Torelli group may be infinitely generated, and derive new constraints on Lagrangian tori. The key input, via homological mirror symmetry, is a result of Bayer and Bridgeland on the autoequivalence
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Combinatorial constructions of derived equivalences J. Am. Math. Soc. (IF 5.413) Pub Date : 2020-05-05 Daniel Halpern-Leistner; Steven Sam
Abstract:Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of Špenko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves of its various geometric invariant theory (GIT) quotients for suitably generic stability parameters. These variations of GIT quotient are examples of more
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Zéro-cycles sur les espaces homogènes et problème de Galois inverse J. Am. Math. Soc. (IF 5.413) Pub Date : 2020-03-10 Yonatan Harpaz; Olivier Wittenberg
Abstract:Soit une compactification lisse d'un espace homogène d'un groupe algébrique linéaire sur un corps de nombres . Nous établissons la conjecture de Colliot-Thélène, Sansuc, Kato et Saito sur l'image du groupe de Chow des zéro-cycles de dans le produit des mêmes groupes sur tous les complétés de . Lorsque est semi-simple et simplement connexe et que le stabilisateur géométrique est fini et
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