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作者：Danciger, Jeffrey; Maloni, Sara; Schlenker, Jean-Marc
作者单位：University of Texas System; University of Texas Austin; University of Virginia; University of Luxembourg
摘要：We study convex polyhedra in three-space that are inscribed in a quadric surface. Up to projective transformations, there are three such surfaces: the sphere, the hyperboloid, and the cylinder. Our main result is that a planar graph Gamma is realized as the 1-skeleton of a polyhedron inscribed in the hyperboloid or cylinder if and only if Gamma is realized as the 1-skeleton of a polyhedron inscribed in the sphere and Gamma admits a Hamiltonian cycle. This answers a question asked by Steiner in...
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作者：Brown, Aaron; Fisher, David; Hurtado, Sebastian
作者单位：University of Chicago; Indiana University System; Indiana University Bloomington
摘要：We prove Zimmer's conjecture for C2 actions by finite-index subgroups of SL(m, Z) provided m > 3. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in SL(m, R) (Brown et al. in Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T), 2016. arXiv:1608.04995) but new ideas are needed to overcome the lack of compactness of the space (G x M)/ (admitting the induced G-action). Non-compactness allows both mea...
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作者：Konno, Hokuto; Taniguchi, Masaki
作者单位：University of Tokyo; RIKEN
摘要：We show 10/8-type inequalities for some end-periodic 4-manifolds which have positive scalar curvature metrics on the ends. As an application, we construct a new family of closed 4-manifolds which do not admit positive scalar curvature metrics.
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作者：Greer, Francois
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：We give examples of Calabi-Yau threefolds containing Lagrangian spheres which are not vanishing cycles of nodal degenerations, answering a question of Donaldson in the negative.
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作者：Gaidashev, Denis; Yampolsky, Michael
作者单位：Uppsala University; University of Toronto
摘要：In this paper we give a new proof of hyperbolicity of renormalization of critical circle maps using the formalism of almost-commuting pairs. We extend renormalization to two-dimensional dissipative maps of the annulus which are small perturbations of one-dimensional critical circle maps. Finally, we demonstrate that a two-dimensional map which lies in the stable set of the renormalization operator possesses attractor which is topologically a circle. Such a circle is critical: the dynamics on i...
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作者：Matomaki, Kaisa; Radziwill, Maksym; Tao, Terence
作者单位：University of Turku; California Institute of Technology; University of California System; University of California Los Angeles
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作者：Kleiner, Bruce; Lang, Urs
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The large-scale geometry of hyperbolic metric spaces exhibits many distinctive features, such as the stability of quasi-geodesics (the Morse Lemma), the visibility property, and the homeomorphism between visual boundaries induced by a quasi-isometry. We prove a number of closely analogous results for spaces of rank n >= 2 in an asymptotic sense, under some weak assumptions reminiscent of nonpositive curvature. For this purpose we replace quasi-geodesic lines with quasi-minimizing (locally fini...
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作者：Nguyen Viet Dang; Guillarmou, Colin; Riviere, Gabriel; Shen, Shu
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille; Universite Paris Cite; Sorbonne Universite
摘要：We study the twisted Ruelle zeta function.X (s) for smooth Anosov vector fields X acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove the Fried conjecture, relating Reidemeister torsion and.X (0). In higher dimensions, we show more generally that.X (0) is locally constant with respect to the vector field X under a spectral condition. As a consequence, we also show the Fried conjecture for Anosov flows near the geodesic flow on the unit tangent bundle of hyperb...
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作者：Davison, Ben; Meinhardt, Sven
作者单位：University of Edinburgh; University of Sheffield
摘要：This paper concerns the cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the integrality conjecture and the wall crossing formula, and furthermore realise the isomorphism in both of these theorems as Poincare-Birkhoff-Witt isomorphisms for the associated cohomological Hall algebra. We do this by defining a perverse filtration on the cohomol...
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作者：Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of measure-endowed random surfaces. LQG is defined in terms of a real parameter gamma, and it has long been believed that when gamma=8/3, the LQG sphere should be equivalent (in some sense) to TBM. However, the LQG sphere comes equipped with a conformal structure, and TBM comes equipped with a metric space structure, and endowing either one with the other's structure has been an open problem for some time. This ...
