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作者：Hermon, Jonathan; Hutchcroft, Tom
作者单位：University of British Columbia; University of Cambridge
摘要：Let G be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. We prove that if G is nonamenable and p > p(c)(G) then there exists a positive constant c(p) such that P-p(n <= vertical bar K vertical bar < infinity) <= e(-cpn) for every n >= 1, where K is the cluster of the origin. We deduce the following two corollaries: 1. Every infinite cluster in supercritical percolation on a transitive non-amenable graph has anchored expansion almost surely. This ans...
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作者：De Philippis, Guido; Spolaor, Luca; Velichkov, Bozhidar
作者单位：New York University; University of California System; University of California San Diego; University of Pisa
摘要：We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.
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作者：Blanco, Guillem
作者单位：KU Leuven
摘要：We present a proof of a conjecture proposed by Yano (Sci Rep Saitama Univ Ser 10(2): 21-28, 1982) about the generic b-exponents of irreducible plane curve singularities.
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作者：Beraldo, Dario
作者单位：University of London; University College London
摘要：We characterize the tempered part of the automorphic Langlands category D(Bun(G)) using the geometry of the big cell in the affine Grassmannian. We deduce that, for G non-abelian, tempered D-modules have no de Rham cohomology with compact support. The latter fact boils down to a concrete statement, which we prove using the Ran space and some explicit t-structure estimates: for G non-abelian and Sigma a smooth affine curve, the Borel-Moore homology of the indscheme Maps(Sigma, G) vanishes.
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作者：Brendle, Simon; Daskalopoulos, Panagiota; Sesum, Natasa
作者单位：Columbia University; Rutgers University System; Rutgers University New Brunswick
摘要：In this paper, we study the classification of kappa-noncollapsed ancient solutions to three-dimensional Ricci flow on S-3. We prove that such a solution is either isometric to a family of shrinking round spheres, or the Type II ancient solution constructed by Perelman.
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作者：Huang, Jingyin; Osajda, Damian
作者单位：University System of Ohio; Ohio State University; University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular, such groups act geometrically on spaces with a convex geodesic bicombing, equipping them with a nonpositive-curvature-like structure. That structure has many properties of a CAT(0) structure and, additionally, it has a combinatorial flavor imp...
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作者：Cascini, Paolo; Spicer, Calum
作者单位：Imperial College London
摘要：We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a Q-factorial projective threefold. As applications, we show the existence of F-dlt modifications and F-terminalisations for foliated pairs and we show that foliations with canonical or F-dlt singularities admit non-dicritical singularities. Finally, we show abundance in the case of numerically trivial fol...
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作者：Bell, Jason; Zelmanov, Efim
作者单位：University of Waterloo; University of California System; University of California San Diego
摘要：We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
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作者：Dougall, Rhiannon; Sharp, Richard
作者单位：University of Bristol; University of Warwick
摘要：The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions seen, for example, in the work of Stadlbauer on symmetric group extensions and of the authors on geodesic flows. Our main application is to growth rates of periodic orbits for covers of an Anosov flow: we reduce the problem of counting periodic orbits in an amenable cover X to counting in a maximal abelian subcover ...
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作者：Sheridan, Nick; Smith, Ivan
作者单位：University of Edinburgh; University of Cambridge
摘要：We prove Kontsevich's homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev-Borisov's 'dual reflexive Gorenstein cones' construction. In particular we prove HMS for all Greene-Plesser mirror pairs (i.e., Calabi-Yau hypersurfaces in quotients of weighted projective spaces). We also prove it for certain mirror Calabi-Yau complete intersections arising from Borisov's construction via dual nef partitions, and also for certain Calabi-Yau complete intersections which d...
