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作者：Gan, Wee Teck; Qiu, Yannan; Takeda, Shuichiro
作者单位：National University of Singapore; University of Missouri System; University of Missouri Columbia
摘要：In this paper, we establish the second term identity of the Siegel-Weil formula in full generality, and derive the Rallis inner product formula for global theta lifts for any dual pair. As a corollary, we resolve the non-vanishing problem of global theta lifts initiated by Steve Rallis.
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作者：Parimala, R.; Suresh, V.
作者单位：Emory University
摘要：Let K be a complete discretely valued field with residue field kappa and F the function field of a curve over K. Let p be the characteristic of kappa and a a prime not equal to p. If the Brauer a-dimensions of all finite extensions of kappa are bounded by d and the Brauer a-dimensions of all extensions of kappa of transcendence degree at most 1 are bounded by d+1, then it is known that the Brauer a-dimension of F is at most d+2 (Lieblich in J. Reine Angew. Math. 659:1-41, 2011; Saltman in J. R...
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作者：Bowen, Lewis
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We determine the range of Furstenberg entropy for stationary ergodic actions of nonabelian free groups by an explicit construction involving random walks on random coset spaces.
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作者：Petersen, Dan; Tommasi, Orsola
作者单位：Royal Institute of Technology; Leibniz University Hannover
摘要：We prove that for N equal to at least one of the integers 8, 12, 16, 20 the tautological ring is not Gorenstein. In fact, our N equals the smallest integer such that there is a non-tautological cohomology class of even degree on . By work of Graber and Pandharipande, such a class exists on , and we present some evidence indicating that N is in fact 20.
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作者：Hairer, M.
作者单位：University of Warwick
摘要：We introduce a new notion of regularity structure that provides an algebraic framework allowing to describe functions and/or distributions via a kind of jet or local Taylor expansion around each point. The main novel idea is to replace the classical polynomial model which is suitable for describing smooth functions by arbitrary models that are purpose-built for the problem at hand. In particular, this allows to describe the local behaviour not only of functions but also of large classes of dis...
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作者：Seidel, Paul
摘要：We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise disjoinable by Hamiltonian isotopies) inside such manifolds. This includes the Milnor fibres of isolated hypersurface singularities which have been stabilized (by adding quadratic terms) sufficiently often.
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作者：Alarcon, Antonio; Forstneric, Franc
作者单位：University of Granada; University of Ljubljana
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作者：Koropecki, Andres; Tal, Fabio Armando
作者单位：Universidade Federal Fluminense; Universidade de Sao Paulo
摘要：This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points is shown to be a disjoint union of periodic topological disks (...
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作者：Gan, Wee Teck; Ichino, Atsushi
作者单位：National University of Singapore; Kyoto University
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作者：Grabowski, Lukasz
作者单位：University of Warwick
摘要：Main theorems of the article concern the problem of Atiyah on possible values of -Betti numbers. It is shown that all non-negative real numbers are -Betti numbers, and that many (for example all non-negative algebraic) real numbers are -Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental -Betti number with respect to an action of the threefold direct product...
