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作者：Guionnet, A.; Shlyakhtenko, D.
作者单位：Massachusetts Institute of Technology (MIT); Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); University of California System; University of California Los Angeles
摘要：By solving a free analog of the Monge-AmpSre equation, we prove a non-commutative analog of Brenier's monotone transport theorem: if an n-tuple of self-adjoint non-commutative random variables Z (1),aEuro broken vertical bar,Z (n) satisfies a regularity condition (its conjugate variables xi (1),aEuro broken vertical bar,xi (n) should be analytic in Z (1),aEuro broken vertical bar,Z (n) and xi (j) should be close to Z (j) in a certain analytic norm), then there exist invertible non-commutative ...
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作者：Cook, Brian; Magyar, Akos
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of British Columbia
摘要：Let p = (p(1), ... , p(r)) be a system of r polynomials with integer coefficients of degree d in n variables x = (x(1), ... , x(n)). For a given r-tuple of integers, say s, a general local to global type statement is shown via classical Hardy-Littlewood type methods which provides sufficient conditions for the solubility of p(x) = s under the condition that each of the x(i)'s is prime.
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作者：Geiges, Hansjoerg; Roettgen, Nena; Zehmisch, Kai
作者单位：University of Cologne; University of Freiburg
摘要：We construct a contact form on , , equal to the standard contact form outside a compact set and defining the standard contact structure on all of , which has trapped Reeb orbits, including a torus invariant under the Reeb flow, but no closed Reeb orbits. This answers a question posed by Helmut Hofer.
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作者：Mironov, Andrey E.
作者单位：Russian Academy of Sciences; Sobolev Institute of Mathematics; Lomonosov Moscow State University
摘要：In this paper we study self-adjoint commuting ordinary differential operators of rank two. We find sufficient conditions when an operator of fourth order commuting with an operator of order 4g+2 is self-adjoint. We introduce an equation on potentials V(x),W(x) of the self-adjoint operator and some additional data. With the help of this equation we find the first example of commuting differential operators of rank two corresponding to a spectral curve of higher genus. These operators have polyn...
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作者：Bloch, Spencer; Esnault, Helene; Kerz, Moritz
作者单位：Free University of Berlin; University of Regensburg
摘要：We study the p-adic deformation properties of algebraic cycle classes modulo rational equivalence. We show that the crystalline Chern character of a vector bundle on the closed fibre lies in a certain part of the Hodge filtration if and only if, rationally, the class of the vector bundle lifts to a formal pro-class in K-theory on the p-adic scheme.
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作者：Gupta, Neena
作者单位：Tata Institute of Fundamental Research (TIFR)
摘要：We show that the Cancellation Conjecture does not hold for the affine space A(k)(3) over any field k of positive characteristic. We prove that an example of T. Asanuma provides a three-dimensional k-algebra A for which A is not isomorphic to k[X (1), X (2), X (3)] although A[T] is isomorphic to k[X (1), X (2), X (3), X (4)].
