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作者：Crainic, Marius; Fernandes, Rui Loja
摘要：We give a soft geometric proof of the classical result due to Conn stating that a Poisson structure is linearizable around a singular point (zero) at which the isotropy Lie algebra is compact and semisimple.
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作者：Goldstein, Michael; Schlag, Wilhelm
摘要：We consider one-dimensional difference Schrodinger equations [H(x, omega)phi] (n) phi(n - 1) phi(n + 1) + V(x + n omega)phi(n) = E phi(n), n is an element of Z, x,omega is an element of [0, 1] with real-analytic potential function V(x). If L(E, omega(0)) is greater than 0 for all E is an element of (E', E '') and some Diophantine omega(0), then the integrated density of states is absolutely continuous for almost every b.) close to omega(0), as shown by the authors in earlier work. In this pape...
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作者：Blomer, Valentin; Brumley, Farrell
摘要：We extend to an arbitrary number field the best known bounds towards Ramanujan for the group GL(n), n = 2, 3, 4. In particular, we present a technique which overcomes the analytic obstacles posed by the presence of an infinite group of units.
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作者：Finis, Tobias; Lapid, Erez
摘要：In Arthur's trace formula, a ubiquitous role is played by certain limiting expressions arising from piecewise smooth functions with respect to projections of the Coxeter fan ((G, M)-families). These include terms resulting from intertwining operators on the spectral side and volumes of polytopes on the geometric side. We introduce the combinatorial concept of a compatible family with respect to an arbitrary polyhedral fan and obtain new formulas for the corresponding limiting expressions in th...
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作者：Kalinin, Boris
摘要：We prove the Livsic Theorem for arbitrary GL(m, R) cocycles. We consider a hyperbolic dynamical system f : X -> X and a Holder continuous function A : X -> GL(m, R). We show that if A has trivial periodic data, i.e. A(f(n-1) p) ... A(fp)A(p) = Id for each periodic point p = f(n)p, then there exists a Holder continuous function C : X -> GL(m, R) satisfying A(x) = C(fx)C(x)(-1) for all x is an element of X. The main new ingredients in the proof are results of independent interest on relations be...
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作者：Cordoba, Antonio; Cordoba, Diego; Gancedo, Francisco
摘要：We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from Darcy's law. The free boundary is given by the discontinuity among the densities and viscosities of the fluids. This physical scenario is known as the two-dimensional Muskat problem or the two-phase He le-Shaw flow. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assu...
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作者：Urban, Eric
摘要：We develop the theory of overconvergent cohomology introduced by G. Stevens, and we use it to give a construction of eigenvarieties associated to any reductive group G over Q such that G(R) has discrete series. We prove that the so-called eigenvarieties are equidimensional and generically flat over the weight space.
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作者：Farah, Ilijas
摘要：We prove that it is relatively consistent with the usual axioms of mathematics that all automorphisms of the Calkin algebra are inner. Together with a 2006 Phillips-Weaver construction of an outer automorphism using the Continuum Hypothesis, this gives a complete solution to a 1977 prolem of Brown-Douglas-Fillmore. We also give a simpler and self-contained proof of the Phillips-Weaver result.
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作者：Finis, Tobias; Lapid, Erez; Mueller, Werner
摘要：We derive a refinement of the spectral expansion of Arthur's trace formula. The expression is absolutely convergent with respect to the trace norm.
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作者：Young, Matthew P.
摘要：We compute the fourth moment of Dirichlet L-functions at the central point for prime moduli, with a power savings in the error term.
