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作者：Bellaiche, Joel
作者单位：Brandeis University
摘要：We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.
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作者：Bader, U.; Gelander, T.; Monod, N.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Hebrew University of Jerusalem; Technion Israel Institute of Technology
摘要：We prove a fixed point theorem for a family of Banach spaces including notably L (1) and its non-commutative analogues. Several applications are given, e.g. the optimal solution to the derivation problem studied since the 1960s.
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作者：Selinger, Nikita
作者单位：Constructor University
摘要：Let f be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map sigma (f) of a finite-dimensional Teichmuller space. We prove that this map extends continuously to the augmented Teichmuller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichmuller space. The resulting classification of inv...
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作者：Bourgain, Jean; Varju, Peter P.
作者单位：Institute for Advanced Study - USA; Princeton University; Szeged University; Hungarian Academy of Sciences
摘要：Let S be a fixed finite symmetric subset of SLd(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi(q)(G) with respect to the generating set pi(q)(S) form a family of expanders, where pi(q) is the projection map Z -> Z/qZ.
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作者：Lin, Chang-Shou; Wei, Juncheng; Ye, Dong
作者单位：National Taiwan University; Chinese University of Hong Kong; Universite de Lorraine
摘要：We consider the following Toda system Delta u(i) + Sigma(n)(j=1)a(ij)e(uj) = 4 pi gamma(i)delta(0) in R-2, integral(R2)e(ui)dx < infinity, for all 1 <= i <= n, where gamma (i) >-1, delta (0) is Dirac measure at 0, and the coefficients a (ij) form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result: Sigma(n)(j=1)a(ij) integral(R2)e(uj)dx = 4 pi(2 + gamma(i) + gamma(n+1-i)), for all 1 <= i <= n This generalizes the c...
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作者：Bridgeland, Tom; Laredo, Valerio Toledano
作者单位：University of Oxford; Northeastern University; Institute for Advanced Study - USA
摘要：Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P-1 with values in the Hall algebra of A. The residues of these connections are given by the holomorphic generating function for counting invariants in A constructed by D. Joyce (in Geom. Topol. 11, 667-725, 2007).
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作者：Smith, Ivan
作者单位：University of Cambridge
摘要：There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. We investigate symplectic aspects of this relationship, with a view to applications in low-dimensional topology.
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作者：Hou, Xuanji; You, Jiangong
作者单位：Nanjing University
摘要：In this paper, we prove that a quasi-periodic linear differential equation in sl(2,ae) with two frequencies (alpha,1) is almost reducible provided that the coefficients are analytic and close to a constant. In the case that alpha is Diophantine we get the non-perturbative reducibility. We also obtain the reducibility and the rotations reducibility for an arbitrary irrational alpha under some assumption on the rotation number and give some applications for Schrodinger operators. Our proof is a ...
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作者：Melbourne, Ian; Terhesiu, Dalia
作者单位：University of Surrey
摘要：We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates L (n) of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In ...
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作者：Paun, Mihai
作者单位：Universite de Lorraine
摘要：In this article we establish a very general non-vanishing statement, as well as several properties of metrics with minimal singularities of adjoint bundles. Our arguments combine the proof of the classical non-vanishing theorem due to V. Shokurov, as well as many ideas from Y.-T. Siu's analytic proof of the finite generation of the canonical ring. An important tool is the notion of relative critical exponent of two closed positive currents with respect to a measure.
