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作者：Oh, Tadahiro; Sosoe, Philippe; Tolomeo, Leonardo
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University; Cornell University; University of Bonn
摘要：We study an optimal mass threshold for normalizability of the Gibbs measures associated with the focusing mass-critical nonlinear Schrodinger equation on the one-dimensional torus. In an influential paper, Lebowitz et al. (J Stat Phys 50(3-4):657-687, 1988) proposed a critical mass threshold given by the mass of the ground state on the real line. We provide a proof for the optimality of this critical mass threshold. The proof also applies to the two-dimensional radial problem posed on the unit...
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作者：Disegni, Daniel
作者单位：Ben-Gurion University of the Negev
摘要：Let G be the group (GL(2) x GU(1))/GL(1) over a totally real field F, and let X be a Hida family for G. Revisiting a construction of Howard and Fouquet, we construct an explicit section P of a sheaf of Selmer groups over X. We show, answering a question of Howard, that P is a universal Heegner class, in the sense that it interpolates geometrically defined Heegner classes at all the relevant classical points of X. We also propose a 'Bertolini-Darmon' conjecture for the leading term of P at clas...
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作者：Berdnikov, Aleksandr; Manin, Fedor
作者单位：Institute for Advanced Study - USA; University of California System; University of California Santa Barbara
摘要：Scalable spaces are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are formal; indeed, scalability can be thought of as a metric version of formality. They are also characterized by particularly nice behavior from the point of view of quantitative homotopy theory. Among other results, we show that spaces which are formal but not scal...
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作者：Brue, Elia; Naber, Aaron; Semola, Daniele
作者单位：Institute for Advanced Study - USA; Northwestern University; University of Oxford
摘要：This paper studies the structure and stability of boundaries in noncollapsed RCD(K,N) spaces, that is, metric-measure spaces (X,d,H-N) with Ricci curvature bounded below. Our main structural result is that the boundary partial derivative X is homeomorphic to a manifold away from a set of codimension 2, and is N - 1 rectifiable. Along the way, we show effective measure bounds on the boundary and its tubular neighborhoods. These results are new even for Gromov-Hausdorff limits (M-i(N), d(gi), p(...
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作者：de Lizaur, Francisco Torres
作者单位：University of Toronto
摘要：We construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting all kinds of qualitative dynamics in the phase space, for example: strange attractors and chaos, invariant manifolds of arbitrary topology, and quasiperiodic invariant tori of any dimension. The main theorem of the paper, from which these families of solutions are obtained, states that for any given vector field X on a closed manifold N, there is a Riemannian manifold ...
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作者：Xu, Daxin; Zhu, Xinwen
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; California Institute of Technology
摘要：We construct the Frobenius structure on a rigid connection Be (sic) on G(m) for a split reductive group (sic) introduced by Frenkel-Gross. These data form a (sic)-valued overconvergent F-isocrystal Be-(sic)(dagger) on G(m), F-p, which is the p-adic companion of the Kloosterman (sic)-local system Kl((sic)) constructed by Heinloth-Ngo-Yun. By studying the structure of the underlying differential equation, we calculate themonodromy group of Be-(sic)(dagger) when (sic) is almost simple (which reco...
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作者：Deng, Yu; Nahmod, Andrea R.; Yue, Haitian
作者单位：University of Southern California; University of Massachusetts System; University of Massachusetts Amherst; ShanghaiTech University
摘要：We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work (Deng et al. in: Invariant Gibbs measures and global strong solutions for 4009 nonlinear Schrodinger equations in dimension two, ), to study the propagation of randomness under nonlinear dispersive equations. By applying this theory we establish almost-sure local well-posedness for semilinear Schrodinger equations in the full subcritical range relative to the probabil...
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作者：Sawin, Will; Shusterman, Mark
作者单位：Columbia University; Harvard University
摘要：We establish cancellation in short sums of certain special trace functions over F-q [u] belowthe Polya-Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the F-q [u]-analog of Chowla's conjecture on cancellation in Mobius sums over polynomial sequences, and of the Bateman-Horn conjecture in degree 2, for some values of q. A final application is to sums of trace functions over primes in F-q [u].
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作者：Chaidez, J.; Edtmair, O.
作者单位：University of California System; University of California Berkeley
摘要：Let X subset of R-4 be a convex domain with smooth boundary Y. We use a relation between the extrinsic curvature of Y and the Ruelle invariant of the Reeb flow on Y to prove that there are constants C > c > 0 independent of Y such that c <= ru(Y).sys(Y)(1/2) <= C Here sys(Y) is the systolic ratio of Y, i.e. the square of the minimal period of a closed Reeb orbit of Y divided by twice the volume of X, and ru(Y) is the volume-normalized Ruelle invariant. We then construct dynamically convex cont...
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作者：Li, Chao
作者单位：Stanford University
