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作者：McLean, Mark
摘要：We show that any two birational projective Calabi-Yau manifolds have isomorphic small quantum cohomology algebras after a certain change of Novikov rings. The key tool used is a version of an algebra called symplectic cohomology, which is constructed using Hamiltonian Floer cohomology. Morally, the idea of the proof is to show that both small quantum products are identical deformations of symplectic cohomology of some common open affine subspace.
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作者：Tikhomirov, Konstantin
摘要：For each n, let M-n, be an n x n random matrix with independent +/- 1 entries. We show that P{M-n is singular} = (1/2 + o(n)(1))(n), which settles an old problem. Some generalizations are considered.
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作者：Kupiainen, Antti; Rhodes, Remi; Vargas, Vincent
摘要：Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996) proposed a remarkable explicit expression, the so-called DOZZ formula, for the three point structure constants of Liouville Conformal Field Theory (LCFT), which is expected to describe the scaling limit of large planar maps properly embedded into the Riemann sphere. In this paper we give a proof of the DOZZ formula based on a rigorous probabilistic construction of LCFT in terms of Gaussian Multiplicative Chaos given ...
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作者：Fournais, Soren; Solovej, Jan Philip
摘要：For a dilute system of non-relativistic bosons interacting through a positive, compactly supported, L-1-potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1 + 128/15 root pi root rho a(3) + o(root rho a(3))), thereby proving the Lee-Huang-Yang formula for the energy density.
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作者：Ivanisvili, Paata; van Handel, Ramon; Volberg, Alexander
摘要：A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. We prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube.
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作者：Bennett, Michael A.; Siksek, Samir
摘要：If k is a sufficiently large positive integer, we show that the Diophantine equation n(n + d) center dot center dot center dot (n + (k-1)d) = y(l) has at most finitely many solutions in positive integers n, d, y and, with gcd(n, d) = 1 and l >= 2. Our proof relies upon Frey-Hellegouarch curves and results on supersingular primes for elliptic curves without complex multiplication, derived from upper bounds for short character sums and sieves, analytic and combinatorial.
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作者：Skinner, Christopher
摘要：Let E be a semistable elliptic curve over Q. We prove that if E has non-split multiplicative reduction at at least one odd prime or split multiplicative reduction at at least two odd primes, then rank(z)E(Q) = 1 and #III(E) < infinity double right arrow ords(s=1)L(E, s) = 1. We also prove the corresponding result for the abelian variety associated with a weight 2 newform f of trivial character. These, and other related results, are consequences of our main theorem, which establishes criteria f...
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作者：Lie, Victor
摘要：We prove affirmatively the one-dimensional case of a conjecture of Stein regarding the L-p-boundedness of the Polynomial Carleson operator for 1 < p < infinity. Our proof relies on two new ideas: (i) we develop a framework for higher-order wave-packet analysis that is consistent with the time-frequency analysis of the (generalized) Carleson operator, and (ii) we introduce a local analysis adapted to the concepts of mass and counting function, which yields a new tile discretization of the time-...
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作者：Masser, David; Zannier, Umberto
摘要：We prove among other things the existence of Hodge generic abelian varieties defined over the algebraic numbers and not isogenous to any Jacobian. Actually, we also show that in various interpretations these abelian varieties make up the majority, and we give certain uniform bounds on the possible degree of the fields of definition. In particular, this yields a new answer (in strong form) to a question of Katz and Oort, compared to previous work of Chai and Oort (2012, conditional on the Andre...
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作者：Piccirillo, Lisa
摘要：A knot is said to be slice if it bounds a smooth properly embedded disk in B-4. We demonstrate that the Conway knot is not slice. This completes the classification of slice knots under 13 crossings and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.
