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作者：Fujino, Osamu
摘要：We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the sense of Kollar. This completes Kollar's projectivity criterion for the moduli spaces of higher-dimensional stable varieties.
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作者：Frankel, Steven
摘要：We prove a conjecture of Calegari's, that every quasigeodesic flow on a closed hyperbolic 3-manifold contains a closed orbit.
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作者：Andreatta, Fabrizio; Goren, Eyal Z.; Howard, Benjamin; Pera, Keerthi Madapusi
摘要：Let M be the Shimura variety associated with the group of spinor similitudes of a quadratic space over Q of signature (n, 2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special divisors and big CM points on M to the central derivatives of certain L-functions. As an application of this result, we prove an averaged version of Colmez's conjecture on the Faltings heights of CM abelian varieties.
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作者：Ionel, Eleny-Nicoleta; Parker, Thomas H.
摘要：The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. Using the methods of symplectic Gromov-Witten theory, we prove that the Gopakumar-Vafa conjecture holds for any symplectic Calabi-Yau 6-manifold, and hence for Calabi-Yau 3-folds. The results extend to all symplectic 6-manifolds and to the genus zero GW invariants of semipositive manifolds.
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作者：Barlow, Martin T.; Murugan, Mathav
摘要：We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well as rough isometrics.
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作者：Yuan, Xinyi; Zhang, Shou-Wu
摘要：The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture, which was also proposed by Colmez.
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作者：Logunov, Alexander
摘要：Let M be a compact C-infinity-smooth Riemannian manifold of dimension n, n >= 3, and let phi lambda : Delta M phi lambda + lambda phi lambda = 0 denote the Laplace eigenfunction on M corresponding to the eigenvalue lambda. We show that Hn-1 ({phi lambda = 0}) <= C lambda(alpha), where alpha > 1/2 is a constant, which depends on n only, and C > 0 depends on M. This result is a consequence of our study of zero sets of harmonic functions on C-infinity-smooth Riemannian manifolds. We develop a tec...
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作者：Bresch, Didier; Jabin, Pierre-emmanuel
摘要：We prove global existence of appropriate weak solutions for the compressible Navier-Stokes equations for a more general stress tensor than those previously covered by P.-L.Lions and E. Feireisl's theory. More precisely we focus on more general pressure laws that are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining prec...
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作者：Gan, Wee Teck; Ichino, Atsushi
摘要：We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group Mp(2), to the metaplectic group Mp(2n) of higher rank. To establish this, we transport Arthur's endoscopic classification of representations of the odd special orthogonal group SO2r+1 with r >> 2n by using a result of J.-S. Li on global theta lifts in the stable range.
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作者：Georgieva, Penka; Zinger, Aleksey
摘要：We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for counts of real positive-genus curves in real algebraic varieties. Our approach to the orientability problem is based entirely on the topology of real bundle pairs over symmetric surfaces; the previous attempts involved direct computations for the determinan...
