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作者：Sun, Song; Zhang, Junsheng
作者单位：University of California System; University of California Berkeley
摘要：We discover a no semistability at infinity phenomenon for complete Calabi-Yau metrics asymptotic to cones, which is proved by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of Kahler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between...
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作者：Bessonov, R.; Denisov, S.
作者单位：Saint Petersburg State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; University of Wisconsin System; University of Wisconsin Madison
摘要：We give a dynamical characterization of measures on the real line with finite logarithmic integral. The general case is considered in the setting of evolution groups generated by de Branges canonical systems. Obtained results are applied to the Dirac operators and Krein strings.
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Geneva; Imperial College London
摘要：We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case...
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作者：Bakker, Benjamin; Brunebarbe, Yohan; Tsimerman, Jacob
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Bordeaux; University of Toronto
摘要：We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic spaces and coherent sheaves that are definable with respect to a given o-minimal structure, and prove a GAGA-type theorem algebraizing definable coherent sheaves on complex algebraic spaces. We then combine this with algebraization theorems of Artin to show that proper definable images of complex ...
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作者：Li, Yingkun
作者单位：Technical University of Darmstadt
摘要：In this paper, we investigate the algebraic nature of the value of a higher Green function on an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of Gross and Zagier in the setting of higher Green functions on the product of two modular curves. In the process, we will study analogue of harmonic Maass forms in the setting of Hilbert modular forms, and obtain results concerning the arithmetic of their holomorphic part Fourier coefficients. As a consequence, we a...
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作者：Novack, Matthew; Vicol, Vlad
作者单位：Purdue University System; Purdue University; New York University
摘要：For any regularity exponent beta < 1/2, we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class C-t(0)(H-beta & cap; L1/(1-2 beta)). By interpolation, such solutions belong to (CtB3,infinity S)-B-0 for s approaching 1/3 as beta approaches 1/2. Hence this result provides a new proof of the flexible side of the L3-based Onsager conjecture. Of equal importance is that the intermittent nature of our solutions matches that of turbulent flows, which are obs...
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作者：Gan, Wee Teck; Savin, Gordan
作者单位：National University of Singapore; Utah System of Higher Education; University of Utah
摘要：We study three exceptional theta correspondences for p-adic groups, where one member of the dual pair is the exceptional group G(2). We prove the Howe duality conjecture for these dual pairs and a dichotomy theorem, and determine explicitly the theta lifts of all non-cuspidal representations.
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作者：Bader, Uri; Fisher, David; Miller, Nicholas; Stover, Matthew
作者单位：Weizmann Institute of Science; Rice University; University of Oklahoma System; University of Oklahoma - Norman; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：For n >= 2, we prove that a finite volume complex hyperbolic n-manifold containing infinitely many maximal properly immersed totally geodesic submanifolds of real dimension at least two is arithmetic, paralleling our previous work for real hyperbolic manifolds. As in the real hyperbolic case, our primary result is a superrigidity theorem for certain representations of complex hyperbolic lattices. The proof requires developing new general tools not needed in the real hyperbolic case. Our main r...
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作者：Ma, Linquan
作者单位：Purdue University System; Purdue University
摘要：The long standing Lech's conjecture in commutative algebra states that for a flat local extension (R, m) -> (S, n) of Noetherian local rings, we have an inequality on the Hilbert-Samuel multiplicities: e(R) <= e(S). In general the conjecture is wide open when dim R > 3, even in equal characteristic. In this paper, we prove Lech's conjecture in all dimensions, provided (R, m) is a standard graded ring over a perfect field localized at the homogeneous maximal ideal. We introduce the notions of l...
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作者：Italiano, Giovanni; Martelli, Bruno; Migliorini, Matteo
作者单位：Scuola Normale Superiore di Pisa
摘要：We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence, we build a finite type subgroup of a hyperbolic group that is not hyperbolic.
