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作者：Davison, Ben
摘要：For various 2-Calabi-Yau categories C for which the classical stack of objects M has a good moduli space p: M. M, we establish purity of the mixed Hodge module complex p!Q M. We do this by using formality in 2CY categories, along with etale neighbourhood theorems for stacks, to prove that the morphism p is modelled etale-locally by the semisimplification morphism from the stack of modules of a preprojective algebra. Via the integrality theorem in cohomological Donaldson-Thomas theory we then p...
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作者：Pasten, Hector
作者单位：Pontificia Universidad Catolica de Chile
摘要：We combine transcendental methods and the modular approaches to the ABC conjecture to show that the largest prime factor of n(2)+1isatleastofsize(log(2)n)(2)/log(3)nwhere log k is the k-th iterate of the logarithm. This gives a substantial improvement on the best available estimates, which are essentially of size log2ngoing back to work of Chowla in 1934. Using the same ideas, we also obtain significant progress on sub expoential bounds for the ABC conjecture, which in a case gives the first i...
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作者：Giri, Vikram; Radu, Razvan-Octavian
作者单位：Princeton University
摘要：For any gamma<1/3, we construct a nontrivial weak solution to the two-dimensional, incompressible Euler equations, which has compact support in time and satisfies u is an element of C gamma(R(t)xT(x)(2)) . In particular, the constructed solution does not conserve energy and, thus, settles the flexible part of the Onsager conjecture in two dimensions. The proof involves combining the Nash iteration technique with a new linear Newton iteration.
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作者：Genevois, Anthony; Tessera, Romain
作者单位：Universite de Montpellier; Sorbonne Universite; Universite Paris Cite
摘要：This article is dedicated to the asymptotic geometry of wreath products F H := H F H where F is a finite group and H is a finitely generated group. Our first main result says that a coarse map from a finitely presented one-ended group to F H must land at bounded distance from a left coset of H. Our second main result, building on the later, is a very restrictive description of quasi-isometries between two lamplighter groups on finitely presented one-ended groups. Third, we obtain a complete cl...
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作者：Bauerschmidt, Roland; Crawford, Nicholas; Helmuth, Tyler
作者单位：University of Cambridge; New York University; Technion Israel Institute of Technology; Durham University
摘要：The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor beta > 0 per edge. It arises as the q -> 0 limit of the -state random cluster model with p = beta q. We prove that in dimensions d >= 3 the arboreal gas undergoes a percolation phase transition. This contrasts with the case of d = 2 where no percolation transition occurs. The starting point for our analysis is an exact relationship between the arboreal gas and a no...
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作者：Gallay, Thierry; Sverak, Vladimir
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Institut Universitaire de France; University of Minnesota System; University of Minnesota Twin Cities
摘要：For the incompressible Navier-Stokes equations in R3 with low viscosity nu>0, we consider the Cauchy problem with initial vorticity omega 0 that represents an infinitely thin vortex filament of arbitrary given strength Gamma supported on a circle. The vorticity field omega(x,t) of the solution is smooth at any positive time and corresponds to a vortex ring of thickness root nu t that is translated along its symmetry axis due to self-induction, an effect anticipated by Helmholtz in 1858 and qua...
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作者：Casals, Roger; Gao, Honghao
作者单位：University of California System; University of California Davis; Tsinghua University
摘要：We show that each cluster seed in the augmentation variety contains an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian fillings to cluster seeds. The main new technique to produce these Lagrangian fillings is the construction and study of a quiver with potential associated to curve configurations. We prove that its deformation space is trivial and show how to use it to manipulate Lagrangian fillings with L \documentclass[12pt]{minimal} \us...
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作者：Oliver, Robert J. Lemke; Thorner, Jesse; Zaman, Asif
作者单位：Tufts University; University of Illinois System; University of Illinois Urbana-Champaign; University of Toronto
摘要：Let k be a number field and G be a finite group. Let F-k(G) (Q) be the family of number fields K with absolute discriminant D-K at most Q such that K/k is normal with Galois group isomorphic to G. If G is the symmetric group S-n or any transitive group of prime degree, then we unconditionally prove that for all K is an element of F-k(G) (Q) with at most O-epsilon(Q(epsilon)) exceptions, the L-functions associated to the faithful Artin representations of Gal(K/k) have a region of holomorphy and...
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作者：Chandra, Ajay; Chevyrev, Ilya; Hairer, Martin; Shen, Hao
作者单位：Imperial College London; University of Edinburgh; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Wisconsin System; University of Wisconsin Madison
摘要：We define a state space and a Markov process associated to the stochastic quantisation equation of Yang-Mills-Higgs (YMH) theories. The state space S \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{S}$\end{document} is a nonlinear metric space of distributions, elements of which can be used as initial condi...
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作者：Dumaz, Laure; Labbe, Cyril
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We investigate the behavior of the spectrum of the continuous Anderson Hamiltonian H-L, with white noise potential, on a segment whose size L is sent to infinity. We zoom around energy levels E either of order 1 (Bulk regime) or of order 1 << E << L (Crossover regime). We show that the point process of (appropriately rescaled) eigenvalues and centers of mass converge to a Poisson point process. We also prove exponential localization of the eigenfunctions at an explicit rate. In addition, we sh...
