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作者：Stokman, J. V.; Reshetikhin, N.
作者单位：University of Amsterdam; Tsinghua University; University of California System; University of California Berkeley
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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：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：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：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...
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作者：Ben-Zvi, David; Chen, Harrison; Helm, David; Nadler, David
作者单位：University of Texas System; University of Texas Austin; Academia Sinica - Taiwan; Imperial College London; University of California System; University of California Berkeley
摘要：Kazhdan and Lusztig identified the affine Hecke algebra H with an equivariant K-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of irreducible representations of reductive groups over nonarchimedean local fields F with an Iwahori-fixed vector. We apply techniques from derived algebraic geometry to pass from K-theory to Hochschild homology and thereby identify H with the endomorphisms of a coherent sheaf on th...
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作者：Blasiak, Jonah; Morse, Jennifer; Pun, Anna
作者单位：Drexel University; University of Virginia; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Catalan functions, the graded Euler characteristics of certain vector bundles on the flag variety, are a rich class of symmetric functions which include k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$k$\end{document}-Schur functions and parabolic Hall-Littlewood polynomials. We prove that Catalan functions indexed...
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作者：Dai, Irving; Kang, Sungkyung; Mallick, Abhishek; Park, Junghwan; Stoffregen, Matthew
作者单位：University of Texas System; University of Texas Austin; University of Oxford; Rutgers University System; Rutgers University New Brunswick; Korea Advanced Institute of Science & Technology (KAIST); Michigan State University
摘要：We prove that the (2,1)-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.
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作者：Vishik, Alexander
作者单位：University of Nottingham
摘要：In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with F p \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Bbb {F}}_{p}$\end{document} -coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In...
