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作者：Frohman, Charles; Kania-Bartoszynska, Joanna; Le, Thang
作者单位：University of Iowa; National Science Foundation (NSF); University System of Georgia; Georgia Institute of Technology
摘要：This paper resolves the unicity conjecture of Bonahon and Wong for the Kauffman bracket skein algebras of all oriented finite type surfaces at all roots of unity. The proof is a consequence of a general unicity theorem that says that the irreducible representations of a prime affine k-algebra over an algebraically closed field k, that is finitely generated as a module over its center, are generically classified by their central characters. The center of the Kauffman bracket skein algebra of an...
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作者：Seward, Brandon
作者单位：New York University
摘要：For an ergodic p.m.p. action G?(X,) of a countable group G, we define the Rokhlin entropy hGRok(X,) to be the infimum of the Shannon entropies of countable generating partitions. It is known that for free ergodic actions of amenable groups this notion coincides with classical Kolmogorov-Sinai entropy. It is thus natural to view Rokhlin entropy as a close analogue to classical entropy. Under this analogy we prove that Krieger's finite generator theorem holds for all countably infinite groups. S...
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作者：Goldring, Wushi; Koskivirta, Jean-Stefan
作者单位：Stockholm University; University of Tokyo
摘要：We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks G-Zip(mu). Restricting to zip data of Hodge type, we obtain a group-theoretical Hasse invariant on every Ekedahl-Oort stratum closure of a general Hodge-type Shimura variety. A key tool is the construction of a stack of zip flags G-ZipFlag(mu), fibered in flag varieties over G-Zip(mu). It provides a simultaneous generalization of the classical case homogeneous complex manifolds studied by Gri...
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作者：Berger, Pierre
作者单位：Universite Paris 13
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作者：Aparicio-Arroyo, Marta; Bradlow, Steven; Collier, Brian; Garcia-Prada, Oscar; Gothen, Peter B.; Oliveira, Andre
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University System of Maryland; University of Maryland College Park; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universidade do Porto; University of Tras-os-Montes & Alto Douro
摘要：Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces of of SO(p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli sp...
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作者：Benameur, Moulay-Tahar; Heitsch, James L.
作者单位：Universite de Montpellier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifold admits no PSC metric; that any metric of PSC on such a foliation is bounded by a multiple of the reciprocal of the foliation K-area of the ambient manifold; and that Connes' van...
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作者：Wang, Yilin
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Loewner's equation provides a way to encode a simply connected domain or equivalently its uniformizing conformal map via a real-valued driving function of its boundary. The first main result of the present paper is that the Dirichlet energy of this driving function (also known as the Loewner energy) is equal to the Dirichlet energy of the log-derivative of the (appropriately defined) uniformizing conformal map. This description of the Loewner energy then enables to tie direct links with regula...
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作者：Barthel, Tobias; Hausmann, Markus; Naumann, Niko; Nikolaus, Thomas; Noel, Justin; Stapleton, Nathaniel
作者单位：University of Copenhagen; University of Regensburg; University of Munster; University of Kentucky
摘要：For a finite abelian group A, we determine the Balmer spectrum of SpA, the compact objects in genuine A-spectra. This generalizes the case A=Z/pZ due to Balmer and Sanders (Invent Math 208(1):283-326, 2017), by establishing (a corrected version of) their logp-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and establish a generalization of Kuhn's blue-shift theorem for Tate-constructions (Kuhn in Invent Math 157(2):345-370, 2004).
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作者：Barilari, Davide; Rizzi, Luca
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients, whose properties are remarkably different with respect to the Riemannian case. As a byproduct, we characterize the cut locus as the set of points where the squared sub-Riemannian distance fails to be semiconvex, answering to a question raised by Figalli and Ri...
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作者：Becker, Simon; Han, Rui; Jitomirskaya, Svetlana
作者单位：University of Cambridge; University System of Georgia; Georgia Institute of Technology; University of California System; University of California Irvine
摘要：We consider a quantum graph as a model of graphene in magnetic fields and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux phi/2 pi\documentclass through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero.
