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作者：Lesieutre, John
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.
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作者：Baladi, Viviane; Demers, Mark F.; Liverani, Carlangelo
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Fairfield University; University of Rome Tor Vergata
摘要：We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L-t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions.
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作者：Beuzart-Plessis, Raphael
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove an integral formula computing multiplicities of square-integrable representations relative to Galois pairs over p-adic fields and we apply this formula to verify two consequences of a conjecture of Dipendra Prasad. One concerns the exact computation of the multiplicity of the Steinberg representation and the other the invariance of multiplicities by transfer among inner forms.
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作者：Oberdieck, Georg; Pixton, Aaron
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Let S be a K3 surface and let E be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold for all curve classes which are primitive in the K3 factor. In particular, we deduce the Igusa cusp form conjecture. The proof relies on new results in the Gromov-Witten theory of elliptic curves and K3 surfaces. We show the generating series of Gromov-Witten classes of an elliptic curve are cycle-valued quasimodular forms and satisfy a holomorphic anomaly equation. The q...
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作者：Das, Mrinal Kanti; Tikader, Soumi; Zinna, Md. Ali
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; National Institute of Science Education & Research (NISER)
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作者：Groechenig, Karlheinz; Romero, Jose Luis; Stoeckler, Joachim
作者单位：University of Vienna; Dortmund University of Technology; Austrian Academy of Sciences
摘要：We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as for (in which case g is called totally positive of Gaussian type). In analogy to Beurling's sampling theorem for the Paley-Wiener space of entire functions, we prove that every separated set with lower Beurling density is a sampling set for the shift-invariant space generated by such a g. In view of the known nece...
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作者：Tsukamoto, Masaki
作者单位：Kyoto University
摘要：Mean dimension is a topological invariant of dynamical systems counting the number of parameters averaged by dynamics. Brody curves are Lipschitz holomorphic maps , and they form an infinite dimensional dynamical system. Gromov started the problem of estimating its mean dimension in 1999. We solve this problem by proving the exact mean dimension formula. Our formula expresses the mean dimension by the energy density of Brody curves. As a key novel ingredient, we use an information theoretic ap...
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作者：Druel, Stephane
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite cover, ,tale in codimension one, that decomposes as a product of an Abelian variety, and singular analogues of irreducible Calabi-Yau and irreducible holomorphic symplectic varieties.
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作者：Jabin, Pierre-Emmanuel; Wang, Zhenfu
作者单位：University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; University of Pennsylvania
摘要：We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space W--1,W-infinity thus including the Biot-Savart law and the point ...
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作者：Linowitz, Benjamin; McReynolds, D. B.; Pollack, Paul; Thompson, Lola
作者单位：University System of Ohio; Oberlin College; Purdue University System; Purdue University; University System of Georgia; University of Georgia
摘要：The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manif...
