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作者：Shende, Vivek; Treumann, David; Zaslow, Eric
作者单位：Boston College; University of California System; University of California Berkeley; Northwestern University
摘要：We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya category of which is equivalent to the category of constructible sheaves on the surface itself. Consequently, our category can be described as constructible sheaves with singular support controlled by the front projection of the knot. We use a theorem of Guillermou-Kashiwara-Schapira to show that the resulting category is i...
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作者：Cao, Junyan; Pun, Mihai
作者单位：Universite Paris Cite; Sorbonne Universite; Korea Institute for Advanced Study (KIAS)
摘要：In this article we provide a proof of the Iitaka conjecture for algebraic fiber spaces over tori.
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作者：Abe, Takuro
作者单位：Kyushu University
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作者：Achinger, Piotr
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Universite Paris Saclay
摘要：We prove that every connected affine scheme of positive characteristic is a space for the ,tale topology. The main ingredient is the special case of the affine space over a field k. This is dealt with by induction on n, using a key Bertini-type statement regarding the wild ramification of -adic local systems on affine spaces, which might be of independent interest. Its proof uses in an essential way recent advances in higher ramification theory due to T. Saito. We also give rigid analytic and ...
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作者：Brendle, Simon; Huisken, Gerhard
作者单位：Columbia University; Eberhard Karls University of Tubingen
摘要：We consider a one-parameter family of closed, embedded hypersurfaces moving with normal velocity , where denote the curvature eigenvalues and is a nonnegative constant. This defines a fully nonlinear parabolic equation, provided that . In contrast to mean curvature flow, this flow preserves the condition in a general ambient manifold. Our main goal in this paper is to extend the surgery algorithm of Huisken-Sinestrari to this fully nonlinear flow. This is the first construction of this kind fo...
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作者：Brock, Jeffrey F.; Dunfield, Nathan M.
作者单位：Brown University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We study the relationship between two norms on the first cohomology of a hyperbolic 3-manifold: the purely topological Thurston norm and the more geometric harmonic norm. Refining recent results of Bergeron, Aengun, and Venkatesh as well as older work of Kronheimer and Mrowka, we show that these norms are roughly proportional with explicit constants depending only on the volume and injectivity radius of the hyperbolic 3-manifold itself. Moreover, we give families of examples showing that some ...
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作者：Potrie, Rafael; Sambarino, Andres
作者单位：Universidad de la Republica, Uruguay; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：We show that the critical exponent of a representation rho in the Hitchin component of PSL(d,R) is bounded above, the least upper bound being attained only in the Fuchsian locus. This provides a rigid inequality for the area of a minimal surface on rho\X where X is the symmetric space of PSL(d,R) The proof relies in a construction useful to prove a regularity statement: if the Frenet equivariant curve of rho is smooth, then rho is Fuchsian.
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作者：Valko, Benedek; Virag, Balint
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Toronto
摘要：We show that , the bulk limit of the Gaussian -ensembles is the spectrum of a self-adjoint random differential operator where is the positive definite matrix representation of hyperbolic Brownian motion with variance in logarithmic time. The result connects the Montgomery-Dyson conjecture about the process and the non-trivial zeros of the Riemann zeta function, the Hilbert-Plya conjecture and de Brange's attempt to prove the Riemann hypothesis. We identify the Brownian carousel as the Sturm-Li...
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作者：Antonakoudis, Stergios M.
作者单位：University of Cambridge
摘要：This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichmuller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a Teichmuller disk. Additionally, a similar result is proved for a large class of disk-rigid domains, which includes strictly convex domains, as well as finite-dimensional Teichmuller spaces.
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作者：Pulvirenti, M.; Simonella, S.
作者单位：Sapienza University Rome; University of L'Aquila; Technical University of Munich
摘要：We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions, the correlation errors, measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order k measures the event where k particles are connected by a chain of interactions preventing the factorization. We show that, provided , such an error flows to...
