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作者：Barany, Balazs; Hochman, Michael; Rapaport, Ariel
作者单位：MTA-BME Stochastics Research Group; Budapest University of Technology & Economics; Hebrew University of Jerusalem
摘要：Let X=?phi iX be a strongly separated self-affine set in R2 (or one satisfying the strong open set condition). Under mild non-conformality and irreducibility assumptions on the matrix parts of the phi i, we prove that dimX is equal to the affinity dimension, and similarly for self-affine measures and the Lyapunov dimension. The proof is via analysis of the dimension of the orthogonal projections of the measures, and relies on additive combinatorics methods.
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作者：Gutierrez-Romo, Rodolfo
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We classify the Rauzy-Veech groups of all connected components of all strata of the moduli space of translation surfaces in absolute homology, showing, in particular, that they are commensurable to arithmetic lattices of symplectic groups. As a corollary, we prove a conjecture of Zorich about the Zariski-density of such groups.
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作者：Bruned, Y.; Hairer, M.; Zambotti, L.
作者单位：Imperial College London; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which comes with an explicit and elegant description of a subgroup of their group of automorphisms. This subgroup is sufficiently large to be able to implement a version of the BPHZ renormalisation prescription in this context. This is in stark contrast to previous...
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作者：Astorg, Matthieu; Gauthier, Thomas; Mihalache, Nicolae; Vigny, Gabriel
作者单位：Universite de Orleans; Universite de Picardie Jules Verne (UPJV); Universite Paris Saclay; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：The moduli space M-d of degree d >= 2 rational maps can naturally be endowed with a measure mu(bif) detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation measure mu bif has positive Lebesgue measure. To do so, we establish a general sufficient condition for the conjugacy class of a rational map to belong to the support of mu bif and we exhibit a large set of Collet-Eckmann rational maps which satisfy this condition. As a consequence, we ge...
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作者：Saito, Takeshi
作者单位：University of Tokyo
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作者：Pop, Florian
作者单位：University of Pennsylvania
摘要：In this note we introduce and prove a wide generalization and sharpening of Ihara's question/Oda-Matsumoto conjecture, for short I/OM. That leads to a quite concrete topological/combinatorial description of absolute Galois groups, in particular of Gal(Q)=Aut((Q) over bar), as envisioned by Grothendieck in his Esquisse d'un Programme.
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作者：Rizzardo, Alice; Van den Bergh, Michel; Neeman, Amnon
作者单位：University of Edinburgh; Hasselt University; Australian National University
摘要：Orlov's famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. In this paper we show that this result is false without the fully faithfulness hypothesis. We also show that our functor does not lift to the homotopy category of spectral categories if the ground field is Q.
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作者：Waldron, Alex
摘要：We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter et al. (Am J Math 120:117-128, 1998). The proof relies on a weighted energy identity and sharp decay estimates in the neck region.
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作者：Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone
作者单位：Princeton University; Universite Paris Saclay; University of Geneva; Swiss Federal Institutes of Technology Domain; ETH Zurich; Technical University of Munich
摘要：The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This perspective is then employed in the proof that the Pfaffian structure of boundary correlations emerges asymptotically at criticality in Ising models on Z2 with finite-range interactions. The analysis is enabled by new results on the stochastic geometry ...
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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...
