Journal: Journal für die reine und angewandte Mathematik

Abbreviation

J. reine angew. Math.

Publisher

De Gruyter

Journal Volumes

ISSN

0075-4102
1435-5345

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Publications1 - 10 of 33
  • A quantitative stability result for the sphere packing problem in dimensions 8 and 24
    Item type: Journal Article
    Böröczky, Károly J.; Radchenko, Danylo; Ramos, João P.G. (2024)
    Journal für die reine und angewandte Mathematik
    We prove explicit stability estimates for the sphere packing problem in dimensions 8 and 24, showing that, in the lattice case, if a lattice is ∼ε close to satisfying the optimal density, then it is, in a suitable sense, close to the E₈ and Leech lattices, respectively. In the periodic setting, we prove that, under the same assumptions, we may take a large “frame” through which our packing locally looks like E₈ or Λ₂₄. Our methods make explicit use of the magic functions constructed in [M. S. Viazovska, The sphere packing problem in dimension 8, Ann. of Math. (2) 185 2017, 3, 991–1015] in dimension 8 and in [H. Cohn, A. Kumar, S. D. Miller, D. Radchenko and M. Viazovska, The sphere packing problem in dimension 24, Ann. of Math. (2) 185 2017, 3, 1017–1033] in dimension 24, together with results of independent interest on the abstract stability of the lattices E₈ and Λ₂₄.
  • Hermitian K-theory via oriented Gorenstein algebras
    Item type: Journal Article
    Hoyois, Marc; Jelisiejew, Joachim; Nardin, Denis; et al. (2022)
    Journal für die reine und angewandte Mathematik
    We show that the hermitian K-theory space of a commutative ring R can be identified, up to A(1)-homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-algebras, i.e., finite locally free R-algebras with trivialized dualizing sheaf. We deduce that hermitian K-theory is universal among generalized motivic cohomology theories with transfers along oriented finite Gorenstein morphisms. As an application, we obtain a Hilbert scheme model for hermitian K-theory as a motivic space. We also give an application to computational complexity: we prove that 1-generic minimal border rank tensors degenerate to the big Coppersmith-Winograd tensor.
  • Stable s-minimal cones in ℝ3 are flat for s ~ 1
    Item type: Journal Article
    Cabré, Xavier; Cinti, Eleonora; Serra, Joaquim (2020)
    Journal für die reine und angewandte Mathematik
    We prove that half spaces are the only stable nonlocal s-minimal cones in ℝ3, for s∈(0,1) sufficiently close to 1. This is the first classification result of stable s-minimal cones in dimension higher than two. Its proof cannot rely on a compactness argument perturbing from s=1. In fact, our proof gives a quantifiable value for the required closeness of s to 1. We use the geometric formula for the second variation of the fractional s-perimeter, which involves a squared nonlocal second fundamental form, as well as the recent BV estimates for stable nonlocal minimal sets. © De Gruyter 2020.
  • Plunnecke inequalities for countable abelian groups
    Item type: Journal Article
    Björklund, Michael; Fish, Alexander (2017)
    Journal für die reine und angewandte Mathematik
    We establish in this paper a new form of Plünnecke-type inequalities for ergodic probability measure-preserving actions of any countable abelian group. Using a correspondence principle for product sets, this allows us to deduce lower bounds on the upper and lower Banach densities of any product set in terms of the upper Banach density of an iterated product set of one of its addends. These bounds are new already in the case of the integers. We also introduce the notion of an ergodic basis, which is parallel, but significantly weaker than the analogous notion of an additive basis, and deduce Plünnecke bounds on their impact functions with respect to both the upper and lower Banach densities on any countable abelian group.
  • Harmonic Maass forms associated with CM newforms
    Item type: Journal Article
    Ehlen, Stephan; Li, Yingkun; Schwagenscheidt, Markus (2024)
    Journal für die reine und angewandte Mathematik
    In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight k ≥ 2 under the {\xi}-operator. As a result, we show that their holomorphic parts have algebraic Fourier coefficients, with compatible Galois action. As an application, we prove rationality properties of coefficients of harmonic Maass forms corresponding to CM newforms, answering a question of Bruinier, Ono and Rhoades.
  • Contracting elements and random walks
    Item type: Journal Article
    Sisto, Alessandro (2018)
    Journal für die reine und angewandte Mathematik
    We define a new notion of contracting element of a group and we show that contracting elements coincide with hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, rank one isometries in groups acting properly on proper CAT(0) spaces, elements acting hyperbolically on the Bass–Serre tree in graph manifold groups. We also define a related notion of weakly contracting element, and show that those coincide with hyperbolic elements in groups acting acylindrically on hyperbolic spaces and with iwips in Out(Fn), n≥3. We show that each weakly contracting element is contained in a hyperbolically embedded elementary subgroup, which allows us to answer a problem in [16]. We prove that any simple random walk in a non-elementary finitely generated subgroup containing a (weakly) contracting element ends up in a non-(weakly-)contracting element with exponentially decaying probability.
  • Regularized theta liftings and periods of modular functions
    Item type: Journal Article
    Bruinier, Jan H.; Funke, Jens; Imamoḡlu, Özlem (2015)
    Journal für die reine und angewandte Mathematik
    In this paper, we use regularized theta liftings to construct weak Maass formsof weight 1/2 as lifts of weak Maass forms of weight 0. As a special case we give a new proofof some of recent results of Duke, Toth and the third author on cycle integrals of the modular j-invariant and extend these to any congruence subgroup. Moreover, our methods allow us tosettle the open question of a geometric interpretation for periods of j along infinite geodesics inthe upper half plane. In particular, we give the ‘central value’ of the (non-existent) ‘L-function’for j. The key to the proofs is the construction of a kind of simultaneous Green function forboth the CM points and the geodesic cycles, which is of independent interest.
  • Variational principles for immersed surfaces with L-2-bounded second fundamental form
    Item type: Journal Article
    Rivière, Tristan (2014)
    Journal für die reine und angewandte Mathematik
  • The Chern character of the Verlinde bundle over ℳ¯g,n
    Item type: Journal Article
    Marian, Alina; Oprea, Dragos; Pandharipande, Rahul; et al. (2017)
    Journal für die reine und angewandte Mathematik
    We prove an explicit formula for the total Chern character of the Verlindebundle of conformal blocks over ℳ¯g,n in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior ℳ¯g,n and the projective flatness of the Hitchin connection.
  • Simultaneous supersingular reductions of CM elliptic curves
    Item type: Journal Article
    Aka, Menny; Luethi, Manuel; Michel, Philippe; et al. (2022)
    Journal für die reine und angewandte Mathematik
    We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show – under additional congruence assumptions on the CM order – that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order becomes large. This variant of the equidistribution theorems of Duke and Cornut–Vatsal is an(other) application of the recent work of Einsiedler and Lindenstrauss on the classification of joinings of higher-rank diagonalizable actions.
Publications1 - 10 of 33