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Acta Mathematica, 2016, Volume 217
ISSN:
0001-5962 (Print)
1871-2509 (Online)
In this volume (6 articles)
Issue 1
[1] Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
Patrick Bernard PSL Research University Vadim Kaloshin University of Maryland at College Park Ke Zhang University of Toronto
Dynamical Systems mathscidoc:1911.43036
Acta Mathematica, 217, (1), 1-79, 2016
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[2] Universality in several-matrix models via approximate transport maps
Alessio Figalli ETH Z¨urich Alice Guionnet Universit´e de Lyon
Probability mathscidoc:1911.43037
Acta Mathematica, 217, (1), 81-176, 2016
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[3] Lower bounds for numbers of real solutions in problems of Schubert calculus
Evgeny Mukhin Indiana University,Purdue University Vitaly Tarasov Indiana University,Purdue University
Quantum Algebra mathscidoc:1911.43038
Acta Mathematica, 217, (1), 177-193, 2016
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Issue 2
[1] Global bifurcation of steady gravity water waves with critical layers
Adrian Constantin King’s College London Walter Strauss Brown University Eugen Varv ˘ aruc ˘ a University of Vienna
Mathematical Physics mathscidoc:1911.43039
Acta Mathematica, 217, (2), 195-262, 2016
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We construct families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed, in particular establishing the existence of waves of large amplitude. A Riemann–Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudodifferential equation with a scalar constraint. The structural properties of this formulation, which arises as the Euler–Lagrange equation of an energy functional, enable us to develop a theory of analytic global bifurcation.
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[2] Maximum independent sets on random regular graphs
Jian Ding University of Chicago Allan Sly University of California, Berkeley Nike Sun Stanford University
Probability mathscidoc:1911.43040
Gold Award Paper in 2020
Acta Mathematica, 217, (2), 263-340, 2016
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We determine the asymptotics of the independence number of the random d-regular graph for all d≥d0. It is highly concentrated, with constant-order fluctuations around nα∗−c∗logn for explicit constants α∗(d) and c∗(d). Our proof rigorously confirms the one-step replica symmetry breaking heuristics for this problem, and we believe the techniques will be more broadly applicable to the study of other combinatorial properties of random graphs.
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[3] Local Hodge theory of Soergel bimodules
Geordie Williamson University of Sydney
Representation Theory mathscidoc:1911.43041
Acta Mathematica, 217, (2), 341-404, 2016
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We prove the local hard Lefschetz theorem and local Hodge–Riemann bilinear relations for Soergel bimodules. Using results of Soergel and Kübel, one may deduce an algebraic proof of the Jantzen conjectures. We observe that the Jantzen filtration may depend on the choice of non-dominant regular deformation direction.
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Impact Factor
3.719
Available
1882 - 2016
Volumes
228
Issues
301
Articles
2167