- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 11:59:39
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JEMS&vol=19&iss=7&update_since=2024-03-29
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
19
2017
7
Mixing and un-mixing by incompressible flows
Yao
Yao
Georgia Institute of Technology, ATLANTA, UNITED STATES
Andrej
Zlatoš
University of California, San Diego, LA JOLLA, UNITED STATES
Incompressible flow, mixing, un-mixing
We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint $\|\nabla u(\cdot,t)\|_p\le 1$ we show that any function can be mixed to scale $\epsilon$ in time $O(|\mathrm {log}\:\epsilon|^{1+\nu_p})$, with $\nu_p=0$ for $p
Partial differential equations
Fluid mechanics
1911
1948
10.4171/JEMS/709
http://www.ems-ph.org/doi/10.4171/JEMS/709
Classical solutions and higher regularity for nonlinear fractional diffusion equations
Juan Luis
Vázquez
Universidad Autónoma de Madrid, MADRID, SPAIN
Arturo
de Pablo
Universidad Carlos III de Madrid, LEGANÉS, SPAIN
Fernando
Quirós
Universidad Autónoma de Madrid, MADRID, SPAIN
Ana
Rodríguez
Universidad Politécnica de Madrid, MADRID, SPAIN
Nonlinear fractional diffusion, nonlocal diffusion operators, classical solutions, optimal regularity
We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion $$\partial_tu+(-\Delta)^{\sigma/2}\varphi(u)=0,$$ posed for $x\in \mathbb{R}^N$, $t>0$, with $0
Partial differential equations
Order, lattices, ordered algebraic structures
1949
1975
10.4171/JEMS/710
http://www.ems-ph.org/doi/10.4171/JEMS/710
The classification of Nichols algebras over groups with finite root system of rank two
István
Heckenberger
Universität Marburg, MARBURG, GERMANY
Leandro
Vendramin
Universidad de Buenos Aires, BUENOS AIRES, ARGENTINA
Hopf algebra, Nichols algebra, Weyl groupoid
We classify all groups $G$ and all pairs $(V,W)$ of absolutely simple Yetter–Drinfeld modules over $G$ such that the support of $V\oplus W$ generates $G$, $c_{W,V}c_{V,W}\ne\mathrm {id}$, and the Nichols algebra of the direct sum of $V$ and $W$ admits a finite root system. As a byproduct, we determine the dimensions of such Nichols algebras, and several new families of finite-dimensional Nichols algebras are obtained. Our main tool is the Weyl groupoid of pairs of absolutely simple Yetter–Drinfeld modules over groups.
Associative rings and algebras
Group theory and generalizations
1977
2017
10.4171/JEMS/711
http://www.ems-ph.org/doi/10.4171/JEMS/711
Poisson algebras via model theory and differential-algebraic geometry
Jason
Bell
University of Waterloo, WATERLOO, CANADA
Stéphane
Launois
University of Kent, CANTERBURY, KENT, UNITED KINGDOM
Omar
León Sánchez
The University of Manchester, MANCHESTER, UNITED KINGDOM
Rahim
Moosa
University of Waterloo, WATERLOO, CANADA
Poisson algebras, differential algebraic geometry, Dixmier–Moeglin equivalence, primitive ideal, model theory, Manin kernel
Brown and Gordon asked whether the Poisson Dixmier–Moeglin equivalence holds for any complex affine Poisson algebra, that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry and model theory. In particular, it is shown that while the sets of Poisson rational and Poisson primitive ideals do coincide, in every Krull dimension at least four there are complex affine Poisson algebras with Poisson rational ideals that are not Poisson locally closed. These counterexamples also give rise to counterexamples to the classical (noncommutative) Dixmier–Moeglin equivalence in finite GK dimension. A weaker version of the Poisson Dixmier–Moeglin equivalence is proven for all complex affine Poisson algebras, from which it follows that the full equivalence holds in Krull dimension three or less. Finally, it is shown that everything, except possibly that rationality implies primitivity, can be done over an arbitrary base field of characteristic zero.
Nonassociative rings and algebras
Mathematical logic and foundations
Field theory and polynomials
Algebraic geometry
2019
2049
10.4171/JEMS/712
http://www.ems-ph.org/doi/10.4171/JEMS/712
Higher genus quasimap wall-crossing for semipositive targets
Ionuţ
Ciocan-Fontanine
University of Minnesota, MINNEAPOLIS, UNITED STATES
Bumsig
Kim
Korea Institute for Advanced Study, SEOUL, SOUTH KOREA
Gromov–Witten invariants, quasimap invariants, mirror symmetry
In previous work we have conjectured wall-crossing formulas for genus zero quasimap invariants of GIT quotients and proved them via localization in many cases. We extend these formulas to higher genus when the target is semipositive, and prove them for semipositive toric varieties, in particular for toric local Calabi–Yau targets. The proof also applies to local Calabi–Yau's associated to some nonabelian quotients.
Algebraic geometry
2051
2102
10.4171/JEMS/713
http://www.ems-ph.org/doi/10.4171/JEMS/713
Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field
Kirsten
Eisenträger
The Pennsylvania State University, UNIVERSITY PARK, UNITED STATES
Alexandra
Shlapentokh
East Carolina University, GREENVILLE, UNITED STATES
Undecidability, Hilbert's Tenth Problem
We prove that the existential theory of any function field $K$ of characteristic $p > 0$ is undecidable in the language of rings augmented by constant symbols for the elements of a suitable recursive subfield, provided that the constant field does not contain the algebraic closure of a finite field. This theorem is the natural generalization of a theorem of Kim and Roush from 1992. We also extend our previous undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of any function field of positive characteristic is undecidable in the language of rings without parameters.
Number theory
Mathematical logic and foundations
2103
2138
10.4171/JEMS/714
http://www.ems-ph.org/doi/10.4171/JEMS/714
The family Floer functor is faithful
Mohammed
Abouzaid
Columbia University, NEW YORK, UNITED STATES
Floer homology, Lagrangian torus fibration, rigid analytic spaces, coherent sheaves, homological mirror symmetry
Family Floer theory is used to construct a functor from the Fukaya category of a symplectic manifold admitting a Lagrangian torus fibration to a (twisted) category of perfect complexes on the mirror rigid analytic space. This functor is shown to be faithful by a degeneration argument involving moduli spaces of annuli.
Differential geometry
Algebraic geometry
2139
2217
10.4171/JEMS/715
http://www.ems-ph.org/doi/10.4171/JEMS/715