Gamburd, Alex Jakobson, Dmitry Sarnak, Peter
Published in
Journal of the European Mathematical Society

We present a new method for establishing the “gap” property for finitely generated subgroups of SU(2), providing an elementary solution of Ruziewicz problem on S2 as well as giving many new examples of finitely generated subgroups of SU(2) with an explicit gap. The distribution of the eigenvalues of the elements of the group ring R[SU(2)] in the N-...

Batyrev, Victor V.
Published in
Journal of the European Mathematical Society

Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata log-terminal pair corresponding to an algebraic variety V having a regular action of a finite group G. In this situation we show that the stringy Euler numbe...

Jost, Jürgen
Published in
Journal of the European Mathematical Society

JEMS is a new mathematical research journal, founded by the EMS, aiming at the highest international scientific level, and edited by Jürgen Jost (managing editor), Luigi Ambrosio, Gerard Ben Arous, John Coates, Helmut Hofer, Alexander Merkurjev and a board of about 30 associate editors. It will be published by Springer. The first issue will appear ...

Kurihara, Masato
Published in
Journal of the European Mathematical Society

In this paper, for a totally real number field k we show the ideal class group of k(∪n>0μn)+ is trivial. We also study the p-component of the ideal class group of the cyclotomic Zp-extension.

Polterovich, Leonid
Published in
Journal of the European Mathematical Society

Let G be the group of Hamiltonian diffeomorphisms of a closed symplectic manifold Y. A loop h:S1→G is called strictly ergodic if for some irrational number α the associated skew product map T:S1×Y→S1×Y defined by T(t,y)=(t+α,h(t)y) is strictly ergodic. In the present paper we address the following question. Which elements of the fundamental group o...

Burger, M. Monod, N.
Published in
Journal of the European Mathematical Society

We prove that the natural map Hb2(Γ)?H2(Γ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for Γ: the stable commutator length vanishes and any C1–action on the circle is almost trivial. We in...

Gromov, M.
Published in
Journal of the European Mathematical Society

The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphi...

Lin, Fanghua Rivière, Tristan
Published in
Journal of the European Mathematical Society

There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S1-valued function defined on the boundary of a bounded regular domain of Rn. When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coup...

Kollár, János
Published in
Journal of the European Mathematical Society

Let fi be polynomials in n variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials gi such that ∑gifi=1. The effective versions of this result bound the degrees of the gi in terms of the degrees of the fj. The aim of this paper is to generalize this to the case when the fi are replaced by arbitrary ideals. Applica...

Müller, S. Šverák, V.
Published in
Journal of the European Mathematical Society

We study solutions of first order partial differential relations Du∈K, where u:Ω⊂ℝn→ℝm is a Lipschitz map and K is a bounded set in m×n matrices, and extend Gromov’s theory of convex integration in two ways. First, we allow for additional constraints on the minors of Du and second we replace Gromov’s P-convex hull by the (functional) rank-one conve...