Boalch, Philip
Published in
Advances in Mathematics

We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matrices). Natural symplectic structures are found and described both explicitly and from an infinite dimensional viewpoint (generalising the Atiyah–Bott approach). This enab...

Graham, C.Robin Lee, John M
Published in
Advances in Mathematics

Patakfalvi, Zsolt
Published in
Advances in Mathematics

We prove Viehwegʼs hyperbolicity conjecture over compact bases and over bases with non-uniruled compactification. The most general case of the conjecture states that the base space of a maximal variation family of smooth projective manifolds with semi-ample canonical sheaf is of log-general type.

Gilkey, Peter B
Published in
Advances in Mathematics

Kokarev, Gerasim
Published in
Advances in Mathematics

We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the general regularity properties of ...

Digne, F. Michel, J.
Published in
Advances in Mathematics

Motivated by the Broué conjecture on blocks with abelian defect groups for finite reductive groups, we study “parabolic” Deligne–Lusztig varieties and construct on those which occur in the Broué conjecture an action of a braid monoid, whose action on their ℓ-adic cohomology will conjecturally factor through a cyclotomic Hecke algebra. In order to c...

Delaunay, Christophe Jouhet, Frédéric
Published in
Advances in Mathematics

The main aim of this article is to compute all the moments of the number of pℓ-torsion elements in some type of finite abelian groups. The averages involved in these moments are those defined for the Cohen–Lenstra heuristics for class groups and their adaptation for Tate–Shafarevich groups. In particular, we prove that the heuristic model for Tate–...

Gillibert, Pierre
Published in
Advances in Mathematics

We denote by ConcA the (∨,0)-semilattice of all finitely generated congruences of an (universal) algebra A, and we define ConcV as the class of all isomorphic copies of all ConcA, for A∈V, for any variety V of algebras.Let V and W be locally finite varieties of algebras such that for each finite algebra A∈V there are, up to isomorphism, only finite...

Felikson, Anna Shapiro, Michael Tumarkin, Pavel
Published in
Advances in Mathematics

We construct geometric realizations for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston [10] to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute the growth rate of these cluster algebras, provide the positivit...

Colliot-Thélène, Jean-Louis
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)