Related papers: mu-constant monodromy groups and marked singularit…

This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…

The middle homology of the Milnor fiber of a quasihomogeneous polynomial with an isolated singularity is a ${\mathbb Z}$-lattice and comes equipped with an automorphism of finite order, the integral monodromy. Orlik (1972) made a precise…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

We give a complete classification of analytic equivalence of germs of parametric families of systems of complex linear differential equations unfolding a generic resonant singularity of Poincare rank 1 in dimension $n = 2$ whose leading…

Mirror symmetry predicts an action by the fundamental group of a conjectural stringy K\"ahler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space is understood, but constructing the…

For a germ of a quasihomogeneous function with an isolated critical point at the origin invariant with respect to an appropriate action of a finite abelian group, H. Fan, T. Jarvis, and Y. Ruan defined the so-called quantum cohomology…

We give essentially unique ``normal forms'' for germs of a holomorphic vector field of the complex plane in the neighborhood of an isolated singularity which is a p:q resonant-saddle. Hence each vector field of that type is conjugate, by a…

Associated to an abelian variety over a number field are several interesting and related groups: the motivic Galois group, the Mumford-Tate group, $\ell$-adic monodromy groups, and the Sato-Tate group. Assuming the Mumford-Tate conjecture,…

Given a Kahler group, we study the set of homomorphisms from this group to the mapping class group which can be realized as the monodromy of a holomorphic family of curves.

This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Building off of prior work of the authors, we show that the…

We show a natural relation between the monodromy formula for focus-focus singularities of integrable Hamiltonian systems and a formula of Duistermaat-Heckman, and extend the main results of our previous note on focus-focus singularities…

Motivic and topological zeta functions are singularity invariants, mainly associated to a function $f$ and a top differential form $\omega$ on a smooth variety. When $\omega$ is the standard form $dx_1\wedge \dots \wedge dx_n$ on affine…

We prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class group of the Milnor fiber, provided the singularity is not a…

Understanding how singularities behave under small perturbations is a central theme in singularity theory. In this paper we establish sufficient conditions for families of analytic function-germs on a germ of a complex analytic space to…

The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by Fendleyet al. that for some rectangular grids, with…

We study the Euler characteristic of the real Milnor fibres of a real analytic map, using a relation between complex monodromy and complex conjugation. We deduce the result of Coste and Kurdyka that the Euler characteristic of the link of…

We prove an automatic convergence theorem for holomorphic modular forms on tube domains. The argument works in some generality, and covers in particular the case of orthogonal groups, symplectic groups, unitary and quaternion unitary…

Let $\A$ be an arrangement of affine lines in $\C^2,$ with complement $\M(\A).$ The (co)homo-logy of $\M(\A)$ with twisted coefficients is strictly related to the cohomology of the Milnor fibre associated to the conified arrangement,…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

We study a class of $\Z^{d}$-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of $\Z^{d}$. We prove that any measurable factor map and even…