Related papers: The monodromy representation and twisted period re…

We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: t\^ete-\`a-t\^ete graphs and twists. We completely characterize mapping…

Computations based on explicit 4-periodic resolutions are given for the cohomology of the finite groups G known to act freely on S^3, as well as the cohomology rings of the associated 3-manifolds (spherical space forms) M = S^3/G. Chain…

We investigate the differential system with affine Weyl group symmetry of type A^{(1)}_4 and construct a space which parametrizes all meromorphic solutions of it. To demonstrate our method based on singularity analysis and affine Weyl group…

Given an arrangement of hyperplanes in $\P^n$, possibly with non-normal crossings, we give a vanishing lemma for the cohomology of the sheaf of $q$-forms with logarithmic poles along our arrangement. We give a basis for the ideal $\cal J$…

We prove that over totally real fields, the $p$-adic Galois representations attached to non-self-dual regular algebraic cuspidal automorphic representations of $\mathrm{GL}(4)$ are irreducible. We then develop the theory of extra-twists in…

Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a…

A general method for computing irreducible representations of Weyl groups and Iwahori-Hecke algebras was introduced earlier by the first author. The representations of the algebras of types $A_n$, $B_n$, $D_n$ and $G_2$ were computed and it…

We study the iterated limit of a quaternary of means of four terms through the period map from the family of cyclic fourfold coverings of the complex projective line branching at six points to the three-dimensional complex ball…

Given a group $G$ of automorphisms of a matroid $M$, we describe the representations of $G$ on the homology of the independence complex of the dual matroid $M^*$. These representations are related with the homology of the lattice of flats…

Tetrahedron equation is a three dimensional analogue of the Yang-Baxter equation. It allows a formulation in terms of the Coxeter group $A_3$. This short note includes miscellaneous remarks on the generalizations along $B_3, C_3, F_4$ and…

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…

We study the representability of sets that admit extended formulations using mixed-integer bilevel programs. We show that feasible regions modeled by continuous bilevel constraints (with no integer variables), complementarity constraints,…

The $N=4$ SU(2)$_k$ superconformal algebra has the global automorphism of SO(4) $\approx$ SU(2)$\times$SU(2) with the {\it left} factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by…

Let $G$ be a split group of type $F_4$ defined over a number field. We study the square-integrable automorphic representations of $G$ that can be realized as leading terms of degenerate Eisenstein series associated to various maximal…

This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…

We consider the GF$(4)$-representable matroids with a circuit-hyperplane such that the matroid obtained by relaxing the circuit-hyperplane is also GF$(4)$-representable. We characterize the structure of these matroids as an application of…

In this paper, we determine the dimensions of the Hochschild cohomology groups of some self-injective special biserial algebra whose Grothendieck group is of rank $4$. This result provides us with a negative answer to Happel's question in…

We study the problem of computing the isolated regular solutions of a system \((f_1,\ldots,f_n)\) of \(n\) polynomial equations in \(n\) variables \((X_1, \dots, X_n)\) over a field of characteristic zero \(k\). We focus on systems with a…

We derive relations for a certain class of terminating ${}_4F_3(4)$ hypergeometric series with three free parameters. The invariance group composed of these relations is shown to be isomorphic to the symmetric group $S_3$. We further study…