Related papers: Gauss-Manin systems, Brieskorn lattices and Froben…
In this paper, we define a set of good basic invariants for a finite complex reflection group under certain conditions. We show that a set of good basic invariants for a finite real reflection group gives a set of the flat invariants…
Taking the St\"uckelberg Lagrangian associated with the abelian self-dual model of P.K. Townsend et al as a starting point, we embed this mixed first- and second-class system into a pure first-class system by following systematically the…
It is expected that the periodic cyclic homology of a DG algebra over the field of complex numbers (and, more generally, the periodic cyclic homology of a DG category) carries a lot of additional structure similar to the mixed Hodge…
In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
We introduce new techniques to study the differential complexes associated to tube structures on $M \times \mathbb{T}^m$ of corank $m$, in which $M$ is a compact manifold and $\mathbb{T}^m$ is the $m$-torus. By systematically employing…
We propose a simple method for the computation of the flat coordinates and Saito primitive forms on Frobenius manifolds of the deformations of Jacobi rings associated with isolated singularities. The method is based on using a conjecture…
Generalizing a construction presented in [3], we show that the orbit space of $B_2$ less the image of coordinate lines under the quotient map is equipped with two Dubrovin-Frobenius manifold structures which are related respectively to the…
We present a brief account of a series of recent results on twisted and untwisted elliptic Calogero-Moser systems, and on their fundamental role in the Seiberg-Witten solution of gauge theories with one massive hypermultiplet in the adjoint…
The Gauss-Manin equations are solved for a class of flat-metrics defined by Novikov algebras, this generalizing a result of Balinskii and Novikov who solved this problem in the case of commutative Novikov algebras (where the algebraic…
We prove the following theorems: 1) The Laurent expansions in epsilon of the Gauss hypergeometric functions 2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z), 2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z),…
In 2001, S. Barannikov showed that the Frobenius manifold coming from the quantum cohomology of the complex projective space is isomorphic to the Frobenius manifold attached to some Laurent polynomial. The purpose of this thesis is to…
The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…
This note defines a family of Laurent polynomials (indexed in the rational projective line) which generalize the Markoff numbers and relate to the character variety of the one-cusped torus. We describe which monomials appear in each…
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau--Ginzburg orbifolds. Namely, for the pairs $(f,G)$, where $f$…
The Gauss-Bonnet theorem for a polyhedron (a union of finitely many compact convex polytopes) in $n$-dimensional Euclidean space expresses the Euler characteristic of the polyhedron as a sum of certain curvatures, which are different from…
In this paper, we examine the unimodality and strict unimodality of certain formal bivariate Laurent series with non-negative coefficients. We show that the sets of these formal bivariate Laurent series form commutative semirings under the…
The motivic nearby fiber is an invariant obtained from degenerating a complex variety over a disc. It specializes to the Euler characteristic of the original variety but also contains information on the variation of Hodge structure…
In this paper two things are done. First it is shown how a four dimensional gauged Wess-Zumino-Witten term arises from the five dimensional Einstein-Hilbert plus Gauss-Bonnet lagrangian with a special choice of the coefficients. Second, the…
We construct an analogue of the classical descent theory of Colliot-Th\'el\`ene and Sansuc in which algebraic tori are replaced with finite supersolvable groups. As an application, we show that rational points are dense in the Brauer-Manin…