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The Fatou-Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to…
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and…
We obtain a generalization of the Kodaira-Morrow stability theorem for cosymplectic structures. We investigate cosymplectic geometry on Lie groups and on their compact quotients by uniform discrete subgroups. In this way we show that a…
A quasitoric manifold is a $2n$-dimensional compact smooth manifold with a locally standard action of an $n$-dimensional torus whose orbit space is a simple polytope. In this article, we classify quasitoric manifolds with the second Betti…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
We show there exists a rigid monoidal category formed out by quantum linear spaces with an additional structure, such that FRT bialgebras and corresponding rectangular generalizations are its internal coEnd and coHom objects, respectively.…
We make a generalization of the type C monomial space of a single variable, which was introduced in the construction of type C N-fold supersymmetry, to several variables. Then, we construct the most general quasi-solvable second-order…
We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.
We describe the singular locus of the compactification of the moduli space $R_{g,l}$ of curves of genus $g$ paired with an $l$-torsion point in their Jacobian. Generalising previous work for $l\le 2$, we also describe the sublocus of…
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…
We define a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the…
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…
In this paper, we prove that the Todd genus of a compact complex manifold $X$ of complex dimension $n$ with vanishing odd degree cohomology is one if the automorphism group of $X$ contains a compact $n$-dimensional torus $\Tn$ as a…
In this note we classify simply connected rationally elliptic compact toric orbifolds up to algebraic isomorphism.
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the Delzant polytope of a toric symplectic manifold.
We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The…
Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original…