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We present a method for generating 2-D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological ch...
Quantization of bending deformations of polygons in E3,hypergeometric in tegrals and the Gassner representation.
In Artin's work on algebraic spaces and algebraic stacks [A2], [A3], a crucial ingredient is the use of his approximation theorem to prove the algebraizability of formal deformations under quite gene...
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of...
We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of K¨ahler manifolds. As applications, we present a construction of globally convergent power ser...
We consider the isometric deformation problem for oriented non simply connected immersed minimal surfaces $f:M \to S^{4}$. We prove that the space of all isometric minimal immersions of $M$ into $S^{4...
Abstract: We define a family of 3-Calabi-Yau algebras by potentials. For some of these algebras, we explicitly compute the Hochschild homology with the help of Poisson homology. The point is that the ...
Abstract: Let X be a Hyperk\"{a}hler variety deformation equivalent to the Hilbert square of points on a K3 surface and let f be an involution preserving the symplectic form. We prove that the fixed l...
Abstract: We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schem...
Abstract: Let $Y \to B$ be a relative smooth projective curve over an affine integral base scheme $B$ of positive characteristic. We provide for all prime characteristics example classes of vector bun...
Abstract: Let $(\mathcal {X},\Omega)$ be a closed polarized complex manifold, $g$ be an extremal metric on $\mathcal X$ that represents the K\"ahler class $\Omega$, and $G$ be a compact connected subg...
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited by showing that the quadratic Poisson structure underlying its integrability structure is ju...
In [L-Y5] (D(6): arXiv:1003.1178 [math.SG]) we introduced the notion of Azumaya C1-manifolds with a fundamental module and morphisms therefrom to a complex manifold. In the current sequel, we use this...
In memory of Marcos Moshinsky, who promoted the algebraic study of the har-monic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed.
We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields.

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