相关论文: An algebro-geometric model for the configuration c…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to…
We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
In this paper we present the core of LoCo, a logic-based high-level representation language for expressing configuration problems. LoCo shall allow to model these problems in an intuitive and declarative way, the dynamic aspects of…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
We construct a configuration space model for a particular 2-colored differential graded operad encoding the structure of two $A_\infty$ algebras with two $A_\infty$ morphisms and a homotopy between the morphisms. The cohomology of this…
For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.
We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…
In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also…
We introduce framed formal curves, which are formal algebraic curves with boundary components parametrized by the punctured formal disk. We study the moduli space of nodal framed formal curves, which we endow with a logarithmic structure.…
In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.
We survey the field of model management and describe a new model management approach based on algebraic specification.
Cohomology of a compatible family of Lie algebroids defined on a family of transverse manifolds is defined. A sheaf of differential forms on a compatible family of Lie algebroids defined over regular open subsets of a simplicial complex is…
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…
We make an attempt to develop "noncommutative algebraic geometry" in which noncommutative affine schemes are in one-to-one correspondence with associative algebras. In the first part we discuss various aspects of smoothness in affine…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
Engineering safe and secure cyber-physical systems requires system engineers to develop and maintain a number of model views, both dynamic and static, which can be seen as algebras. We posit that verifying the composition of requirement,…
We construct a proper moduli space which is a Deligne-Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class…