Related papers: A geometric proof of the classification of complex…
We give an explicit description for the nerve of crossed module of categories.
For finite q, we classify the countable, descendant-homogeneous digraphs in which the descendant set of any vertex is a q-valent tree. We also give conditions on a rooted digraph G which allow us to construct a countable…
We study thick subcategories of derived categories of gentle algebras. Any thick subcategory of a derived category of a gentle algebra is generated by a set of string objects or a set of band objects. We show the thick subcategories…
In this article, we classify all the Hermitian metrics on a complex product manifold with nonpositive holomorphic bisectional curvature. It is a generalization of a result by Zheng.
We suggest a geometric visualization of the process of constructing a triangle with prescribed bisectors that makes the existence of such a triangle geometrically evident.
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.
This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.
We consider the classification problem for several classes of countable structures which are "vertex-transitive", meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that…
Crossed products whose unit group is locally solvable
We give bounds for the module sectional category of products of maps which generalise a theorem of Jessup for Lusternik-Schnirelmann category. We deduce also a proof of a Ganea type conjecture for topological complexity. This is a first…
We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac-Moody algebra. As byproducts, we obtain a geometric realization of Lusztig's canonical bases of these representations as well…
In this article, we rigorously establish the consistency of generalized cross-validation as a parameter-choice rule for solving inverse problems. We prove that the index chosen by leave-one-out GCV achieves a non-asymptotic, order-optimal…
In the present work, we continue the research initiated in the preprint: V. G. Bardakov, A. L. Iskra, Orders of products of horizontal class transpositions, arXiv:2409.13341, and related to S. Kohl's question on the orders of products of…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
We give a geometric approach to the proof of the $\lambda$-lemma. In particular, we point out the role pseudoconvexity plays in the proof.
For each graph, we construct a bigraded chain complex whose graded Euler characteristic is a version of the Tutte polynomial. This work is motivated by earlier work of Khovanov, Helme-Guizon and Rong, and others.
We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that…
We classify the thick subcategories of discrete derived categories. To do this we introduce certain generating sets called arc-collections which correspond to configurations of non-crossing arcs on a geometric model. We show that every…
In this note, we present a relationship between Lelong numbers and complex singularity exponents. As an application, we obtain a new proof of Siu's semicontinuity theorem for Lelong numbers.