A. Kaygun

collaborators

8 papers

math.RA2026

Local Smith Profiles of Twisted Calabi--Yau Algebras

Atabey Kaygun

The matrix Hilbert series of a locally finite elementary twisted Calabi--Yau algebra is the inverse of a matrix polynomial. The Smith normal form of this polynomial over the power…

math.AT2026

Combinatorial Models for Linear Homotopy Theories

Atabey Kaygun

For a field $k$ of characteristic $0$ , we compare $k$ -linear chain complexes, semisimplicial vector spaces, augmented semisimplicial vector spaces, semicubical vector spaces, and a…

math.AT2026

Arboreal Objects and Their Homotopy Theory

Atabey Kaygun

We construct a category $\OrdFor$ as an arboreal extension of $I^_{epi} \subseteq I^$ , whose morphisms are ordered forests composed by grafting. We define a full functor $Ï…

math.AG2026

Geometric Rigidity in Moduli Stacks of Algebras

Atabey Kaygun

We study quadratic moduli schemes $X$ of algebra laws on a fixed vector space $W$ under the transport-of-structure action of $G L (W)$ on $H o m (W^{\otimes 2}, W)$ . We construct an intr…

math.RA2025

Geometry of Deformations via Incidence Varieties

Atabey Kaygun

We provide a unified geometric realization of the classical deformation complexes. We construct GL-equivariant bilinear incidence varieties whose diagonal slices recover the variet…

math.KT2025

Birational Equivalences and Generalized Weyl Algebras

Atabey Kaygun

We calculate suitably localized Hochschild homologies of various quantum groups and PodleÅ spheres after realizing them as generalized Weyl algebras (GWAs). We use the fact that e…