Research

Research interests

• Homological algebra
• Abstract homotopy theory
• Category theory
• Model categories

Current work

I am working on a model-categorical generalization of the Dold–Kan correspondence for crossed simplicial groups.

Preprints & papers

A Model Categoric Equivalence for Crossed Simplicial Modules (joint with Atabey Kaygun)
in preparation

Research overview

My research lies at the intersection of homological algebra, category theory, and homotopical algebra, with a particular focus on categorical and model-categorical generalizations of classical Dold-Kan correspondence.

A central theme of my work is the interaction between simplicial methods and algebraic structures, especially through equivalences that allow one to pass between homological and simplicial data in a controlled and conceptual way.

Main research directions

Dold–Kan type correspondences

The classical Dold–Kan correspondence establishes an equivalence between simplicial abelian groups and non-negatively graded chain complexes. My work investigates how this phenomenon extends beyond the classical setting.

In particular, I study Dold–Kan type equivalences for crossed simplicial groups, where additional symmetry leads to enriched algebraic and homotopical structures. These extensions are developed not only at the categorical level but also within a model-categorical framework, allowing for homotopically meaningful comparisons.

Model categories and homotopical algebra

A significant part of my research concerns the use of model category structures to formalize and transfer homotopical information.

I am interested in:

• transferring model structures along adjunctions,
• understanding when categorical equivalences lift to Quillen equivalences,
• and analyzing homotopical invariants arising from simplicial and crossed simplicial objects.

These techniques play a key role in establishing robust versions of generalized Dold–Kan theorems.

Simplicial and crossed simplicial structures

Simplicial objects provide a unifying language for homological and homotopical constructions. I study simplicial and crossed simplicial groups as algebraic models encoding both homological data and symmetry.

This perspective connects naturally with areas such as cyclic and dihedral homology, and offers a conceptual framework for organizing related invariants.

Future directions

Possible future directions include:

• applications to cyclic and higher Hochschild-type homology,
• interactions with higher category theory,
• and further generalizations to enriched or higher-dimensional settings.

Notes

Informal notes, expository material, and exploratory ideas related to these topics may appear here over time.