## Atabey Kaygun

Associate Professor
Istanbul Technical University, Istanbul

## A description of my research

### Mathematics

I do homological and homotopical algebra in the context of noncommutative geometry. You can find a detailed exposition of my past research, my present and future research interests in my research statement. Specifically I am interested in, Hopf equivariant cohomology theories, various flavors of Hochschild (co)homology, cyclic (co)homology and K-Theory. I am also intrested in abstract homotopical algebra, operads, PROPs and their algebras. For the visually inclined, I have a map of my slanted view of the noncommutative geometry landscape.

### Applied Statistics and History

As an ongoing project with Prof. Boğaç Ergene at University of Vermont, we investigate social mobility patterns in 18th Century Ottoman Empire. While he provided the historical context and the analysis of the results we obtained, I did the necessary data processing and performed the statistical analyses needed for the particular data set Prof. Ergene painstakingly generated from historical sources and archives. We wrote four papers together so far, with more to come in the future.

## Articles and Preprints

You can download the an abridged version of the following list from here.

### Mathematics

The asymptotic Connes-Moscovici characteristic map and the index cocycles [with S. Sütlü]

[arXiv]

Hochschild Cohomology of Reduced Incidence Algebras [with S. Sütlü and M. Kanuni] Journal of Algebra and Its Applications, [DOI: 10.1142/S0219498817501687]

Hopf-dihedral (co)homology and $L$-theory [with S. Sütlü] (Accepted for publication at the Journal of Noncommutative Geometry).

A characteristic map for compact quantum groups [with S. Sütlü] Journal of Homotopy and Related Structures, [DOI: 10.1007/s40062-016-0138-y]

Hopf-cyclic Cohomology of Quantum Enveloping Algebras [with S. Sütlü] Journal of Noncommutative Geometry; Volume 10, Issue 2, 2016, pp. 429–446 [DOI: 10.4171/JNCG/238]

Global Dimensions of Some Artinian Algebras [with M. Kanuni]

[arXiv]

Finite closed coverings of compact quantum spaces. [With P.M. Hajac and B. Zielinski] Operator Algebras and Quantum Groups Banach Center Publ. 98 (2012) P.M. Soltan and W. Pusz Eds.

Quantum projective space from Toeplitz cubes. [With P.M. Hajac and B. Zielinski] Journal of Noncommutative Geometry, Volume 6, Issue 3, 2012, pp. 603–621

Jacobi-Zariski exact sequence for Hochschild homology and cyclic (co)homology, Homology, Homotopy and Applications, Vol. 14 (2012), No. 1, pp.65-78.

A survey on Hopf-cyclic cohomology and Connes-Moscovici characteristic map. Contemporary Mathematics, Vol. 546 pp. 171-179, (2011) Proceedings of Henrifest.

[journal]

Uniqueness of pairings in Hopf-cyclic cohomology, Journal of K-Theory, Vol. 6 (2010), No. 1, pp.1-21

Products in Hopf-cyclic cohomology, Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.115-133.

The Universal Hopf cyclic theory, Journal of Noncommutative Geometry, Vol. 2 (2008), No. 3, pp. 333-351.

Bivariant Hopf cyclic cohomology. [With M. Khalkhali], Communications in Algebra, Vol. 38 (2010), No. 7, pp 2513-2537.

Hopf-Hochschild (co)homology of module algebras, Homology, Homotopy and Applications, Vol. 9 (2007), No. 2, pp.451-472.

Hopf modules and noncommutative differential geometry. [With M. Khalkhali], Letters in Mathematical Physics, Vol. 76 *(2006) No. 1.

Excision in Hopf cyclic cohomology. [With M. Khalkhali], K-Theory, Vol. 37 (2006), No. 1-2.

Bialgebra cyclic homology with coefficients, K-Theory, Vol. 34 (2005), No. 2.

[journal]

Loday-Quillen-Tsygan theorem for coalgebras

[arXiv]

Bialgebra cyclic homology with coefficients, Part II

[arXiv]

Bialgebra cyclic homology with coefficients, Part I.

[arXiv]

### Applied Statistics and History

Log-linear Analysis of Intergenerational Mobility in Eighteenth-Century Ottoman Anatolia. [With B.A. Ergene] Journal of the Economic and Social History of the Orient, Vol. 57, (2014), pp 669-702.

[journal]

Temporal Analysis of Wealth and Inequality in Eighteenth-Century Ottoman Empire [With B.A. Ergene and M.M. Coşgel] Continuity and Change, Volume 28, Issue 01 (May 2013), pp 1-­26.

[journal]

Spouse Selection and Marital Mobility in the Ottoman Empire: Observations from Eighteenth-Century Kastamonu. [With B.A. Ergene] Historical Methods: A Journal of Quantitative and Interdisciplinary History, Volume 45, Issue 1, 2012.

[journal]

Intergenerational Mobility in the Ottoman Empire: Observations from Eighteenth-Century. [With B.A. Ergene] The History of the Family, Volume 16, Issue 1, 15 March 2011, Pages 30-46.

[journal]