Atabey Kaygun

Assistant Professor
Bahçeşehir University, Istanbul

News and other bits of information

Prof. Müge Kanuni at Boğaziçi University and I organized a workshop here in Istanbul titled Noncommutative Geometry Days in Istanbul. We would like to thank all of the participants and speakers once again. Those who are interested can find our workshop picture at our workshop webpage. We are in the planning stages of another workshop in July 2011 with the same title. So, if you would like to join, please drop me an e-mail.

Brief description of my research

Mathematics

You can find a detailed exposition of my past research, my present and future research interests in my research statement. And for the visually inclined, I have a map of my slanted view of the noncommutative geometry landscape. Very shortly, I can describe my research interest as homological and homotopical algebra in the context of noncommutative geometry.  Specifically I am interested in

  • Hopf equivariant cohomology theories.
  • Various flavors of Hochschild (co)homology, cyclic (co)homology and K-Theory
  • Homological and homotopical invariants of (co)associative (co)algebras; Lie, Leibniz, Poisson (co)algebras; bialgebras and Hopf algebras.
  • Operads, PROPs and their algebras.

Applied Statistics and History

Recently, with Prof. Boğaç Ergene at University of Vermont, we looked at social mobility patterns in 18th Century Ottoman Empire. While he provided the historical context and the analysis of the results we obtained, I performed the necessary statistical analyses needed for the particular data set Prof. Ergene painstakingly generated from historical sources and archives. In the process we used variety of tools such as as R, perl and awk to process and analyze the data. We wrote two papers together so far, with more to come in the future.

Articles and preprints

Here is a printable list of my publications with abstracts. All of my papers are available below for download.

Mathematics

  1. Quantum projective space from Topelitz cubes (with P.M. Hajac and B. Zielinski), arXiv:math/1008.0673. [SUBMITTED]
  2. Finite closed coverings of compact quantum spaces (with P.M. Hajac and B. Zielinski), arXiv:math/0901.0074. [SUBMITTED}
  3. Uniqueness of pairings in Hopf-cyclic cohomology, Journal of K-Theory, Vol. 6 (2010), No. 1, pp.1-21
    also available at arXiv:math/0808.3202v1
  4. Products in Hopf-cyclic cohomology, Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.115-133,
    also available at arXiv:0710.2559v1.
  5. The Universal Hopf cyclic theory, Journal of Noncommutative Geometry, Vol. 2 (2008), No. 3, pp. 333-351,
    also available at arXiv:math/0609311v2.
  6. Bivariant Hopf cyclic cohomology (with M. Khalkhali), Communications in Algebra, Vol. 38 (2010), No. 7, pp 2513 - 2537,
    also available at arXiv:math/0606341v1.
  7. Hopf-Hochschild (co)homology of module algebras, Homology, Homotopy and Applications, Vol. 9 (2007), No. 2, pp.451-472,
    also available at arXiv:math/0606340v2.
  8. Hopf modules and noncommutative differential geometry (with M. Khalkhali), Letters in Mathematical Physics, Vol. 76 (2006) No. 1,
    also available at arXiv:math/0512031v2.
  9. Excision in Hopf cyclic cohomology (with M. Khalkhali), K-Theory, Vol. 37 (2006), No. 1-2,
    and also available at arXiv:math/0511026v1.
  10. Bialgebra cyclic homology with coefficients, K-Theory, Vol. 34 (2005), No. 2.
  11. Loday-Quillen-Tsygan theorem for coalgebras, arXiv:math/0411661v1.
  12. Bialgebra cyclic homology with coefficients, Part II, arXiv:math/0409191v1.
  13. Bialgebra cyclic homology with coefficients, Part I, arXiv:math/0408094v3.

Applied Statistics and History

  1. Partner choice in the Ottoman Empire: Observations from Eighteenth-Century. (With B.A. Ergene) [SUBMITTED]
  2. Intergenerational Mobility in the Ottoman Empire: Observations from Eighteenth-Century. (With B.A. Ergene) [SUBMITTED]