Payman Eskandari

Assistant Professor
Department of Mathematics and Statistics
University of Winnipeg
email: p.eskandari@uwinnipeg.ca

CV

Research

My research interests are in number theory and algebraic geometry. Some of the keywords that describe my research are mixed motives and their periods, tannakian formalism, motivic Galois groups, Mumford-Tate groups, Hodge theory, and algebraic cycles.

Publications

(Note that the published versions might be slightly different from the versions posted here.)

  1. An integrable connection on the configuration space of a Riemann surface of positive genus, C. R. Math. Acad. Sci. Paris, Vol 356, no. 3, pages 312-315 (2018) pdf
  2. Quadratic periods of meromorphic forms on punctured Riemann surfaces, in Geometry, Algebra, Number Theory, and Their Information Technology Applications, edited by A. Akbary and S. Gun, Springer Proceedings in Mathematics and Statistics, Vol. 251, 2018, pages 183-205 pdf
  3. Algebraic cycles and the mixed Hodge structure on the fundamental group of a punctured curve, Mathematische Annalen, Vol. 375, pp 1665-1719 (2019) pdf
  4. (with Kumar Murty) On the harmonic volume of Fermat curves, Proc. Amer. Math. Soc. 149 (2021), no. 5, 1919-1928 pdf
  5. (with Kumar Murty) On Ceresa cycles of Fermat curves, Journal of Ramanujan Mathematical Society, Volume 36, No. 4 (2021) 363-382 pdf
  6. (with Kumar Murty) The fundamental group of an extension in a Tannakian category and the unipotent radical of the Mumford-Tate group of an open curve, Pacific Journal of Mathematics, Vol. 325 (2023), No. 2, 255-279 pdf
  7. (with Kumar Murty) On unipotent radicals of motivic Galois groups, Algebra & Number Theory, Vol. 17 (2023), No. 1, 165-215 pdf
  8. (with Kumar Murty) The unipotent radical of the Mumford-Tate group of a very general mixed Hodge structure with a fixed associated graded, preprint pdf (arXiv:2201.05713) Note: After writing the paper we found out that a much shorter proof of a stronger version of the main result can be given using the characterization of Mumford-Tate groups in terms of the Deligne torus (which is also valid in the mixed setting by a result in Green-Griffiths-Kerr's book on Mumford-Tate groups). So in its current form, this paper is not for publication.
  9. On endomorphisms of extensions in tannakian categories, Bulletin of the Australian Mathematical Society, Published online 2023:1-12. doi:10.1017/S0004972723001090 pdf
  10. On blended extensions in filtered tannakian categories and motives with maximal unipotent radicals, submitted pdf (revised version of arXiv:2307.15487)

Thesis

Some slides

These are the slides of some recent talks. Please beware of typos and check the results with the papers!

Current activities

I help to organize the Fields Number Theory Seminar (at the Fields Institute). For the 2023-2024 edition of the seminar, please see here.

Teaching

Current courses (University of Winnipeg)

All courses are run through Nexus .

Past courses (University of Winnipeg)

Past courses (University of Toronto)