Assistant Professor

Department of Mathematics and Statistics

University of Winnipeg

email: p.eskandari@uwinnipeg.ca

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.

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

- 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
- 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
- Algebraic cycles and the mixed Hodge structure on the fundamental group of a punctured curve, Mathematische Annalen, Vol. 375, pp 1665-1719 (2019) pdf
- (with Kumar Murty) On the harmonic volume of Fermat curves, Proc. Amer. Math. Soc. 149 (2021), no. 5, 1919-1928 pdf
- (with Kumar Murty) On Ceresa cycles of Fermat curves, Journal of Ramanujan Mathematical Society, Volume 36, No. 4 (2021) 363-382 pdf
- (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
- (with Kumar Murty) On unipotent radicals of motivic Galois groups, Algebra & Number Theory, Vol. 17 (2023), No. 1, 165-215 pdf
- (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 So in its current form, this paper is not for publication.
- On endomorphisms of extensions in tannakian categories, Bulletin of the Australian Mathematical Society, Published online 2023:1-12. doi:10.1017/S0004972723001090 pdf
- On blended extensions in filtered tannakian categories and motives with maximal unipotent radicals, submitted pdf (arXiv:2307.15487)
- Tannakian fundamental groups of blended extensions, preprint pdf (arXiv:2407.01379)

- Algebraic cycles, fundamental group of a punctured curve, and applications in arithmetic, PhD thesis, 2016 pdf

- Slides 1 (UBC-PIMS Colloquium, December 2022)
- Slides 2 (UWinnipeg Colloquium, Fall 2023)
- Slides 3 (Fields Institute, Winter 2024)
- Slides 4 (Fields Institute, Winter 2024)
- Slides 5 (ICERM, Brown University, Spring 2024)

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

All courses are run through Nexus .

- MATH-4202 Rings and Fields (Winter 2024)
- MATH-1103 Calculus I (Fall 2023)
- MATH-2202 Cryptography and Algebra (Winter 2023)
- MATH-4101 Complex Analysis (Winter 2023)
- MATH-1103 Calculus I (Fall 2022)

- Fall-Winter 2021-2022: MAT329 Concepts in Elementary Mathematics
- Fall-Winter 2020-2021: MAT329 Concepts in Elementary Mathematics
- Winter 2020: MATD01 Fields and Groups (UTSC campus) course webpage
- Winter 2020: MAT344 Intro to Combinatorics
- Fall 2019: MAT334 Complex Variables
- Summer 2019: MAT135 Calculus I
- Winter 2019: MAT247 Algebra II course webpage
- Fall 2018: MAT301 Groups and Symmetries course webpage (The course webpage includes a full set of lecture notes for a first course in group theory.)
- Summer 2018: MAT224 Linear Algebra II
- Winter 2018: MAT315 Intro to Number Theory
- Fall 2017: MAT327 Intro to Topology
- Winter 2017: MAT301 Groups and Symmetries
- Fall 2016: MAT224 Linear Algebra II
- Summer 2016: MAT401 Polynomial Equations and Fields
- Summer 2016: MAT224 Linear Algebra II (Mississauga campus)
- Winter 2016: MAT315 Intro to Number Theory (Mississauga campus)
- Fall 2015: MAT224 Linear Algebra II
- Summer 2015: MAT334 Complex Variables
- Winter 2015: MAT315 Intro to Number Theory (Mississauga campus)