The PIMS Postdoctoral Fellow Seminar: Abbas Maarefparvar

  • Date: 03/06/2024
Abbas Maarefparvar, ULethbridge



On Pólya groups of Number Fields


Number fields and their ideal class groups are two main objects in al- gebraic number theory. There are specific subgroups of ideal class groups generated by Bhargava’s generalized factorial ideals, called Pólya groups. Number fields with trivial Pólya groups, called Pólya fields whose study dates back to works of George Pólya and Alexander Ostrowski, in 1919, on ring of integer-valued polynomials, or even more classically back at the time of Hilbert in terms of Galois action on ideal class groups. Pólya fields encompass all number fields with class number one, and their classification of a specific degree has recently become an active research subject in algebraic number theory. In this talk, I briefly review some results in the literature concerning Pólya fields and Pólya groups, including the ones obtained in my research works, and then present some new approaches to these notions.


Speaker biography: Abbas Maarefparvar got his Ph.D. in 2018 under the supervision of Professor Ali Rajaei at the Tarbiat Modares University, Tehran, Iran. From 2018 to 2019, he was a researcher in cryptography at the Research Center for Development of Advanced Technologies, Tehran, Iran. For three years, from 2020 to 2023, he was a postdoctoral fellow at the Institute for Research in Fundamental Sciences (IPM), Tehran, Iran. Currently, he is a PIMS postdoctoral fellow under the supervision of Professor Amir Akbary at the University of Lethbridge. His main research area lies in algebraic number theory, especially the local-global class field theory, the Galois cohomology of number fields, and the arithmetic of elliptic curves.



This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series

Other Information: 

This seminar takes places across multiple time zones: 9:30 AM Pacific/ 10:30 AM Mountain / 11:30 AM Central


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See past seminar recordings on MathTube. 


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