Farshid Hajir
Research Page

Research Interests

My main area of study is Number Theory. I am particularly interested in units and class groups of number fields; extensions of global fields with restricted ramification; the arithmetic of elliptic curves; and special values of L-functions.   My other academic interests include coding theory, cryptography, history of mathematics, mathematics education at all levels, and communication of mathematics and its role in society for the public at large.
Curriculum Vitae

Some Preprints & Publications

Prime decompositon and the Iwasawa mu-invariant, F. Hajir and C. Maire, submitted.

Invariant factors of ideal class groups in towers of number fields, F. Hajir and C. Maire, submitted.

(An older version of) Heuristics for $p$-class towers of imaginary quadratic fields, joint with Nigel Boston and Michael Bush. To appear in Math. Annalen.

Primes of prescribed congruence class in short intervals, appeared in Integers.

Fundamental Groups of Number Fields Extended abstract of a talk given at the Oberwolfach Workshop: Explicit Methods in Number Theory, published in Oberwolfach Reports.

Non-abelian Cohen-Lenstra heuristics for imaginary quadratic fields, Reporting on joint work with Nigel Boston and Michael Bush, Extended abstract of a talk given at the Oberwolfach Workshop on Low-dimensional topology and number theory, published in Oberwolfach Reports.

Modular Forms and Elliptic Curves over the Field of Fifth Roots of Unity, joint with Paul Gunnells and Dan Yasaki, J. Exp. Math.

Ramification in Iterated Towers for rational functions, joint with John Cullinan.

Algebraic Properties of a family of Jacobi Polynomials, joint with John Cullinan and Elizabeth Sell.

Finitely Ramified Iterated Extensions, joint with Wayne Aitken and Christian Maire, IMRN

Extensions of Number Fields with Wild Ramification of Bounded Depth, joint with Christian Maire, IMRN

Tame pro-p Galois groups: a survey of recent work, Proceedings of the 9th conference on Algebraic Geometry and Coding Theory, Luminy.

On the Galois Group of Generalized Laguerre Polynomials.

Algebraic Properties of a Family of Generalized Laguerre Polynomials

Specializations of One-parameter Families of Polynomials, joint with Siman Wong, Ann. Inst. Fourier (Grenoble)