Fall 2026
Time & Location: All talks are on Tuesdays in _______ at 3:30 PM unless otherwise noted.
Organizer: Moslem Uddin; Joshua Agbomola
September 01, 2026
Graduate Student Colloquium
Title: Enumerative Geometry and Tevelev Degrees
Speaker: Naufil Sakran - Tulane Math Department
Abstract: Recently, enumerative geometry has received a lot of attention. In my talk, I will give an overview of this topic and discuss my current work on counting maps from a genus g curve to projective space \mathbb{P}^n.
Time: 3:00 PM
Location: Richardson Building 108
___________
September 08, 2026
Graduate Student Colloquium
Title: Factorization of x^m − 1 over Finite Fields
Speaker: Usama Muhammad - Math department
Abstract: This talk explores the factorization of the polynomial \(x^m-1\) over finite fields, a classical problem that connects finite field theory, polynomial factorization, and field extensions. We begin with a brief introduction to finite fields and their basic properties, including the role of extension fields and primitive elements. We then introduce cyclotomic cosets and show how they organize the roots of \(x^m-1\), revealing the structure of roots of unity in finite field extensions. Using minimal polynomials of elements in finite field extensions, we derive an explicit factorization formula. The theory is illustrated through concrete examples, including the factorization of \(x^{13}-1\) over \(\mathbb F_3\) using a primitive element of the extension field \(\mathbb F_{27}\), and the contrasting factorizations of \(x^3-1\) over \(\mathbb F_2\), where it does not split completely, and over \(\mathbb F_4\), where it splits completely. We conclude by noting that the factorization of \(x^m-1\) has important applications in algebraic coding theory, particularly in the construction of cyclic codes—an area we will explore further in future presentations.
Time: 3:30 PM
Location: Richardson Building 108
___________