Fall 2026
Time & Location: All talks are on Tuesdays in Richardson Building 108 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
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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
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September 15, 2026
Graduate Student Colloquium
Title: Enter Comparison of Protocols for Private Set Intersection and 2-Party Secure Computation
Speaker: Ahmed Khan - Math department
Abstract: It's a comparative study of various cryptographic protocols designed for 2-Party Secure Computation (2PSC) and, more precisely, for Private Set Intersection (PSI), with a particular focus on their implementation and performance under malicious adversary models. Among the protocols explored, the OPA-based and PSZ protocols were selected for detailed analysis due to their strong security guarantees and efficiency. Both protocols were implemented using Python and subjected to empirical testing. The OPA-based protocol employs algebraic constructions such as Oblivious Linear Function Evaluation (OLE), its enhanced version OLE+, and Oblivious Polynomial Addition (OPA), whereas the PSZ protocol leverages modern Oblivious Transfer (OT) extensions and Pseudo-Random Functions (PRFs). The study evaluates these protocols in terms of computational cost and communication overhead. The results offer a practical perspective on using such cryptographic primitives in real-world applications.
Time: 3:30 PM
Location: Richardson Building 108
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September 22, 2026
Graduate Student Colloquium
Title: Connections on Smooth Complex Vector Bundles
Speaker: Harsh Mishra - Tulane Math Department
Abstract: In this talk, we will survey the sheaf theoretic treatment of connections on smooth complex vector bundles. Here we explain the main tools to come out with a sensible definition of connection in full generality. Then we go on to see some of the properties of connections such as its local description and its transformation under a change of frame.
Time: 3:30 PM
Location: Richardson Building 108
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