Spring 2025
Time & Location: All talks are on TBA in Gibson Hall 126A at 1:00 P.M. unless otherwise noted.
Organizer: Mahir Can
October 25
Title: Reed-Solomon Codes in the Uniform Tree Metric
Dillon Montero - Tulane University
Abstract: The classical theory of error-correcting codes primarily uses the Hamming metric to measure distances. Within this framework, Maximum Distance Separable (MDS) codes are highly valued due to their optimal parameters, enabling the correction of the maximum number of errors for a given code rate. In 1997, Rosenbloom and Tsfasman introduced the m-metric codes (now known as NRT metric codes), identifying analogs of Reed-Solomon codes that still possess the MDS property. Later, Skriganov provided an explicit construction of these codes using Hasse derivatives.
In this talk, we will introduce and discuss our analogs of Reed-Solomon codes in a related context, also employing Hasse derivatives for our construction.
This is joint work with Mahir Bilen Can.
Location: Gibson Hall 126A
Time: 1:00
November 1
Title: Relative Ideals & Unipotent Numerical Monoids
Naufil Sakran - Tulane University
Abstract: In earlier work, we introduced unipotent numerical monoids as complement finite submonoids within a finitely generated submonoids in the unipotent linear algebraic group $(U(n,\mathbb{N})$. This talk further develops the theory by defining relative ideals and their associated invariants. We will introduce irreducible relative ideals and classify their structure with respect to symmetric and pseudo-symmetric ideals. Additionally, we will introduce the notion of reduction number, blowup, and the Arf closure of an ideal, and study the structure of a unipotent numerical monoid with respect to them.
Location: Gibson Hall 126A
Time: 1:00
November 15
Title: An Algebraic-Combinatorial Construction of QC-LDPC Codes
Henry Chimal-Dzul - UT San Antonio
Abstract: An Algebraic-Combinatorial Construction of QC-LDPC Codes
Abstract: Quasi-Cyclic LDPC (QC-LDPC) codes constitute one of the most attractive family of linear codes. This is because of their compact representation, existence of efficient encoding and decoding algorithms, rich algebraic structure and their excellent performance when compared to random LDPC codes. These are some of the reasons why QC-LDPC codes now appear in many industry standards, including those developed by the Consultative Committee for Space Data System, NASA deep-space explorations, Digital Video Broadcast, IEEE 802.11a, and the 5G New Radio Mobile communication standard. One of the required properties that a QC-LDPC code must have for all these applications is that their Tanner graph should not have a small girth (often 4 or 6). In this talk we will discuss the problem of designing QC-LDPC codes with Tanner graphs having girth at least 6. To this order, we will present an algebraic representation of QC-LDPC codes from which we will derive combinatorial problems to design them.
Location: Gibson Hall 126A
Time: 1:00
Special Algebraic Geometry
November 20
Title: Lower Bounding the Gromov–Hausdorff Distance on Manifolds and Graphs
Majhi Sushovan - George Washington University DC
Abstract: The Gromov–Hausdorff distance between two abstract metric spaces provides a (dis)-similarity measure quantifying how far the two metric spaces are from being isometric. Although the inception of the distance was due to M. Gromov in the context of hyperbolic groups, it has recently been shown to provide a robust theoretical framework for shape and dataset comparison. Consequently, the computational aspects and various bounds on the Gromov–Hausdorff distance are receiving a lot of attention from both applied and theoretical communities. In this talk, I give an overview of the Gromov–Hausdorff distance, delineating its relation to the well-known Hausdorff distance. The main focus of the talk is to present interesting lower bounds on the former by a constant multiple of the latter on interesting spaces like the circle, closed Riemannian manifolds, and metric graphs.
Location: Gibson Hall 325
Time: 2:00
