Research Seminars: Graduate Student Colloquium

Fall 2025

Time & Location: All talks are on Tuesdays in _______ at 3:30PM unless otherwise noted.
Organizer: Moslem Uddin; Joshua Agbomola

Archives

September 02

Title: Rosenbrock Time Integration for Proper Orthogonal Decomposition(POD) based Reduced-Order Modeling (POD-ROM) of Dynamical System
Moslem Uddin - Tulane University

Abstract: Proper Orthogonal Decomposition (POD) provides an efficient method for obtaining low-dimensional, physically meaningful models from high-dimensional dynamical systems. In this talk, we use the Brusselator reaction-diffusion system as a guide to demonstrate the mathematics behind and application of POD-based reduced-order modeling (POD-ROM). We discuss how to construct the POD basis from simulation data, highlight its optimality and interpretability, and show how it enables significant dimensionality reduction without sacrificing essential dynamics. Stable simulation of reduced-order systems is ensured by the incorporation of Rosenbrock-Wanner (ROW) time-stepping techniques. We discuss computational complexity, elucidating the distinction between offline (basis construction) and online (ROM evolution) costs, and show how mode selection affects physical fidelity, speed, and accuracy. The talk concludes with views on current directions, potential difficulties, and best practices in data-driven model reduction for complex systems.

Time: 3:30 pm
Location: Dinwiddie Hall DW-102

___________

September 09

Title: Tevelev Degrees for genus-zero curves in blowup of P^3 at a point.
Naufil Sakran - Tulane University

Abstract: In this talk, I would like to answer the following question:

Let $X$ denote the space of blow-up of $\mathbb{P}^3$ at a point. If we fix $n$-points, then how many genus 0 curves can be drawn on $X$ passing through the $n$-points?

The study of such questions lies in the field of enumerative geometry, and I would like to give a glimpse of this subject by answering the above question completely.

Time: Dinwiddle Hall 102
Location: 3:30 PM

___________

September 16

Title: Markov Chains and their Applications to Game State Modeling
Rebecca Kahler - Tulane University

Abstract: Markov Chains are (stochastic) processes where the probability of the next state depends solely on the current state (the past states don’t tell you anything about the next state). My talk will introduce Markov Chains, cover a few simple examples, and then we will use the processes to model simple games like Rock, Paper, Scissors.

Time: 3:30
Location: Dinwidie Hall 102

___________

September 23

Title: Generating Functions and Modular Forms
Peter Marcus - Tulane University

Abstract: A generating function is a series whose coefficients are a sequence of interest. They are one of the most important tools in analytic number theory. I will give an introduction to generating functions and talk about an example from my research, the generating function for k-regular partition numbers.

Time: 3:30 PM
Location: Dinwiddie Hall 102

___________

September 30

Title: TBA
Joshua Agbomola - Tulane University

Abstract: TBA