Spring 2026
Time & Location: All talks are on Tuesdays in _______ at 3:30PM unless otherwise noted.
Organizer: Moslem Uddin; Joshua Agbomola
January 27, 2026
Graduate Student Colloquium
Title: Microscale flows around a sphere under random forcing or minimal microorganism models
Speaker: Erene Erazo - Tulane University
Abstract: In this talk, I will discuss microscale flows around a sphere under random forcing or minimal microorganism models. First, I will introduce a model that describes the dynamical behavior of small spherical particles immersed in a viscous fluid under the influence of thermal fluctuations. We perform theoretical and numerical analyses of particle diffusion to characterize their motion across varying particle sizes. Second, using the same framework, I will present a minimal model for swimmers and discuss some preliminary results.
Time: 2:15 pm
Location: Dinwiddie Hall 102
___________
February 3, 2026
Graduate Student Colloquium
Title: Riesz-Type Sums Involving Real Quadratic $L$-Values
Speaker: Tushar Karmakar - Tulane University
Abstract: In analytic number theory, summation formulas are often useful for understanding the properties of sequences which grow erratically. We explore Riesz type sums involving class number of real quadratic field. In particular, we extend recent work of Beckwith, Diamantis, Gupta, Rolen, and Thalagoda from harmonic Maass forms to sesquiharmonic Maass forms of weight $1/2$. Our approach adapts a method of Chandrasekharan and Narasimhan, which we apply to a sesquiharmonic Maass form first introduced by Duke, Imamo{\u g}lu, and T\'{o}th. (This is ongoing joint work with Professor Olivia Beckwith)
Time: 2:45 pm
Location: Dinwiddie Hall 102
___________
February 10, 2026
Graduate Student Colloquium
Title: Introduction to dynamical systems
Speaker: Lahiri Sinchita - Tulane University
Abstract: Dynamical systems provide a unifying framework for understanding the time evolution of mathematical models arising across science and engineering. In this talk, I will begin with a gentle introduction to dynamical systems generated by ordinary differential equations, focusing on fundamental concepts. These finite-dimensional systems serve as a conceptual foundation for more complex models. I will then outline how this framework extends to partial differential equations, where the dynamics evolve in infinite-dimensional phase spaces. Emphasis will be placed on the basic ideas rather than technical details, including the interpretation of PDEs as dynamical systems on function spaces. In the final part of the talk, I will briefly indicate how these ideas connect to my recent research, where tools from infinite-dimensional dynamical systems are used to analyze the qualitative behavior of solutions to linear evolution equations.
Time: 2:45 pm
Location: Dinwiddie Hall 102
___________
February 24, 2026
Graduate Student Colloquium
Title: An Introduction to Principal Component Analysis
Speaker: Naveed Ahmed - Tulane University
Abstract: Principal Component Analysis (PCA) is a foundational technique in scientific computing for extracting structure from high-dimensional data. In this talk, I will introduce the mathematical ideas underlying PCA, beginning with its formulation through covariance matrices and eigendecomposition. I will then show how the singular value decomposition (SVD) provides an equivalent and numerically robust perspective. Emphasis will be placed on the geometric interpretation of PCA as a change of coordinates that identifies directions of maximal variance.
To illustrate these ideas in practice, I will present an implementation of PCA on the Fisher Iris dataset and demonstrate how a small number of principal components can capture most of the variation in the data. I will conclude with brief remarks on low-rank approximation and data reconstruction, highlighting the broader role of PCA in scientific computing.
Time: 2:45 pm
Location: Dinwiddie Hall 102
___________
March 03, 2026
Graduate Student Colloquium
Title: Congruences for k-regular partition numbers
Speaker: Peter Marcus - Tulane University
Abstract: Ramanujan discovered surprising congruence relations between integer partition numbers, which arise because of properties of modular forms, in particular, the Dedekind eta-function. Finding more congruences among similar sequences has become a major application of the continually-developing theory of modular forms. I will discuss my thesis research, in which I study congruence relations between k-regular partition numbers, a variant of partition numbers which counts the number of partitions where no part is divisible by k.
Time: 2:45 pm
Location: Dinwiddie Hall 102
___________
