Mathematics Graduate Seminar - Spring 2025 and Fall 2025
The seminar is scheduled from 10:00 am - 10:50 am on Tuesday mornings in Bruner Hall 308.
DATE |
SPEAKER |
TITLE/Abstract |
---|---|---|
9/30/2025 |
Gayan Maduranga |
Title: "Getting Started with 成年人深夜福利在线观看 Tech鈥檚 HPC Cluster: A Practical Guide for Research and Coursework"
Abstract: High Performance Computing (HPC) resources at 成年人深夜福利在线观看 Tech provide students and faculty with powerful tools for research in data science, deep learning, and computational modeling. However, many first-time users find the environment unfamiliar compared to local computing. This seminar will introduce the fundamentals of using TTU鈥檚 HPC system, including access via the Open OnDemand portal, interactive sessions with hpcshell, software modules, and job submission with Slurm. Practical examples will be presented, such as setting up Python/Conda environments, running GPU-enabled deep learning tasks, and managing files between /home and /work directories. Attendees will leave with a clear workflow for starting their own HPC jobs, along with best practices to make effective use of TTU鈥檚 HPC resources for both coursework and research projects. |
9/23/2025 |
David Smith |
Title: "Modeling Blood Coagulation Times using a Hierarchical Bayes Model with Gibbs Sampling."
Abstract: Markov Chain Monte Carlo (MCMC) methodology and the development of faster processors have allowed growth in statistical research areas that were not accessible 20 years ago. One area that has relied heavily on MCMC techniques is Bayesian data analysis. In this presentation, we will implement MCMC using a Gibbs sampling algorithm for a Hierarchical Bayes approach to modeling blood coagulation times. |
9/16/2025 |
Debra Bryant |
Title: "STP for Underprepared Students"
Abstract: In this discussion, we will refer to the scientific idea of STP. Most instructors, as students, were highly satisfied 90%-100% with the classroom environments. As students, we loved to learn and when any disruptions occurred in the classroom or in us as individuals, we quickly dealt with it and moved on. Underprepared students who experience disruptions in a classroom environment may react adversely to that disruption and be unable to move on. These disruptions may result in gaps or glitches in critical problem solving steps, a dislike or hatred for the particular subject, fear of or actual failure, acting out, etc. You will be able to identify and use specific strategies to minimize a drop in STP using ideas from this discussion. You will be able to develop multiple types of strategies to encourage learning, successful learning skills and retention. |
9/9/2025 |
Damian Kubiak |
Title: "The Banach Fixed Point Theorem"
Abstract: The Banach Fixed Point Theorem will be presented together with a proof, its history and some applications. |
9/2/2025 |
Motoya Machida |
Title: "Logistic Regression is All You Need."
Abstract: Even though a database contains millions of reports, medical incidents of adverse reactions for example, detecting previously undiscovered associations is often compared to ``finding needles in a haystack.'' For many years such detections have been an important research area in pharmacovigilance. The earlier investigation by DuMouchel proposed the use of empirical Bayes to adjust signal levels, providing elegant solutions to the problem of signal detections. However, it has been known for significant biases due to ``hidden confounding.'' An application of logistic regression model for drug-event combinations has been suggested by Hauben et al., as a promising approach. Genkin et al., devised algorithms to find the maximum a posteriori (MAP) estimates. However, due to a large dimension it has not been practical to analyze the characteristics of posterior distribution such as percentiles for credible intervals by Monte Carlo methodology. The talk communicates the following ideas: 1. A logistic regression can be viewed as a simple encoder model consisting of bijective embedding of one-hot representations and a single layer transformer. 2. Langevin algorithm uses stochastic differential equations (SDE) for Monte Carlo simulations. We present a recent development of the construction of strong stationary time and the exact sampling algorithm using Langevin diffusions. |
8/26/2025 |
Jared Daniels |
Title: "The Tradition of the 成年人深夜福利在线观看 Tech Mathematics Department"
Abstract: As times and values change, it's always important to remember the culture and history that we came from. It's from this that sets the positive trajectory for our future and determines our forward-thinking goals. The objective of this talk is to get all of us, past and present, to reflect upon the positive impact that the 成年人深夜福利在线观看 Tech Mathematics Department has had on our heritage. The end result being a well-balanced perspective that provides us all with the motivation required to achieve our desired goals. |
3/12/2025 |
Jacob Copeland |
Title: "Interpreting the structure of a quadratic regular algebra of global dimension three using its point scheme"
Abstract: Over the last few decades, work in quantum physics has given rise to algebraic structures which can be viewed as noncommutative analogs of polynomial rings. These algebraic structures are algebras known as Artin-Schelter regular algebras. Classifying and understanding these algebras using modified methods from commutative algebraic geometry is an active area of research in noncommutative algebra. One particular example of such algebras emerged from Poisson geometry as a generalization of a deformation on a Poisson bracket in complex projective three-space. The result of this generalization was a family of AS-regular algebras denoted as R(n,a) for n<=1 and are henceforth referred to as the LS-algebras. In this thesis, we compute the point scheme of the LS-algebra of global dimension three, R(2,a). We then use this scheme to classify the algebra and demonstrate that R(2,a) can be expressed as a twist by a graded automorphism of an Ore extension of the polynomial ring on two variables. |
3/5/2025 |
Professor Joachim Kerner (University of Hagen) |
Title: Spectral comparison results on metric and discrete graphs
Abstract: In recent years, various authors have derived spectral comparison results in different settings including Euclidean domains and metric graphs. In this talk we review the results on metric graphs and provide a generalization to the discrete setting. We also discuss possible extensions to infinite graphs and applications in inverse spectral theory. Along the way, we study so-called local Weyl laws which are of independent interest. This talk is based on joint work with P. Bifulco (Hagen) and C. Rose (Potsdam). |
2/26/2025 |
Dr. Damian Kubiak |
Title: The (metric) Space of Fractals Abstract. In this talk we present the definition of the metric space of fractals and the Hausdorff metric. We should see how to obtain the Sierpinski triangle as the limit of a certain sequence constructed via an iterated function system. The existence of the limit of that sequence is guaranteed by the Banach Contraction Principle. The talk is based on the book 鈥淔ractals Everywhere鈥 by Michael Barnsley. |
2/12/2025 |
Dr. David Smith |
Title: Improved small sample inference for the Generalized Pareto distribution through a Monte Carlo adjustment to the signed root of the log-likelihood ratio statistic.
Abstract: Estimation methods for the Generalized Pareto distribution have been well studied. While the maximum likelihood method may yield adequate results for cases in which the shape parameter falls between -.5 to 5 and large sample sizes, very little has been done for small sample sizes. Small sample sizes can occur when fitting the exceedances over a threshold. We study an adjustment which centers and scales the signed root of the log-likelihood ratio statistic. The Monte Carlo adjustment is easily derived and does not require complex calculations that are often required to condition on ancillary statistics. One-sided inference and confidence intervals for shape, scale, and m-year return levels are compared to profile likelihood and delta methods. Considerable improvement is shown for small samples and demonstrated with examples. |
1/22/2025 |
Dr. Motoya Machida |
Title: Coalescing solutions to Langevin diffusions and their applications
Abstract: We can construct the inverse image of a strong solution to Langevin diffusion as a random boundary, and introduce a coalescing solution to the same diffusion by running backward and reflecting it at the random boundary. It allows us to propose a set-valued intertwining dual of the Langevin diffusion and formulate a Lambda-linked coupling which extends Pitman's 2M-X theorem for multi-dimensional Langevin diffusions. In particular we use the Lambda-linked coupling for Monte Carlo applications and examine an adaptive stopping mechanism when the drift coefficient is monotone. |