Below is the schedule or speakers for the Math and Stats Seminar at Grinnell for Spring 2025. We will meet at 12PM in Noyce 2517. Lunch will be provided (usually sandwiches or pizza).
Speaker: Kate Bartz from Grinnell College
Title: A Continuous Optimization Approach to Graph Cuts Based Phase Unwrapping
Abstract: This talk will outline my work as a Summer Undergraduate Research Fellowship (SURF) Student at Mayo Clinic Graduate School of Biomedical Sciences on the Biomedical Engineering and Physiology Track. I will briefly describe my day-to-day life as a SURF student, as well as my experience working in a more applied engineering environment. I will then lay the foundation of my research, which focuses on using a mathematical approach to solve phase wrapping problems in Magnetic Resonance Imaging. I will describe the problem and walk through the algorithm I derived to solve it and follow this with empirical results and a discussion of applications of this research.
Speaker: Deven Platt from Grinnell College
Title: Connectivity of n-Tuple Graphs
Abstract: Over the summer, I did an REU at University of Salisbury in graph theory. We studied n-tuple graphs, a class of graphs that can be created using a starting graph and an integer parameter. They often have a very symmetrical structure and can be investigated using purely combinatorics. In this talk, I will give an introduction to these graphs and describe some results that my group came up with or conjectured about. In particular, we focused on the connectivity of these graphs, which is a precise way to measure how interconnected the vertices in a graph are.
Title: Information Session for Summer MAPs in Statistics
Abstract: Are you interested in doing a summer research project in statistics at Grinnell? Curious to hear what sorts of projects will be offered? Come to our information session on Mentored Advanced Projects (MAPs) in Statistics! Professors Miller, Nolte, and Wells will be giving short introductions to their summer MAPs, and there will be time to ask questions about the MAP process. We look forward to seeing you there! (There will be a Math MAP Info Session next Thursday, February 20. We encourage students who think they might be interested in math or stats to attend both sessions!)
Title: Information Session for Summer MAPs in Math
Abstract: Are you interested in doing a summer research project in mathematics at Grinnell? Curious to hear what sorts of projects will be offered? Come to our information session on Mentored Advanced Projects (MAPs) in Math! We will have projects in applied and pure mathematics. Professors Bhattacharya, Hazel, Hebbar, Kenkel, and Webster will be giving short introductions to their summer MAPs, and there will be time to ask questions about the MAP process. We look forward to seeing you there!
Visiting Speaker: James Mills from University of Iowa
Title: Biostatistics: Overview and Opportunities
Abstract: Biostatistics is the application of statistical methods to biological and health-related data in fields such as epidemiology and public health. Biostatisticians collaborate with investigators on many aspects of research from study design and data collection to analysis and interpretation. The importance of biostatistics in healthcare will be detailed and examples of biostatistical analysis will be presented, including models developed in the research of Huntington’s disease (HD). HD is an inherited neurological disorder that results in substantial motor, cognitive, and functional decline for afflicted individuals. Lastly, opportunities for interested undergraduates to learn more about biostatistics will be discussed.
Visiting Speaker: Dan Dugger from University of Oregon
Title: A taste of hyperbolic geometry
Abstract: Hyperbolic geometry was invented in the 1820s, independently by Gauss, Lobachevsky, and Bolyai. It is a system of geometry that satisfies all of Euclid's axioms except for the parallel postulate. It has a number of strange features: lines that are not parallel but also do not intersect, triangles where the angles add up to less than 180 degrees, weird formulas for the circumference and area of a circle, just to name a few. This talk will give a gentle introduction to hyperbolic geometry, and along the way we'll see how it connects to the famous "Circle Limit" woodcuttings by M.C. Escher.
Visiting Speaker: Tyler Cassidy from University of Leeds
Title: Understanding new treatments for chronic hepatitis B infection using mathematical modelling
Abstract: Chronic hepatitis B virus (HBV) infection is responsible for approximately one million deaths per year, worldwide. While existing therapies effectively block the production of new virus, viral rebound occurs rapidly if treatment is stopped. As a result, no cure for chronic HBV infection is currently available. Patients therefore receive treatment indefinitely with a resulting lifelong treatment burden. Consequently, there is interest in new treatment options that block crucial steps in the viral life cycle. I'll discuss how mathematical modelling can illuminate biological mechanisms that would otherwise be inaccessible during typical clinical trials, answer important questions in drug development, and help understand new treatments as possible cures for HBV.
Speakers: Xuyi Ren from Grinnell and Christian Roettger from Iowa State University
Title: Ternary Digits of Powers of Two
Abstract: Any number has a ternary (base-3) representation. From looking at the first few powers of Two, it seems that their ternary digits look 'random'. Using that as a heuristic, we can study several conjectures. To begin with, here is a simple question: What is the 'probability' that the highest digit equals 1?
There are several conjectures about the number of 1s, 2s, 0s etc., all motivated by the idea that these digits 'should' behave like they were random, although of course they are not. These are quite natural questions, but they are surprisingly hard to answer. We have some related results, proven using the theory of Uniform Distribution. And we will show some experimental data which suggest that the digits behave indeed very much randomly. The talk should be accessible to undergraduates.
Speakers: Boston Gunderson and Bella Villareal from Grinnell College
Title: Ruled Surfaces in Virtual Reality
Abstract: We have designed and developed a virtual reality experience with the intent of representing ruled surfaces as visual models of study as well as mathematical concepts. By locating this project in virtual reality, we are able to create precise models, inspired by a history of mathematical modeling. Additionally, we are able to construct unique tools for better understanding these surfaces; for example, models of surfaces in virtual reality can be shifted and stretched into models of entirely different surfaces at the discretion of the user. Our virtual reality experience aims to be a self-paced lesson on ruled surfaces, with the opportunity to explore and discover math by working with virtual models. We hope that this experience opens new doors for the visual exploration of mathematics.