Friday, September 6th -- Holt 175, 4:00pm
Where do Kepler's laws hold?
Abstract: The Kepler Problem is among the oldest and most fundamental problems in mechanics. Its solution describes the motion of a planet around a sun, and famously yields Kepler's Three Laws of Planetary Motion. The problem makes sense in curved geometries like spheres and hyperbolic spaces. Do the laws still hold? We answer this question and investigate the Kepler problem in a new and strange geometry: the Heisenberg group, where a straight line is a helix.
Friday, September 27th -- Holt 175, 4:00pm
Abstract: Error correcting codes are systems for incorporating redundancy into stored or transmitted data, so that errors can be identified and even corrected. A good error correcting code is efficient and can correct many errors relative to its efficiency. These codes are ubiquitous in the digital age, and many excellent codes arise from algebraic constructions. The increasing importance of cloud computing and storage has created a need for codes that protect against server failure in large computing facilities. One way of approaching this problem is to ask for local recovery. An error correcting code is said to be locally recoverable if any symbol in a code word can be recovered by accessing a subset of the other symbols. This subset is known as the helper or recovery set for the given symbol. It may be desirable to have many disjoint recovery sets for each symbol, in case of multiple server failures or to provide many options for recovery. Barg, Tamo, and Vladut recently constructed LRCs with one and two disjoint recovery sets from algebraic curves. This talk presents a generalization of this construction to three or more recovery sets, using fiber products curves over finite fields. This is joint work with Kathryn Haymaker and Gretchen Matthews.
Friday, October 4th -- Holt 175, 4:00pm
Abstract: I will present a new type of generative music based on the "abelian sandpile model"--a discretized model for the flow of heat which is full of interesting combinatorial structures. The music is created by encoding the mathematics into an algorithm which then plays synthesizers according to the rules laid out by the dynamical system. I will explain how this works, and we will listen to examples. I will also discuss how the mathematics behind the music is regulated by a discrete form of the Laplacian operator and an analogy between graphs and Riemann surfaces.
Friday, October 25th -- Holt 175, 4:00pm
Abstract: Gerrymandering is generally understood to be the drawing of political districts in order to benefit one group and dilute the voting power of another group. In recent years, mathematicians have become deeply involved in the geometry of redistricting and the evaluation of districting maps. In this talk, we will discuss some techniques that have recently been used in court cases to argue the presence of partisan gerrymandering. We will discuss research on particular metrics intended to detect gerrymandering, as well as statistical techniques using Markov Chain Monte Carlo.
Friday, November 1st -- Holt 175, 4:00pm
Abstract: Although there has been a national call to increase the number of STEM graduates in the United States, high failure rates in mathematics courses such as Calculus I continue acting as gatekeepers (PCAST, 2012). While the reasons contributing to high failure rates are complex, the traditional Calculus I course model does not necessarily “provide the desired level of support” for students to be successful (Voigt et al., 2017, p. 32). Experiences in Calculus I play an important role in the retention of STEM majors (Bressoud & Rasmussen, 2015; Ellis, Fosdick, & Rasmussen, 2016; Seymour & Hewitt, 1997), and institutions often find that their students, while placing into Calculus I, lack the necessary prerequisite knowledge to be successful in Calculus I (e.g. Agustin & Agustin, 2009; Sonnert & Sadler, 2014).
In this interactive talk, I will share an example of a successful stretched Calculus I model implemented to support students who self-identified as being unprepared for Calculus I. The stretched course (1) utilized evidence-based practices (as supported by Freeman et al., 2014), (2) addressed prerequisite knowledge, and (3) supported the development of study habits and metacognitive strategies (e.g. Ohtani & Hisasaka, 2018; Schneider & Artelt, 2010). Students who completed the stretched course outperformed their “regular” Calculus I student counterparts, were successful in subsequent mathematics courses and Engineering programs, and spoke of the continued impacts the course had a year after completion.
Friday, November 8th -- Holt 175, 4:00pm
Abstract: Physics education researchers (PER) commonly use complete-case analysis to address missing data. For complete-case analysis, researchers discard all data from any student who is missing any data. Despite its frequent use, no PER article we reviewed that used complete-case analysis provided evidence that the data met the assumption of missing completely at random (MCAR) necessary to ensure accurate results. Not meeting this assumption raises the possibility that prior studies have reported biased results with inflated gains that may obscure differences across courses. To test this possibility, we compared the accuracy of complete-case analysis and multiple imputation (MI) using simulated data. We simulated the data based on prior studies to have students who earned higher grades be more likely to participate so that the data were missing at random (MAR). PER studies seldom use MI, but MI uses all available data, has less stringent assumptions, and is more accurate and more statistically powerful than complete-case analysis. Results indicated that complete-case analysis introduced more bias than MI and this bias was large enough to obscure differences between student populations or between courses.
Friday, November 13th -- Holt 175, 4:00pm
Abstract: The control of malaria and in particular it’s deadliest variety, Plasmodium falciparum, depends on population and transmission dynamics in its vectors, in particular anopheles gambiae. Multiple studies have shown statistical links between P. falciparum prevalence and temperature, rainfall, topography and land use. We describe the causal forces proposed that drive these correlations, including rise and fall of temporary aquatic habitat, flushing of larvae during heavy rainfall, dependence of maturation and death rates on temperature, as well as other factors. We describe the results of mechanistic models of some of these forces. Data and studies from the Western Kenya highlands serve as the working example.