All meetings will be virtual, Mondays at 4pm. zoom link
|9/28/20||Peter Maceli||Graphs and Algorithms||Graph theory is a young and exciting area of discrete mathematics. Visually, a graph is just a collection of dots together with lines joining certain pairs of these dots. Though at first glance graphs may seem like simple objects to study, the field of graph theory contains some of the deepest and most beautiful mathematics of the last fifty years. Being an extremely visual field, many questions and problems in graph theory are easily stated,yet have complex solutions with far reaching implications and applications.In this talk, we will explore the close relationship shared between graphs and algorithms. Describing how certain families of graphs “look” and can be“built,” and how, in turn, this allows one to efficiently solve certain important combinatorial problems.|
|10/5/20||A Virtual Escape Room||Today we change gears from our typical talk. We'll break into teams to try out a virtual escape room! If you have a team in mind, email Matt Thomas (email@example.com) with your team. Otherwise, just show up and we'll make some teams!|
|10/12/20||Priya V. Prasad, University of Texas at San Antonio||Teaching Geometric Congruence||Euclid and Hilbert both based their developments of axiomatic geometry on metric definitions of congruence, but current state standards (such as the Common Core State Standards for Mathematics and the Texas Essential Knowledge and Skills Standards) implicitly rely on an isometric definition of congruence. So how can teacher educators prepare future secondary geometry teachers to teach an axiomatically coherent geometry based on this definition? We developed a task using Taxicab geometry that can perturb students’ internalized metric definition of congruence. This talk is based on work done with Steven Boyce at Portland State University.|
|10/19/20||Benjamin Levy, Fitchburg State University||An Introduction to Disease Modeling with an Application to HIV/AIDS in Kenya||
One can use mathematical techniques to model disease outbreaks such as COVID-19, Ebola, or HIV/AIDS. We can then use model simulations to make future projections about the number of cases, consider the impact of intervention strategies, or analyze other key characteristics of an epidemic.
This presentation will begin by introducing the compartmental framework commonly used to model infectious diseases, which will be illustrated by some simple models. After we lay some groundwork, a specific application to modeling HIV/AIDS in Kenya will be presented. In this application we formulate a compartmental system of ordinary differential equations (ODEs) to consider how stigma towards people living with HIV/AIDS has impeded the response to the disease. We take a data-driven approach to embed a time-dependent stigma function within our model for HIV dynamics and estimate model parameters from published data. We then explore a range of scenarios to understand the potential impact of different public health interventions on key HIV metrics such as prevalence and disease-related death, and to see how close Kenya will get to achieving UN Goals for these HIV and stigma metrics by 2030.
|10/26/20||Emilie Wiesner, Ithaca College||Ping Pong and Sleeping Beauty: Playing with Paradoxes||We'll spend the first part of the hour thinking and talking about ping pong and Sleeping Beauty (two of my favorite paradoxes). The second part of the hour we'll have some paradox show and tell, so come prepared with your own favorite paradox.|
|11/2/20||John Gemmer, Wake Forest University||Why is Lettuce so Wrinkly?||Many patterns in Nature and industry arise from the system minimizing an appropriate energy. Examples range from the periodic rippling in hanging drapes to the six-fold symmetries observed in snowflakes. Torn plastic sheets and growing leaves provide striking examples of pattern forming systems which can transition from single wavelength geometries (leaves) to complex fractal like shapes (lettuce). These fractal like patterns seem to have many length scales - the same amount of extra detail can be seen when looking closer (“statistical self-similarity”). It is a mystery how such complex patterns could arise from energy minimization alone. In this talk I will address this puzzle by showing that such patterns naturally arise from the sheet adopting a hyperbolic non-Euclidean geometry. However, there are many different hyperbolic geometries that the growing leaf could select. I will show using techniques from analysis, differential geometry and numerical optimization that the fractal like patterns are indeed the natural minimizers for the system.|
|11/16/20||Gabe Pesco, Rachel King, and Jake Brown||Summer research/jobs panel||Come join us to hear about some of the work being done over the summers! Hear about what they did, and how they applied for and did their work. Ask questions to start thinking about what you might do next summer.|
|12/7/20||Mingyue Wang, Incyte||On selecting the t best Bernoulli Treatments||
In many situations we are faced with the problem of choosing among several alternatives. We may want to make a decision about which alternative(s) are the best. Considering a typical clinical trial setting, we set the goal of selecting among k ( > 0) experimental Bernoulli treatments the t (1 < t < k) best treatments provided that they are significantly better than the control. If fewer than t treatments are significantly better than the control, our goal is to retain the control. A fixed-sample-size procedure and a curtailed procedure are proposed to reach the goal. We adopt the two-stage selection/testing approach considered by Thall, Simon, and Ellenberg (1988) in both procedures. Properties of the proposed procedures will be presented through theorems and numerical results.