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Opportunities for Research in Mathematics-Summer 2021

Please note that these are subject to change

Dr. Taylor Arnold:

  1. Focus: Text mining of multilingual Wikipedia comments.
  2. Length of research: 10 weeks
  3. Required student skills: Math 289 and 389.

Dr. James Davis:

  1. Focus: We will investigate classifying and counting all semibent functions on 7 variables. Our investigation will require understanding the theoretical and computational work done on bent functions.
  2. Length of Research: 10 weeks.
  3. Required student skills: I am willing to take students at any level. In fact, I prefer taking students as early as possible so they can work with me for more than one summer.

 Dr. Jeremy LeCrone:

  1.  Focus: We will study the properties of medial axis structures in settings relevant to motion planning and robotics in confined spaces. Intuitively, the medial axis is composed of all points at which a moving robot is “maximally safe” from impacting nearby obstacles. Using a variety of definitions (which may or may not be equivalent), we will explore the properties of resulting medial axis structures in general (theoretical) settings and/or specific settings relevant to real-world applications.
  2. Length of Research: 10 weeks
  3. Required Student skills: At or beyond Calculus II.

Dr. Marcella Torres:

  1. Focus: Developing a mathematical model of macrophage mediated inflammation in response to inhaled toxicants and/or pathogen. We will work on the development of an ordinary differential equation model of inflammation that includes pro- and anti-inflammatory macrophage phenotypes (M1 and M2) and pro- and anti-inflammatory mediators (TNF-alpha, nitric oxide, IL-10,...). We will fit the model to in vitro data collected in the Jones lab and, ultimately, use the model to simulate treatment with antioxidants.You will work on a cross-disciplinary team, across mathematics and biology. Learn Matlab and the Simbiology toolbox for modeling biological systems. Learn parameter estimation and data fitting techniques. Learn about using the ELISA (to measure cytokine release) and the nitric oxide assay, colorimetric assays that involve spectrophotometry. Learn how to perform traditional and quantitative PCR analysis to measure expression of pro-inflammatory genes.
  2. Length of Research: 10 weeks
  3. Required Student skills: Calculus.

Math Summer Research Opportunites 2021