The Mathematical Association of America Maryland-District of Columbia-Virginia Section

The Fall 2020 Meeting of the MD-DC-VA section of the MAA was held virtually on Saturday, November 7, 2020. The Saturday morning address, Complete Leibniz algebras, was be given by Kristen Boyle of Longwood University. The Saturday noontime address, A Survey of Applied Mathematics Applications in Metrology at NIST, was given by Anthony J. Kearsley of NIST. The Saturday afternoon address, The power of polynomials: polynomials in distributed storage, was given by Gretchen Matthews of Virginia Tech.

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Kristen Boyle

Longwood University

Saturday Morning Address Complete Leibniz algebras

Abstract: Leibniz algebras are certain generalizations of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In some cases, the generalizations of definitions and theorems extend directly from those established for Lie algebras. In other cases, modifications must be made to ensure the signature results from Lie theory will carry over to Leibniz algebras. In this talk, we will consider examples of Leibniz algebras which are not Lie algebras. We will discuss the trial-and-error process used to determine a definition for completeness in Leibniz algebras; and finally, we will introduce the notion of complete Leibniz algebras as a generalization of complete Lie algebras.

Biographical Sketch: Kristen Boyle is an assistant professor of mathematics at Longwood University. She has been teaching at Longwood since 2018, when she finished her Ph.D. at North Carolina State University. While at NC State, Kristen studied Leibniz algebras under the direction of Dr. Ernest Stitzinger and Dr. Kailash Misra. Kristen and her co-advisors published their work, “Complete Leibniz algebras”, in the September 2020 issue of the Journal of Algebra. Prior to earning a Ph.D. in mathematics, Kristen earned a B.S. and an M.A. in Mathematics Education from Appalachian State University in Boone, NC, and she taught high school mathematics for four years in Lexington, NC. Based on her experiences in high school teaching, Kristen's further research interests include mathematical pedagogy and mathematics teacher preparation

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Anthony J. Kearsley

Mathematician, Applied and Computational Mathematics Division, National Institute of Standards and Technology

Saturday Noontime Address:A Survey of Applied Mathematics Applications in Metrology at NIST

Abstract: Estimating optimal parameters, locating desirable regimes and proposing best practices are issues that arise often in measurement science applications. In this talk, a survey of research at NIST will be presented, each of which will demonstrate the need for optimization. The examples will draw from current research at NIST in disparate fields.

Biographical Sketch: Anthony was born in Washington DC and attended the University of Maryland Baltimore County (UMBC) and University of Maryland College Park (UMCP) as an undergraduate and Rice University for his graduate work. He received a BA in Mathematics in 1990 from the University of Maryland. While a graduate student at Rice he spent a year at the Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) in Toulouse France. He received a PhD in 1995 from the department of Computational and Applied Mathematics at Rice under the advisement of Professors Roland Glowinski and Richard Tapia. His thesis work dealt with the solution of Partial Differential Equations (PDE) arising in science and engineering using optimization methods. Anthony has been a member of the faculty of the University of Massachusetts and Carnegie Mellon University. He is now a staff research mathematician at NIST in Gaithersburg Maryland. Anthony was awarded the Presidential Early Career Awards for Scientists and Engineers (PECASE) award in 1999 and the Arthur S. Flemming award in 2001. His current research interests include the optimal design of microfluidic devices and cytometry, simulation and control of freezing in cryobiology, data analysis in chemometrics and other applications of optimization to measurement science

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Gretchen Matthews

Virginia Tech

Saturday Afternoon Address:The power of polynomials: polynomials in distributed storage

Abstract: Polynomials over finite fields have been employed to protect information in a variety of ways, starting with Reed-Solomon codes in the 1960s. They are responsible for error-correction in CDs, DVDs, and QR codes, among many other behind-the-scenes uses. The data deluge of the past decade has prompted a new application. In this talk, we consider the use of polynomials in distributed storage.

Biographical Sketch: Gretchen Matthews is a Professor of Mathematics at Virginia Tech and Director of the Commonwealth Cyber Initiative Southwest Virginia. She is affiliated faculty with Virginia Tech's Hume Center for National Security & Technology and Computational Modeling & Data Analytics program. Her research is in applied algebra, with a focus on coding theory and cryptography and applications in data storage, protection, and privacy. She is passionate about diversity and inclusion in STEM and has developed a number of programs to broaden participation. She earned a BS in Mathematics at Oklahoma State University and a PhD from Louisiana State University. She spent time as a postdoc at University of Tennessee and on the faculty at Clemson University before joining Virginia Tech in 2018