Fairmont State University's Dr. Tom Cuchta, assistant professor of mathematics, was invited to two international conferences this summer and gave four lectures.
The first conference was at the Dynamical Equations on Time Scales workshop held at the Mathematical Research and Conference Center in Bȩdlewo, Poland, which was funded mostly by a Fairmont State University foundation grant. The second conference was the International Conference on Differential & Difference Equations and Applications in Lisbon, Portugal. All four lectures were in the area of time scales calculus.
In Poland, Dr. Cuchta spoke about an undergraduate research project he has been organizing for the past year. The project involves a student writing "open source" (i.e. freely available) code (https://github.com/tomcuchta/timescalecalculus) to help make doing computer calculations in the area of time scales calculus more feasible. The second talk in Poland concerned a class of q-hypergeometric functions related to research Cuchta published in 2018 (https://www.degruyter.com/view/j/dema.2018.51.issue-1/dema-2018-0007/dema-2018-0007.xml).
In Portugal, Dr. Cuchta gave two further lectures. The first was on a population model on time scales developed by him and his coauthor Dr. Sabrina Streipert, Ph.D. of University of Queensland, inspired by the Gompertz differential equation. The second lecture concerned a new matrix special function on time scales developed with coauthors Dr. David Grow of Missouri University of Science & Technology and Dr. Nick Wintz of Lindenwood University. Manuscripts associated with these two talks were recently accepted for publication and will be published soon.
Slides associated with all four lectures may be found at Dr. Cuchta's webpage (see http://tomcuchta.com/talks/). Time scales calculus is a relatively new branch of mathematics, first investigated in 1988, that unifies and also extends the old subjects of differential equations, difference equations, and q-difference equations into a single framework. Dr. Cuchta studied this subject as a graduate student under his Ph.D. advisor Dr. Martin Bohner at Missouri University of Science & Technology. Cuchta has worked at Fairmont State since August 2016.