Academics
Teaching Experience
- Assistant professor at Farmingdale State College (2020-present)
- Teaching post-doctoral fellow at Colorado School of Mines (2017-2020)
- Graduate Teaching Assistant at University of Nebraska-Lincoln (2012-2017)
Research Interests
- Feature Selection for Activity Detection: Given a large set of collected data from smart home sensors, I attempt to determine which features help best predict current occupant’s activity.
- Energy Effenciency from Smart Home Data: Given data from several smart home environmental sensors, I work on measuring energy effeciency of the building.
- Fractional Difference Equations: I study self-adjoint difference equations that contain fractional difference operators.
- Fractional Difference Operators: I investigate properties of the Caputo fractional difference and its relationship to the Riemann-Liouville fractional difference.
Education
- PhD in Mathematics (2017) University of Nebraska-Lincoln
- MS in Mathematics (2014) University of Nebraska-Lincoln
- BS in Mathematics, minor in German (2012) University of Nebraska-Lincoln
Presentations
- Uniqueness and Stability of Solutions for a Coupled System of Caputo Type Nabla Fractional Difference Boundary Value Problems, Celebration of Scholarship; Farmingdale State College, December 10, 2021 (based on work with Christina Jones, Danyil Blyschak, and Areeba Ikram)
- Uniqueness and Stability of Solutions for a Coupled System of Caputo Type Nabla Fractional Difference Boundary Value Problems, Young Mathematicians Conference; The Ohio State University, August 22, 2021 (co-faculty advisor to presenters Christina Jones and Danyil Blyschak with Areeba Ikram)
- Solutions to a Three Point Boundary Value Problem in Nabla Fractional Calculus, Joint Mathematics Meeting; Denver, Colorado, January 2020 (based on work with Cameron Kissler)
- Application of the Contraction Mapping Theorem for Existence and Uniqueness of Solutions to Nonlinear, Fractional Difference Boundary Value Problems, Joint Mathematics Meeting; Balitmore, MD, January 2019
- Unique Solutions to Nonlinear Boundary Value Problems with a Fractional Self-Adjoint Difference Equation, Joint Mathematics Meetings; Atlanta, GA, January 2017
- Introduction to the Nabla Discrete Fractional Calculus, Joint Mathematics Meetings (poster session); Boston, MA, January 2012 (with Lucas Castle and Katie Yochman)
- Nabla Laplace Transforms and Fractional Calculus, Fall Central AMS Section Meeting; University of Nebrasksa-Lincoln, October 2011
- Some Results on the Convergence of the Generalized Exponential Function on Time Scales, Fall Central AMS Section Meeting; University of Nebrasksa-Lincoln, October 2011 (with Chris Ahrendt)
Journal Publications
- Green’s Function for Boundary Value Problems Involving a Nabla Caputo Fractional Operator, Journal of Difference Equations and Applications, Volume 25 Issue 6 (2019), pp 788-800 (with Cameron Kissler) arxiv.org preprint
- Initial and Boundary Value Problems for the Caputo Fractional Self- Adjoint Difference Equations, Enlightenment in Pure and Applied Mathematics, Volume 2 Issue 1 (2016), (with Lydia Dewolf, Liam Mazurowski, Kelsey Mitchell, Tim Rolling, and Dominic Veconi).
- Laplace Transforms for the Nabla-Difference Operator and a Fractional Variation of Parameters Formula, Communications in Applied Analysis, Volume 16 Issue 3 (2012), (with Lucas Castle, Michael Holm, and Katie Yochman).
- Some results on the convergence of the generalized exponential function on time scales, Communications in Applied Analysis, Volume 16 Issue 3 (2012), (with Chris Ahrendt).
Dissertation and Thesis