*An exploration of approximating semigroups*; Graduate Student Colloquium; Department of Mathematical Sciences, University of Arkansas; Fayetteville, Arkansas (November 10, 2021) (invited).*Structure-preserving nonlinear operator splitting methods for singular partial differential equations*; Fourth Annual Meeting of SIAM Texas-Louisiana Section; South Padre, Texas (November 6, 2021) (invited).*Localization properties of discrete non-local Hamiltonian operators*; Applied Mathematics Seminar; Department of Mathematics and Statistics, Auburn University; Auburn, Alabama (October 21, 2021) (invited).*Explicit neural network constructions for overcoming the curse of dimensionality in the approximation of semilinear parabolic equations*; Numerical Analysis Seminar; Department of Mathematics, Baylor University; Waco, Texas (July 30, 2021) (invited).*Lecture Series on Pure and Applied Mathematics Lecture #2: Algebra and Applied Mathematics*; Applied Mathematics Seminar; Department of Mathematical Sciences, University of Arkansas; Fayetteville, Arkansas (March 3, 2021) (invited).*Lecture Series on Pure and Applied Mathematics Lecture #1: Analysis and Applied Mathematics*; Applied Mathematics Seminar; Department of Mathematical Sciences, University of Arkansas; Fayetteville, Arkansas (February 3, 2021) (invited).*Beating the curse of dimensionality in high-dimensional stochastic fixed-point equations*; Third Annual Meeting of SIAM Texas-Louisiana Section; online (October 17, 2020) (invited).*Beating the curse of dimensionality in high-dimensional partial differential equations*; Applied Mathematics Seminar; Department of Mathematical Sciences, University of Arkansas; Fayetteville, Arkansas (September 20, 2020) (invited).*A proof that deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations*; Applied Mathematics Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (March 11, 2020) (invited).*A nonlinear splitting algorithm for preserving asymptotic features of stochastic singular differential equations*; Joint Mathematics Meeting, Special Session; Denver, Colorado (January 2020) (invited).*Modeling physical systems with the fractional Laplace operator and its use in the Anderson localization problem*; The Center for Astrophysics, Space Physics, and Engineering Research; Baylor University; Waco, Texas (November 2019) (invited).*A semi-analytical approach to approximating non-local equations arising in porous media*; SIAM Northern States Section; Laramie, Wyoming (September 2019) (invited).*A nonlinear splitting algorithm for approximating population models with self- and cross-diffusion*; Biomathematics Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (September 2019) (invited).*Hopf algebraic structure of numerical integrators for integro-differential equations*; Geometry, Compatibility, and Structure-Preserving Conference; Issac Newton Institute, Cambridge University; Cambridge, United Kingdom (July 2019).*Semi-analytical methods for the aproximation of abstract fractional extension problems*; Applied Mathematics Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (April 2019) (invited).*Anderson localization in nonlocal models*; Analysis Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (February 2019) (invited).*Operator splitting methods for approximating singular nonlinear differential equations*; Numerical Analysis Seminar; Department of Mathematical Sciences, University of Delaware; Newark, Delaware (November 2018) (invited).*Operator splitting methods for approximating singular nonlinear differential equations*; Department Colloquium; Department of Mathematics, Baylor University; Waco, Texas (November 2018) (invited).*Numerical integration techniques on manifolds and their Hopf algebraic structure*; Geometry Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (October 2018) (invited).*Analysis of exponential-type integration method for nonlocal diffusion problems*; SIAM Annual Meeting; Special Session; Eugene, Oregon (June 2018) (invited).*Lie-Butcher series from an algebraic geometry point of view*; Geometry Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (April 2018) (invited).*Approximating the fractional Laplace equation via operator theoretical methods*; West Texas Applied Math Symposium; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (April 2018) (invited).*An introduction to geometric numerical integration*; Geometry Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (March 2018) (invited).*Operator splitting methods for approximating differential equations*; Junior Scholar Symposium; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (February 2018) (invited).*An operator theoretical approach to nonlocal differential equations*; Analysis Seminar; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (November 2017) (invited).*Operator splitting and Lie group methods for geometric integration*; Seminar in Applied Mathematics; Department of Mathematics and Statistics, Texas Tech University; Lubbock, Texas (November 2017) (invited).*An exploration of quenching-combustion via globalized fractional models*; SIAM Annual Meeting, Special Session; Pittsburgh, Pennsylvania (July 2017) (invited).*Solving degenerate stochastic Kawarada equations via adaptive operator splitting methods*; University of Central Arkansas; Conway, Arkansas (January 2017) (invited).*An approach to the numerical solution of multidimensional stochastic Kawarada equations via adaptive operator splitting*; Joint Mathematics Meeting; Atlanta, Georgia (January 2017).*Using Matlab to solve nonlinear PDE*; AMS Student Meeting; Baylor University; Waco, Texas (October 2016).*Using an adaptive Crank-Nicolson scheme to solve the degenerate stochastic Kawarada equation on nonuniform grids*; SIAM Central States Section Meeting, Special Session; Little Rock, Arkansas (September 2016) (invited).*Positive and monotone solutions to quenching differential equations*; Differential Equations Seminar; Baylor University; Waco, Texas (April 2016, 6 lectures).*A semi-adaptive LOD method for solving three-dimensional degenerate Kawarada equations*; AMS Spring Southeastern Sectional Meeting; Athens, Georgia (March 2016).*A novel LOD method for solving degenerate Kawarada equations*; CASPER Seminar; Waco, Texas (February (2016) (invited).*Numerical solutions to singular differential equations*; AMS Student Meeting; Baylor University; Waco, Texas (October 2015).*An exploration of exponential splitting*; Joint Mathematics Meeting, Special Session; San Antonio, Texas (January 2015) (invited).