Postdoctoral Fellow at Notre Dame, United States
Profiles
Summary
👨🎓 PhD candidate in Mathematics with a minor in Computer Science, specializing in probabilistic and data-driven methods for numerical PDEs and hybrid Monte Carlo methods for complex systems simulations. Experienced in statistical modeling, computational physics, and advanced simulations with a strong background in teaching and academic leadership. Currently working as a Postdoctoral Researcher at the University of Notre Dame.
Education
🎓 PhD in Mathematics (Minor in CS)
University of Tennessee Knoxville, 2021–2024
- Dissertation on Probabilistic & Data-Driven Methods in Numerical PDEs
- GPA: 4.0
📊 M.Sc. in Statistics
University of Tennessee, 2022–2024
📚 M.Sc. in Mathematics
Oregon State University, 2019–2021
⚛️ M.Sc. in Physics
University of Konstanz, 2015–2019
🔢 B.Sc. in Mathematics & Physics
University of Konstanz, 2012–2018
- GPA: 3.5 (Mathematics), 3.3 (Physics)
Professional Experience
🔬 Postdoctoral Researcher
University of Notre Dame, 2024–Present
- Research on hybrid Monte Carlo & deterministic kinetic transport algorithms for exascale simulations in neutron transport.
🧑💻 Graduate Research Assistant (GRA)
University of Tennessee/ORNL, 2023–2024
- Advancing dynamic likelihood filters for stochastic advection-diffusion equations in collaboration with ORNL and UTK.
💼 Research Intern
Oak Ridge National Lab (ORNL), 2021–2022
- Developed hybrid algorithms for simulating complex particle systems in 2D & 3D.
🌍 Research Intern
Los Alamos National Lab (LANL), 2020
- Focus on high-fidelity discrete fracture networks and Poisson-disk sampling algorithms for triangulations.
Research Interests
- 🧠 Computational Mathematics: Hybrid Monte Carlo methods, kinetic transport equations, and numerical simulations for complex physical systems.
- 🔍 Stochastic Processes: Advanced data-driven filtering techniques and applications in fluid dynamics, advection-diffusion, and PDEs.
- 💻 Statistical Modeling: Development of methods for high-dimensional data and stochastic modeling.
- 🌐 Interdisciplinary Work: Collaborating across fields of mathematics, physics, and engineering to tackle real-world computational challenges.
🏆 Awards
- 1st & 3rd place at the UTK SIAM Research Showcase (2023, 2024)
- Randall E. Cline Award (2022) for research excellence
🖥 Technical Skills
- Python, C++, R, Matlab, LATEX, and more
- Basic Fortran, AWK
🔗 Professional Memberships
Publications
A Hybrid Monte Carlo, Discontinuous Galerkin Method for Linear Kinetic Transport Equations
- Authors: Johannes Krotz, Cory D. Hauck, Ryan G. McClarren
- Journal: Journal of Computational Physics, Vol. 514
- Year: 2024
- Authors: Johannes Krotz, Matthew R. Sweeney, Jeffrey D. Hyman, Juan M. Restrepo, Carl W. Gable
- Journal: Journal of Computational and Applied Mathematics, Vol. 407
- Year: 2022
- Authors: Johannes Krotz, Jorge M. Ramires, Juan M. Restrepo
- Journal: The Monthly Weather Review
- Year: Under review
- Authors: Johannes Krotz
- Journal: Arxiv (preprint)
- Year: 2024