• Research Interests:

My primary research interest lies in the geometry of neural and cardiac signal propagation within spatially and temporally multidimensional domains of the heart and brain. I investigate these processes through the framework of moving frames, curvature tensors, and high-order computational schemes. This work resides at the intersection of scientific computing, differential geometry, and partial differential equations, with applications spanning computational neuroscience, cardiac electrophysiology, and computational electrodynamics. 

For numerical simulations, my focus is on high-order Galerkin and spectral/hp methods applied to multi-dimensional complex domains, particularly spacetime manifolds exhibiting strong anisotropy. These approaches enable precise modeling of coupled electrical phenomena and provide insights into the underlying geometric and physiological structures governing bioelectrical propagation.

My recent research activities focus on simulating neural spike propagation in multidimensional domains, aiming to provide computational insights into high-order brain functions, including the mechanisms underlying human consciousness.

Keywords: Moving frames, Neural dynamics, Multidimensional spacetime, and Human Consciousness.

• Publications:

1. S. Chun and L. Peng. A Multidimensional Neural Bidomain Model with Ephaptic Coupling via Moving Frames, in revision, 2026.

2. [Book] Sehun Chun, Moving Frames for the Numerical Solution of Partial Differential Equations in Complex Domains: Computation Using Orthonormal Basis Vectors, Springer, 2026, ISBN: 978-9819544943, available at Amazon.

3. S. Chun and J. H. Jung, Time map method for spatiotemporal simulation of cardiac and neural signal propagation, Math. Comput. Simul., 239, 155-171, 2026, Download.

4. Sehun Chun, Relative acceleration of orthonormal basis vectors for the geometric conduction blocks of the cardiac electric signal propagation on anisotropic curved surfaces,  J. Compt. Phys: X, 17, 100135, 2023. Download.

5. Sehun Chun, High-order method with moving frames to compute the covariant derivatives of vectors on general 2D curved surfaces, Comm. Appl. Math. Comp., 5, 1534-1563, 2023. Download.

6.  S. Chun, J. Marcon, J. Peiro, S. J. Sherwin, Reducing errors caused by geometrical inaccuracy to solve partial differential equations with moving frames on curvilinear domain, Compt. Meth. Appl. M. Eng. 398, 1, 115261, 2022. Download.

7. Sehun Chun and Taejin Oh, Divergence/connection preservation scheme in the curvilinear domain with a small geometric approximation error, J. Sci. Compt., 92(15), https://doi.org/10.1007/s10915-022-01865-0, 2022, Download 

8. D. Moxey, C. D. Cantwell, Y. Bao, A. Cassinelli, G. Castiglioni, S. Chun, E. Juda, E. Kazemi, K. Lackhove, J. Marcon, G. Mengaldo, D. Serson, M. Turner, H. Xu, J. Peiro, R. M. Kirby, S. J. Sherwin, Nektar++: Enhancing the capability and application of high-fidelity spectral/hp element methods, Compt. Phys. Comm., 249, 107110, 2020,  Download.

9. Sehun Chun, Method of moving frames to solve the time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation,  J. Comput. Phys., 340, 85-104, 2017. Download

10. S. Chun and C. Eskilsson, Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces,  J. Compt. Phys., 333, 1-23, 2017. Download

11. Sehun Chun, An electromagnetic field model of cardiac excitation on the transverse electric current to induce the magnetic field, Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2016, WCE 2016, 29 June - 1 July, 2016, London, UK, pp. 1-9. Download

12. Sehun Chun, A mathematical model of the unidirectional block caused by the pulmonary veins for anatomically-induced atrial reentry, J. Biol. Phys., 40(3), 219-258, 2014. Download

13. Sehun Chun, Method of moving frames to solve (an)isotropic diffusion equations on curved surfaces, J. Sci. Compt., 59(3), 626-666, 2014. Download

14. Book: S. Chun and Jan S. Hesthaven, High-order accurate methods for solving Maxwell's equations: applications to photonic crystals and thin layer coatings (ISBN 978-3-639-51280-9), Saarbrucken, Germany, 2013, Scholars-Press. Preview.

15. Sehun Chun, Quantum electrodynamic theory of the cardiac excitation propagation I: construction of quantum electrodynamics in the bidomain, http://arxiv.org/abs/1310.3035, 2013.

16. Sehun Chun, Method of moving frames to solve conservation laws on curved surfaces, J. Sci. Compt., 53(2), 268-294, 2012. Download

17. Peter E. J. Vos, C. Eskilsson, A. Bolis, S. Chun, R.M. Kirby and S. J. Sherwin. A Generic Framework of Time-Stepping PDEs: general linear methods, object-orientated implementation and application to fluid problems, Int. J. Compt. Fluid. Dyn., 24(3), 2011. Download

18. S. Chun, H. Haddar and J.S. Hesthaven. High-order accurate thin layer approximations for time-domain electromagnetics, Part II: Transmission layers, J. Compt. Appl. Math., 2587-2608, 234(8), 2010. Download

19. S. Chun and J.S. Hesthaven. High-order accurate thin layer approximations for time-domain electromagnetics, Part I: General metal backed coatings, J. Compt. Appl. Math., 598-611, 231, 2009. Download

20. S. Chun and J.S. Hesthaven. PDE constrained optimization and design of frozen mode crystals, Comm. Compt. Phys.  878-898, 3(4), 2008. Download

21. S. Chun and J.S. Hesthaven. Modeling of the frozen mode phenomenon and its sensitivity using Discontinuous Galerkin Methods, Comm. Compt. Phys., 611-639, 2(4), 2007. Download

• Patents:

1. S. Chun and H. J. Park, Brain/Heart Electric Current Analysis Algorithm Using Relative Acceleration, 10-2022-0039715, Republic of Korea, 2022.

2. Y. W. Kim and S. Chun, White matter tractography algorithm using excitation time map of brain DTI image, 10-2024-0109219 (2024-08-14), Republic of Korea, 2024.

3. S. Chun and J. H. Jung, Time Map for fast time-dependent multidimensional diffusion-reaction simulation  with ordinary differential equations, 10-2022-0170891 (2022-12-08), Republic of Korea, 2025.

4. S. Chun and J. H. Jung, Time Map for fast time-dependent multidimensional diffusion-reaction simulation  with ordinary differential equations, in progress, US, 2026

• Grants:

1. Study of white matter connectivity using moving frames for the geometric properties of diffusion tensor image, Korea-Japan Basic Science Cooperation Program between NRF and JSPS, 21,000 USD, National Research Foundation of Korea, 2025-2026.

2. A mathematical modeling of time map for spacetime analysis of brain and heart’s electric flows and its application to diagnosis, prediction, and surgical plans of electric flow disorder,  Principal researcher,   550,000 USD,  National Research Foundation of Korea, 2021 - 2026, 

3. Mathematical and computational heart modeling center, Project leader, Principal researcher, 9,000 USD, Institute of Convergence Science, Yonsei University, 2016 - 2019.

4.  An electrodynamic field model of cardiac restitution and cardiac memory for geometric conduction block to induce functional reentry (renewed), Principal researcher,  164,800 USD, National Research Foundation of Korea, 2017 - 2019, 

5. An electrodynamic field model of cardiac restitution and cardiac memory for geometric conduction block to induce functional reentry, Principal researcher,  41,200 USD, National Research Foundation of Korea, 2016 - 2017.

• Selected Conference Talks:

1. High-order method with moving frames for the ephaptic coupling of the general 2D neural fibers with non-aligned Ranvier nodes,  Advances in High-order Methods - fluid dynamics, biomedical science, and exascale computing, June, Pohang, 2024.

2. Relative acceleration of orthonormal basis vectors for a cardiac conduction block on 2D general curved surfaces, ICOSAHOM, August, Seoul, 2023.

3. Finding the "geometry" of the heart and brain with moving frames, {\it Symmetry, Invariants, and their Applications}, Dalhousie University, July 2022.

4. Moving frames for the numerical solution of PDEs and beyond in applications to Meteorology, Cardiology, and Neuroscience., {\it Moving Frames and their Modern Application}, Virtual conference, Banff International Research Station, November 2021.

5. High-order time map for the electric flow in the heart and brain, {\it International Conference on Spectral and High order Methods (ICOSAHOM) 2021}, Virtual conference, June 2021.

6. Action potential propagation along ephaptically coupled white matter fiber from DTI data, {\it SIAM Conference on Computational Science and Engineering (CSE21)}, Virtual conference, March 2021.

7. Excitation time map for fast multidimensional simulation with ODEs beyond PDEs, {\it 2020 KSIAM Annual Meeting}, Jeju, South Korea, Nov. 2020.

8. Computing Riemannian curvature tensor for stopping conditions of cardiac electric flow in multidimensional anisotropic cardiac tissue,  Modeling of Cardiac Function, Varese, Italy, July 2019.

9. High-order curvilinear mesh in the numerical solution of PDEs with moving frames on the sphere, PDE on the sphere, Montreal, Canada, May, 2019.

10. Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces, International Conference on Spectral and High order Methods (ICOSAHOM), London, United Kingdom, July, 2018.

11. Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces, Partial Differential Equations on the Sphere (PDEs), Paris, France, April 2017.

12. An electromagnetic field model of cardiac excitation on the transverse electric current to induce the magnetic field (Invited Talk), International Conference of Applied and Engineering Mathematics, World Congress on Engineering 2016, London, United Kingdom, June 2016.

13. An electrodynamic model of the cardiac electric signal propagation, Latest Advances in Cardiac Modelling, Munich, Germany,  March 2015.

14. Lagrangian and Hamiltonian approach in the mathematical analysis of the cardiac excitation propagation, Southern Africa Mathematical Sciences Association, Stellenbosch, South Africa, November 2013.

15. How to solve PDEs numerically in Riemannian geometry?, South African Symposium on Numerical and Applied Mathematics (SANAM), Stellenbosch, South Africa, April 2013.

16. Introducing the method of moving frames to solve PDEs on curved surfaces, International Conference on Spectral and High order Methods (ICOSAHOM), Tunis, Tunisia, June 2012. 

17. Curvature in the Heart, KMS and AMS annual meeting, Seoul, South Korea, December 2009.

18. High-order methods for simulating cardiac electrophysiological phenomena, Bioengineering, Oxford, UK, September 2009.

19. High-order methods for simulating cardiac electrophysiological phenomena, International Conference on Spectral and High order Methods (ICOSAHOM), Trondheim, Norway, June 2009.

• Academic Courses taught:

• Calculus and Vector Analysis I and II

• Engineering Mathematics (Ordinary Differential equations, Linear Algebra)

• Computer Programming (Python)

• Concepts in Bioinformatics.

• Introduction to Computational Neuroscience.

• Introduction to Neural Networks. 

• Former Students and Postdocs: 

1. Ms. Faraniana Rasolofoson, Jul. 2012 - Dec. 2013, M. Sc. Program, Comparative studies on the impacts of various fluxes in a discontinuous Galerkin scheme for two-dimensional shallow water equations, African Institute for Mathematical Sciences and Stellenbosch University, South Africa.

2. Mr. Mamadou Ballo Sall, Oct. 2013 - Jul. 2015, M. Sc. Program, Numerical solution of Maxwell's equations in two dimensional domain by the discontinuous Galerkin method, African Institute for Mathematical Sciences and Stellenbosch University, South Africa.

3. Dr. Ehsan Kazemi Foroushani, Jan. 2017 - Aug. 2017, Postdoctoral fellowship granted by NRF, Incorporation of the MMF schemes into Nektar++, Underwood International College, Yonsei University, South Korea.

4. Ms. Haley Kim, Jan. 2018 - Aug. 2018, Research Assistant, Neural Network and Deep Learning, Underwood International College, Yonsei University, South Korea.

5. Ms. Yoon InYoung, Jan. 2018 - Dec. 2018, Research Assistant, Neural Network and Deep Learning, Underwood International College, Yonsei University, South Korea.

6. Ms. Sarah Park, Jan. 2018 - Dec. 2018, Research Assistant, Neural Network and Deep Learning, Underwood International College, Yonsei University, South Korea.

7. Mr. Vincent Graham, Dec. 2018 - May. 2019, Research Assistant, Neural Network and Deep Learning, Underwood International College, Yonsei University, South Korea.

8. Ms. Dajung Park, Undergraduate research assistantship}, May -  July 2019: Development of algorithms for deep Learning with physical constraints.

9.  Ms. Jungmin Nam, Undergraduate research internship}, Dec. 2019 - Feb. 2020: MRTrix3 for white matter tractography.

10. Mr. JaeYoung Lee, Undergraduate research internship}, Dec. 2019 - Feb. 2020: MRTrix3 for white matter tractography.

11. Mr. Woojong Kang, Undergraduate research assistantship}, Dec. 2019 - June. 2020: An Effective Computational Method for Fiber Tractography (senior thesis).

12. Dr. Abdoulkadri Chama, Postdoctoral research}, Jan. 2022 - June 2022: Implementation of white matter tracking and analysis in Nektar++ and NekRS.

13. Mr. YoungWoo Kim, Undergraduate research assistantship}, Sept. 2021 - 2024: High-order method to compute white matter tractography from DTI.

14. Mr. Hoeyoung Kim, Undergraduate research assistantship}, Sept. 2021 - 2023: Effect of fiber curvature for the fiber bundle with the Ranvier node through mutual information.

15. Mr. Dongwon Jung, Undergraduate research assistantship}, Dec. 2022 - Present: Machine learning for time map analysis.

16. Mr. Junyoung Jung, Undergraduate research assistantship}, June. 2022 - 2024: Energy grid system for electric car using neural network.

17. Mr. Woosung Choi, Undergraduate research assistantship}, Sept.. 2023 - Present: Consciousness, Ephaptic coupling 2D

18. Mr, Taehyun Hahn, Undergraduate research assistantship}, Jan.. 2024 - Present: High-order white matter tracking with parcellation