Merlin Pelz
Welcome to my personal website! I'm a Dunham Jackson (postdoctoral) assistant professor in the School of Mathematics at the University of Minnesota, Twin Cities, mentored by Prof. Gregory Handy and Prof. Arnd Scheel. Before my current position, I earned my Ph.D. in Applied Mathematics at the University of British Columbia, advised by Prof. Michael J. Ward and Prof. Daniel Coombs. In my work, I'm focusing on further developing mathematical biology with nonlinear dynamics, asymptotic analysis, and (S)PDE theory. Specifically, I have been working on the emergence of spatio-temporal symmetry-breaking and synchronization in compartmental-reaction diffusion systems.
Short CV
Employment
| Year | Employer | Position |
|---|---|---|
| 2024 – now | University of Minnesota, Twin Cities | Dunham Jackson Assistant Professor |
Education
| Year | University | Degree | Advisors |
|---|---|---|---|
| 2020 – 2024 | University of British Columbia | Ph.D. (Appl. Mathematics) | Prof. Michael J. Ward & Prof. Daniel Coombs |
| 2017 – 2019 | Technical University of Munich | M.Sc. (Mathematics) | Prof. Mary Silber & Prof. Christian Kühn |
| 2013 – 2017 | University of Bayreuth | B.Sc. (Technomathematics) | Prof. Anton Schiela |
Further Research & Work Experience
Research
Here is a selection of figures to my research. For the corresponding developed theory, please go to the tab Publications. The figures for the 1-D domain were created with Julia, the steady-state figures for the 2-D domain with FlexPDE, and the oscillatory figures for the 2-D domain with our fast accurate marching scheme algorithm in Fortran and Julia. Intracellular kinetics used are FitzHugh-Nagumo, Gierer-Meinhardt, Rauch-Millonas, and Sel'kov reaction kinetics.

Symmetry-breaking in periodic 1-D domain with two compartments with FitzHugh-Nagumo kinetics. © Merlin Pelz

Convergence to symmetry-broken state in periodic 1-D domain with two compartments with Rauch-Millonas kinetics. © Merlin Pelz

Convergence to asymmetric state for which one cell is up- and two cells downregulated ("silenced") in periodic 1-D domain with cell Gierer-Meinhardt reaction kinetics. © Merlin Pelz

Bifurcation diagram showing degenerate pitchfork bubble in which stable symmetry-breaking takes place, no-flux 2-D domain with two Rauch-Millonas cells. Hysteresis occurs. © Merlin Pelz

Asymmetric steady-state in no-flux 2-D domain with two diffusion-coupled Gierer-Meinhardt cells. © Merlin Pelz

Numerical experiment: pattern formation in the no-flux 2-D domain with three big and close diffusion-coupled cells with Gierer-Meinhardt reaction kinetics. © Merlin Pelz

Convergence to stochastic attractor after stochastic bifurcation point in periodic 1-D domain with two nonlinearly randomly perturbed Rauch-Millonas cells. © Merlin Pelz

Extracellular diffusivity as bifurcation type parameter for phase transition of a Kuramoto order parameter for synchronization in system with two cells with oscillatory intracellular kinetics in ℝ² © Merlin Pelz

Synchronization of 4 equally separated cells with oscill. intracellular Sel'kov reaction kinetics in ℝ². Only cells 1 & 3 would oscillate if they were alone, but in the cell group cells 2 & 4 oscillate heavily. This is more than usual quorum sensing. ©MP
Publications
Articles
2026
Dynamical behavior of diffusively coupled scalar differential equations as Wentzell boundary conditions by M. P.
Oscillations in a scalar differential equation coupled to a diffusive field by M. P. & Arnd Scheel
2025
Compartmental-reaction diffusion framework for microscale dynamics of extracellular serotonin in brain tissue
by M. P. & Skirmantas Janušonis & Gregory Handy
2024
Synchronized Memory-Dependent Intracellular Oscillations for a Cell-Bulk ODE-PDE Model in ℝ² by M. P. & Michael J. Ward
2023
Symmetry-Breaking Bifurcations for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities in 2-D by M. P. & Michael J. Ward
The Emergence of Spatial Patterns for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities by M. P. & Michael J. Ward
A δf PIC Method with Forward-Backward Lagrangian Reconstructions by Martin Campos Pinto & M. P. & Pierre-Henri Tournier
Conferences
2026
Order and Function in Complex Systems Conference: co-organizer
Talks
2026
Order and Function in Complex Systems Conference: talk as conference co-organizer
Title: Dynamical Behavior of Diffusively Coupled Scalar Differential Equations as Wentzell Boundary ConditionsSIAM NWCS26 Conference: invited talk
Title: Spatial Heterogeneity of Extracellular Serotonin Induced by Firing Dynamics of Neural Fiber MeshworksICERM Workshop on Nonlinear Waves: contributed poster
Title: Oscillations in Scalar Boundary Dynamics Coupled to a Diffusive FieldAMS Spring Central Sectional Meeting: invited talk
Title: Oscillations in Scalar Boundary Dynamics Coupled to a Diffusive Field
2025
SMB Annual Meeting: invited talk
Title: Effect of Compartmentalization: Synchronization and Symmetry-Breaking of Diffusively Coupled Cells in 2-D and 3-DCNS*2025 Conference: invited talk
Title: Mathem. Insights into the Spatial Heterogeneity of Extracellular Serotonin Induced by the Geometry and Dynamics of Serotonergic FibersJoint Alabama-Florida Conference on Diff. Equations, Dynamical Systems and Applications: invited talk
Title: Symmetry-Breaking and Synchronized Memory-Dependent Oscillations in Compartmental-Reaction Diffusion SystemsSIAM DS25 Conference: contributed talk and chaired contributed session
Title: Synchronized Memory-Dependent Intracellular Oscillations in Compartmental-Reaction Diffusion SystemsNITMB Workshop on Biological Systems that Learn: poster
Title: Symmetry-Breaking in Compartmental-Reaction Diffusion Systems with Comparable Diffusivities
2024
CMS Winter Meeting: invited talks
Title 1: Synchronized Memory-Dependent Intracellular Oscillations in Compartmental-Reaction Diffusion Systems
Title 2: Symmetry-Breaking in Compartmental-Reaction Diffusion Systems with Comparable DiffusivitiesCAIMS Annual Meeting: invited talk
Title: The Analysis and Simulation of Memory-Dependent Oscillations for a Cell-Bulk ModelSIAM LS24 Conference: contributed talk
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D, 2-D, and 3-D
2023
SIAM PNW Conference: invited talk
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DSMB Annual Meeting: invited talk
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DDynamical Systems in the Life Sciences: invited poster presentation
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DCAIMS Annual Meeting: invited talk
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DSIAM DS23: jumped in
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DUBC & University of Utah Mathematical Biology Seminar
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-D
Teaching
| Year | Course | Number | Role | In-Class Notes |
|---|---|---|---|---|
| 2026 | Honors Calculus I | UMN Math 1571H | Instructor (30 students, 1 GTA) | (in progress) |
| 2026 | Mathematical Analysis of Biological Networks | UMN Math 5445 | Instructor (25 students, 1 GTA) | NotesM5445MPelz |
| 2025 | Calculus and Dynamical Systems in Biology | UMN Math 1241 | Instructor (75 students, 2 GTAs & 4 UTAs) | (via doenet.org) |
| 2025 | Linear Algebra & Differential Equations | UMN Math 2243 | Instructor (30 students, no TA) | NotesM2243MPelz |
| 2024 | Linear Algebra & Differential Equations | UMN Math 2243 | Instructor (30 students, online section, no TA) | (same as above) |
| 2023 | Calculus 2 | UBC Math 101 | Small Class Instructor (4⋅60 students) | |
| 2022 | Differential Equations for Mechanical Engineers | UBC Math 258 | Tutorial Leader (4⋅30 students) |
Contact
For email contact, please use mpelz {at} umn.edu.




