I am an assistant professor in the Mathematics Department at the University of Wisconsin - Madison (my hometown <3).
Previously I was an Instructor and NSF Postdoctoral Fellow in the Mathematics Department at Princeton University (2021-23) and an NSF Postdoctoral Fellow at the Courant Institute of Mathematical Sciences at NYU (2020-2021), where my sponsor was Michael Shelley. I completed my Ph.D. in mathematics in spring 2020 at the University of Minnesota, where I was advised by Yoichiro Mori and Daniel Spirn.
Contact:
lohm2 [at] wisc.edu
Van Vleck 609
Broadly, I am interested in the analysis of partial differential equations arising in biofluid mechanics. My overarching aim is to place fundamental biophysical modeling techniques on firm mathematical footing, and, in the process, help develop a deeper understanding of both the physical phenomena and the models themselves.
My recent work focuses on classical PDEs for swimming microorganisms, both single (via elastohydrodynamics) and collective (via kinetic theory for active suspensions). My earlier work centers on developing a rigorous PDE framework for slender body theory, a common approximation for describing thin fibers immersed in a viscous fluid.
Here are my CV and Google Scholar profile.
19. A hierarchy of blood vessel models, Part II: 3D-3D to 3D-1D and 1D. With S. Strikwerda.
(2025). [arXiv]
18. A hierarchy of blood vessel models, Part I: 3D-1D to 1D. With S. Strikwerda.
(2025). [arXiv]
17. Rods in flows: the PDE theory of immersed elastic filaments. With D. Albritton.
(2025). [arXiv]
16. Arrested development and traveling waves of active suspensions in nematic liquid crystals. With J. Li, S. Spagnolie.
To appear in Physical Review Fluids (2025). [arXiv]
15. A free boundary problem for an immersed filament in 3D Stokes flow.
(2024). [arXiv]
14. On an angle-averaged Neumann-to-Dirichlet map for thin filaments.
Archive for Rational Mechanics and Analysis (2024). [journal] [arXiv]
13. Well-posedness of a viscoelastic resistive force theory and applications to swimming.
Journal of Nonlinear Science (2024). [journal] [arXiv]
12. Well-posedness and applications of classical elastohydrodynamics for a swimming filament. With Y. Mori.
Nonlinearity (2023). [journal] [arXiv]
11. On the stabilizing effect of swimming in an active suspension. With D. Albritton.
SIAM Journal of Mathematical Analysis (2023). [journal] [arXiv]
10. Weakly nonlinear analysis of pattern formation in active suspensions. With M. Shelley.
movie1 movie2 movie3 movie4 movie5 movie6 movie7
Journal of Fluid Mechanics (2022). [journal] [arXiv]
9. Remarks on regularized Stokeslets in slender body theory.
Fluids (2021). [journal] [arXiv]
8. A single-layer based numerical method for the slender body boundary value problem. With W. Mitchell, H. Bell, Y. Mori, D. Spirn.
Journal of Computational Physics (2021). [journal] [arXiv]
7. An integral model based on slender body theory, with applications to curved rigid fibers. With H. Andersson, E. Celledoni, B. Owren, B. Tapley.
Physics of Fluids (2021). [journal] [arXiv]
6. Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations. With R-Y. Lai.
Inverse Problems and Imaging (2021). [journal] [arXiv]
5. Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid. With Y. Mori.
Studies in Applied Mathematics (2021). [journal] [arXiv]
4. An error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flow. With Y. Mori.
Research in the Mathematical Sciences (2020). [journal] [arXiv]
3. Theoretical justification and error analysis for slender body theory with free ends. With Y. Mori, D. Spirn.
Archive for Rational Mechanics and Analysis (2019). [journal] [arXiv]
2. Theoretical justification and error analysis for slender body theory. With Y. Mori, D. Spirn.
Communications on Pure and Applied Mathematics (2019). [journal] [arXiv]
1. Model for breast cancer diversity and spatial heterogeneity. With J.R. Romero-Arias, G. Ramírez-Santiago, J.X. Velasco-Hernández, M. Hernández-Rosales.
Physical Review E (2018). [journal]
Mathematical foundations of slender body theory. University of Minnesota (2020). [PDF] (or see papers 2 - 5)
PDE seminar, Mondays 3:30-4:30pm
PhAM group meeting, Wednesdays 4:00-5:00pm
ACMS Seminar, Fridays 2:25-3:25pm
At UW-Madison:
MATH 234 (Multivariable Calculus), Fall 2023 & Spring 2024
MATH 514 (Numerical Analysis), Fall 2024 & Spring 2025
At Princeton:
MAT-175 (Calculus for Economics and Life Sciences), Fall 2021 & 2022
MAT-JRSEM (Mathematics of microswimmers), Spring 2022 & 2023
At UMN:
Math 1241 (Calculus and Dynamical Systems in Biology), Fall 2018
Math 3283W (Sequences, Series, and Foundations), Fall 2017
Math 2263 (Multivariable Calculus), Spring 2016