Laurel Ohm

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.

I can be reached at lohm2 [at] wisc.edu .

Research

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. 

Left to right: me, 2019 Abel Prize winner Karen Uhlenbeck, and Elena Celledoni at the Abel Prize ceremony in Oslo

Here are my  CV  and Google Scholar profile.


Papers and preprints:

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.

(2023). [arXiv]


13.  Well-posedness of a viscoelastic resistive force theory and applications to swimming. 

  Journal of Nonlinear Science (2024). [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]


Dissertation:

Mathematical foundations of slender body theory. University of Minnesota (2020). [PDF] (or see papers 2 - 5)

Recent/Upcoming Activities

Teaching

At UW-Madison:

At Princeton:

At UMN: