# 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.

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.

(2022). [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

ICIAM, Tokyo, Japan (Aug. 2023)

SIAM Conference on Optimization and Control, Philadelphia, PA (July 2023)

RISM, Villa Toeplitz, Varese, Italy (July 2023)

Shocking developments: new directions in compressible and incompressible flows, Leipzig, Germany (June 2023)

Recent advances in mathematical fluid dynamics, Duke University (May 2023)

Applied math postdoc seminar, Johns Hopkins University (virtual) (Mar. 2023)

SIAM SEAS, Virginia Tech (Mar. 2023)

AMS Sectional, Georgia Tech (Mar. 2023)

SIAM CSE23, Amsterdam, NL (Mar. 2023)

Coorganizer, AMS EDGE session, Joint Mathematics Meetings, Boston, MA (Jan. 2023)

PDE Seminar, Brown University (Oct. 2022)

Applied and Computational Math Seminar, Tulane University (Oct. 2022)

EDGE panel, Birthday Conference for Karen Uhlenbeck, IAS (Sept. 2022)

AWM Symposium, University of Minnesota (June 2022)

Mechanics of Life workshop, Flatiron Institute (May 2022)

PDE/Applied Math seminar, Drexel University (May 2022)

Applied and Computational Math seminar, University of Minnesota (May 2022)

Coorganizer, AMS EDGE session, Joint Mathematics Meetings (virtual) (Apr. 2022)

PDE seminar, University of Tennessee - Knoxville (virtual) (Feb. 2022)

CCM colloquium, Flatiron Institute, NYC (Dec. 2021)

APS DFD, Phoenix, AZ (Nov. 2021)

Analysis of Fluids seminar, Princeton University (Sept. 2021)

Fluids and Waves seminar, NJIT (Sept. 2021)

SIAM Conference on Applications of Dynamical Systems (virtual) (May 2021)

HA-GMT-PDE seminar (virtual) (March 2021)

Coorganizer, MAA EDGE session, Joint Mathematics Meetings (virtual) (Jan. 2021)

Modeling and Simulation Group (MSG) seminar, Courant Institute, NYU (virtual) (Nov. 2020)

Analysis, Dynamics, and Applications seminar, University of Arizona (virtual) (Oct. 2020)

Coorganizer, MAA EDGE session, Joint Mathematics Meetings, Denver, CO (Jan. 2020)

AWM poster session, Joint Mathematics Meetings, Denver, CO (Jan. 2020)

SIAM Conference on Analysis of Partial Differential Equations, La Quinta, CA (Dec. 2019)

ICIAM Session on Fluids Physics and Statistical Mechanics, Valencia, Spain (July 2019)

Visiting researcher, Norwegian University of Science and Technology (NTNU), Trondheim, Norway (March - May 2019)

Coorganizer, MAA EDGE session, Joint Mathematics Meetings, Baltimore, MD (Jan. 2019)

SIAM Conference on the Life Sciences, Minneapolis, MN (Aug. 2018) [Link to talk]

SIAM Conference on Mathematical Aspects of Materials Science, Portland, OR (July 2018)

## Teaching

At UW-Madison:

MATH 234 (Multivariable Calculus), Fall 2023 & Spring 2024

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