Postdoctoral Research Scholar · Applied Mathematics, UC Merced
Stephen Williams
I build mathematical models to predict how partnerships between hosts and microbes form, and how they break down under stress, especially climate-driven warming. My work combines low-Reynolds-number fluid dynamics, mathematical modeling and data-driven inference, developed in close collaboration with experimental labs. My main systems are the bobtail squid and its bioluminescent symbiont Vibrio fischeri, and the sea anemone Exaiptasia diaphana, a laboratory model for coral bleaching.
I am part of NSF INSITE, the Institute for Symbiotic Interactions, Training, and Education in the Face of a Changing Climate, working with Profs. Erica Rutter and Shilpa Khatri. I did my PhD in physics at the University of Warwick with Prof. Marco Polin.
Research
All research →Symbioses can fail at any scale: in the flows a host uses to recruit its microbes, in how microbes adapt to stress, or in host populations. I build mechanistic models at each scale, then use sensitivity and identifiability analysis to show experimental collaborators which measurements matter most.
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News
All updates →- Jun 2026CassiopeaBase MATH-BIO 2026 · A contributed talk in Key Largo, Florida, on the flows bobtail squid use to recruit their symbionts, plus a conference travel award.
- Mar 2026COOGRE Class 2026 · A hands-on workshop on mathematical modeling for UC Merced's Cooperative-based Graduate Research Experience.
- Mar 2026AMS Western Sectional 2026 · An invited talk in Boise, Idaho, on how thermal stress disrupts the flows bobtail squid use to recruit their symbionts.
- Jan 2026Hawaiʻi field work, January 2026 · Collecting Hawaiian bobtail squid at night at Paikō on Oʻahu, working out of the University of Hawaiʻi's Kewalo Marine Laboratory.
- Nov 2025Thermal Stress Disrupts Symbiotic Fluid Dynamics in Bobtail Squid · A fluid-dynamics model of the squid's mantle cavity shows that heat stress can cut young squid's ability to capture the bacteria they depend on.
Publications
Google Scholar →Identifiability, sensitivity, and genetic algorithms in bacterial biofilm selection models
Thermal stress disrupts symbiotic fluid dynamics in bobtail squid
Confinement-induced accumulation and de-mixing of microscopic active–passive mixtures
* Student I mentored.
In preparation
- Williams, S., Khatri, S., Polin, M. Controlling passive particle distributions in mixed systems through active scattering events.
- Williams, S., Muffett, K. M. Deep learning measures the timing of strobilation in Cassiopea from daily photographs.
Ongoing projects
- Williams, S., Muffett, K. M., Sindi, S. S., Sogin, E. M., Khatri, S., Rutter, E. M. Modeling and identifiability in size-structured populations of Exaiptasia diaphana.
- Williams, S., Ruiz, K. A.*, Heath-Heckman, E., Rutter, E. M., Khatri, S. Exploring the impacts of squid breathing dynamics on bacterial symbiont acquisition.
Interactive
Open the interactive page →Two models from my papers that you can run in the browser: one day of a biofilm selection model with sliders, and Stokes flow from point forces.
Talks & posters
| Date | Event | Type |
|---|---|---|
| Jun 2026 | CassiopeaBase MATH-BIO 2026, Key Largo, FL | Talk |
| Mar 2026 | Spring AMS Western Sectional Meeting, Boise, ID | Invited talk |
| Oct 2025 | Interdisciplinary Center for Quantitative Modeling in Biology, UC Riverside | Invited seminar |
| Jul 2025 | NITMB Workshop: Mathematical Modeling, Computational Methods, and Biological Fluid Dynamics, Chicago, IL | Talk & poster |
| Jan 2025 | Mathematics of Data, Dynamics, and Life Sciences, UC Irvine | Poster |
| Nov 2024 | 77th Annual Meeting of the APS Division of Fluid Dynamics, Salt Lake City, UT | Talk |
| Jun 2024 | SIAM Conference on the Life Sciences (LS24), Portland, OR | Talk |
Earlier talks and posters are listed in my CV. Slides and posters will be linked here.
Positions & education
- 2023 – presentPostdoctoral Research ScholarApplied Mathematics, UC Merced · NSF INSITE
- 2022 – 2023Postdoctoral Research FellowSoft Matter Physics, University of Warwick
- 2022Research TechnicianSoft Matter Physics, University of Warwick
- 2018 – 2022PhD, PhysicsUniversity of Warwick · Mixed Active–Passive Systems in Confinement
- 2014 – 2018MMathPhys, Mathematics and PhysicsUniversity of Warwick