Life After Davis: An Exercise in Nonlinear Navigation

The last time UC Davis saw me was when graduated in the summer of 2018 with a Ph.D. in Mathematics. My dissertation was in low-dimensional topology under Abby Thompson, focusing on Heegaard splittings of knot complements in the 3-sphere (with additional mentorship of Javier Arsuaga in the application of knot theory to molecular biology, particularly the folding of chromosomes in yeast). Only a few months prior to that, I had accepted an offer to join the faculty at University of the Pacific (UOP) in Stockton, CA, as a tenure-track assistant professor of applied mathematics. I eagerly started that position at the end of August 2018.

At UOP I was focused on undergraduate mathematics teaching, which was something that I had always intended on doing. This was much of my motivation for going into graduate school, and teaching and mentoring still drive much of what I do today. I was very proud of the work I did there and loved the relationships I was building with my colleagues and students. Eventually, however, there was a mismatch of expectations in teaching with my department chair. Additionally, my interest in the research I had done in graduate school had waned significantly. In discussion with a friend from my undergraduate days at Cal Poly, she mentioned she needed a postdoctoral research associate in her group at Los Alamos National Laboratory (LANL). Although this seemed like a step backward in the traditional career ladder, I saw an opportunity to start fresh with new research and develop my academic footprint that I had been lacking without postdoc experience.

We moved out to New Mexico, and I started at LANL in July 2020 working for two teams: the Subcritical Weapons Experiments team and the Advanced Imaging team. The Subcritical Weapons team worked on the stewardship of the United States’ nuclear stockpile. That stockpile degrades over time, and my role in this team was to help in understanding that degradation. Our experiments involved studying the results of impacting thin metal sheets with shock waves of high explosives. We recorded holograms of the field of particles sprayed from the metal (digital holographic microscopy), used those holograms to produce 3D reconstructions in a computer, and then characterized the kinetics and particle size distributions from the resulting volume reconstructions. The math for this work involved studying the wave equation via Fourier analysis (wave optics) and computer vision techniques for image segmentation, which included some differential geometry.

The Advanced Imaging team worked very closely with the National Ignition Facility (NIF) at Lawrence-Livermore National Laboratory, whose mission is to achieve nuclear ignition and further progress in developing a means of commercial energy production from fusion reactions. My team at LANL operated the sole neutron imaging diagnostic in these experiments and produced analyses that informed the modification of parameters in the fusion experiments carried out at NIF. My role in the team was to carry out these analyses, which primarily focused on the 3D reconstruction of neutron sources in the fusion reactions (limited view tomography). The work involved a significant amount of inverse problem analysis, numerical linear algebra, and mathematical statistics, and my work resulted in a first-author publication.

I liked image processing a lot more than I expected, and I also developed an affinity for statistical estimation. However, postdoctoral appointments are only for 2-3 years, after such point you are expected to either convert to Laboratory staff or depart. After the combined isolations of northern New Mexico and social distancing due to COVID, my wife (also with LANL) and I decided that we would like to move on. The two-body problem, though, can be difficult to navigate.

During my job hunt I put out over 100 applications; I was contacted for 4 of them. I came in second for a search for a teaching-track assistant professor at Worcester Polytechnic Institute in Massachusetts. I was offered a tenure-track assistant professorship at Sweet Briar College in Virginia, which I declined due to value differences. West Point Academy in New York offered an appointment as a professor, which I also declined because it was effectively a postdoctoral appointment. I started the interview process with Northern Arizona State University; but my wife and I looked at each other and realized that, while the positions were tantalizing in their own rights, we needed to compromise with each other and look where we could both find work. We decided that the greater Boston area was ideal due to the rich academic and industrial opportunities there. Soon after, my wife applied for and received an offer to join Draper Laboratory as an Environmental Health & Safety professional—so we moved to the Boston area at the end of September 2022, and I continued my job search there.

It didn’t take long; less than 20 applications this time! A small defense contractor called STR (formerly Systems Technology & Research) was quickly outgrowing its startup boots, saw my application, called me in for an interview, and offered me a position as a Senior RF Signal Processing Engineer. The pay is indeed significantly better than entry-level academic positions. I still had a queasy feeling after working for the stewards of the first weapons of mass destruction, so felt better not directly compromising my morals, since STR’s motto is to “win without a fight.” They specialize in the conceptualization of defense capabilities and technologies rather than their manufacture and fielding. (Yes, this kind of company exists!) I started with them on Halloween of 2022.

My work at STR was initially focused on the development of novel algorithms for electronic warfare (like radar jamming and false target projection), but it eventually developed into path planning for uncrewed aerial and undersea vehicles (UAV and UUV, respectively), and then into tracking and state estimation of radio frequency (RF) signals. While I can’t mention specifics, I can tell you about the diverse mathematics involved. RF signal modification requires applied/numerical linear algebra, dynamic programming, information theory, geometry, and non-convex optimization (and a good amount of physics); path planning for uncrewed aerial and undersea vehicles path planning emphasizes geometry, optimal control, and variational calculus; and tracking gathers mathematical statistics, estimation and detection theory, and stochastic processes under the common umbrella of sensor and data fusion. I was by no means an expert in any of these fields apart from geometry and linear algebra, but I learned a good amount about all of them while working on various programs. Even among the diversity in technical skills I had to develop, I was still able to publish a preprint of work that used topological data analysis for detecting anomalous ship tracks (that is, a spoofed-track detector).

I found that I really liked the optimal control work for UAVs and UUVs, and I determined that autonomous navigation was the right place to be looking for this kind of work. Unfortunately, STR does not specialize in this work, so programs they get in this vein are few and far between (nor are they funded well). Moreover, the work that does come through is on a fast track and needs quick execution, so the work naturally goes to my more experienced colleagues, and doesn’t offer much of a chance to learn from them on the job. This prompted me to look for jobs where this work was more regular and I could learn it along the way.

This leads us to the present, where I start a new position with MITRE at the beginning of May 2026. The group is comprised of applied mathematicians and focuses on communications, signal intelligence (SIGINT), and positioning, navigation, and timing (PNT). This group often focuses on guidance, navigation, and control (GNC), so there will be many opportunities to explore autonomous navigation. Who knows? Maybe I’ll find other things that interest me along the way. I’m excited to see how this next chapter unfolds (and relieved that changing jobs doesn’t mean moving to a new state!).

I still consider myself a teacher and a mentor first and foremost, so I want to leave you with the lessons I have learned in this nontraditional journey into life after graduate school.

First, as someone who has many interests, it’s hard to decide on one thing to specialize in (I am strongly resistant to it); so if you must specialize, look for fields that are central to many others where you can pursue the adjacencies in parallel. I planned for this early on in choosing mathematics as my field of study, but what I didn’t realize is that the pressure to specialize increases the longer you stay in technical fields. I have found success in “specializing” in linear algebra, dynamical systems, and mathematical statistics. (Don’t skip out on the probability and statistics courses! I did, and it’s biting me hard now.)

Second, sometimes you need to take a step back to move forward. It was difficult for me to step away from the allure of a tenure-track position, but it ultimately made me happier and led to a diversity of study that made me more marketable for future opportunities. If you find that you want to press forward through resistance, you will find a way to do it. This is the subtle difference in the confidence in ability and the confidence in navigating uncertainty. Both paths require the courage to act, but passion can be a strong motivator to see your choice through.

Finally, quit telling yourself that there is a “right way” to do this. Sure, there are traditional paths, but that doesn’t mean there aren’t others that could work for you, too. I hope that my story gives you some solace that, whatever direction you choose from here, there are opportunities to receive you. They may not be what you expected, but they can often be what you need. I can advise you to be open to the possibilities, but that’s all advice is: advice, which you can choose whether or not to take.

I can’t wait to see where I go from here.