Interviewer: Sarah Liaw

Trivia

• Favorite book: Hard to pick a favorite book!
• Favorite place: I love traveling a lot, and I do not have a favorite place, but I particularly enjoy spending time in Africa. Currently, I am in Kigali, Rwanda (as of March). I consider myself cosmopolitan—a citizen of the world.
• Favorite food: Avocados! The best avocados I have tried are from Kenya.
• Favorite equation: The aggregation-diffusion equation. I did my PhD on it, and it is the type of equation that I often encounter in various contexts. Whether it is something diffusing and attracting, or repelling and attracting, there are many scenarios and applications where this equation applies. It is quite a general equation! 

Could you give an overview of your research and its potential applications?

My research has evolved since I arrived at Caltech. Before coming to Caltech, my Ph.D. was in PDE theory and analysis, focusing particularly on long-time asymptotics. This involves predicting the patterns and behaviors observed in various systems, such as fluids, population modeling, animal behavior, bacterial dynamics, and gas particle interactions. 

The applications of this research are big. Whenever there are particles involved interacting with each other—whether they are people, cells, gas molecules, or chemical molecules, describing the evolution or trajectory of each individual particle becomes challenging, especially with a large number of particles. In such cases, it is more manageable to describe the distribution of particles using a probability density that solves the PDE. 

What I find particularly intriguing is the presence of these equations across various disciplines. By understanding the mathematical structure of these equations, one can contribute to a wide range of fields, including biology, chemistry, material science, sociology, and data analysis. This versatility allows for meaningful contributions to diverse applications. 

What aspects of research do you most enjoy? What led/motivated you to work on PDE approaches and analysis? 

I ended up working on PDEs by chance. I met some really inspiring people, and I liked how they related to the work and the research. I really enjoy the collaborative aspect of it, and I also appreciate the intellectual challenge. There is no easy or hard mathematics. You either understand it, and then it’s easy; or you don’t understand it, and then it’s hard. Making progress on a research problem in mathematics is very psychological. It is about not giving up, having self-confidence, and actually trusting that if you try hard enough, you will eventually progress.

What I most enjoy about research is the interdisciplinary aspect of it. I know some mathematicians that spend their life on one specific topic, and I’m not cut out to do that [laughs]. I like challenging myself by jumping into many different areas and trying to make connections. Technology transfer plays a significant role. If you use techniques from one area and find that they can achieve progress in another area, you have to be involved in many different communities. Since I arrived at Caltech, I have changed my research a bit simply because I was exposed to so many other topics. Now, I play an interdisciplinary role between different fields. 

As a mathematician, how do you strike a balance between theoretical rigor in mathematical analysis and the practical considerations of real-world problems if there are any conflicts? Does this balance influence your research approach?

That’s a very good question! I do not think there should be a conflict. You need both, and some applications would benefit from more rigor and appreciation of theory. Also, a lot of theory would benefit from being exposed to the needs that people who usually use the techniques actually have. Silos are dangerous. Both are equally important, and Caltech is a very good place to bridge this gap. In general, engineers I have met here at Caltech are more mathematical than most engineers I know in other places, and vice versa. The mathematicians here are very interested in talking to people doing more applied sciences, or beyond that, solving real-world problems. 

What are the biggest challenges that you have faced while doing research? How did you overcome them? 

There are many challenges in different stages of life. In particular, moving from an undergraduate degree, bachelor’s, or master’s, to engaging in research, you often find yourself without a clear answer. There is no set curriculum or clear definition of when you have done enough. You will never finish answering all the questions in the universe, and you will never complete all the research out there to be done. It is important to measure yourself against your own progress, rather than comparing yourself to others around you. Once you are in advanced research, everyone follows a very different path, with different skills and skill sets. In a highly competitive environment, especially in academia, it is important to ensure you maintain a balanced life, which is beneficial in the long term. 

What do you see as the short-term or long-term directions of your work and the field as a whole? Is there anything you are very excited about in your work currently? 

Overall, I would characterize the work I am doing as operating at the interface between model-driven and data-driven approaches. Often, you will have some knowledge about the process you want to model or predict, but not complete knowledge. You might have a partial understanding of the physics or biology involved, with other aspects remaining uncertain. You also have data, which may come from real-world observations or experiments. Usually, the best approach [to learn about the system] lies somewhere between extremes. You do not want to rely solely on data while disregarding the knowledge you have, nor do you want to rely solely on models without considering the data that can test them. 

The overarching challenge is how to effectively integrate models with data. Almost all my work revolves around that question in some shape or form. What I find very exciting is that there is a role for mathematicians in the current evolution of data science, more broadly in machine learning and artificial intelligence, but also in many new technological advances where theoretical insights are needed and can influence the direction of algorithm development or resource allocation. I really enjoy engaging in theoretical work, but at the same time, I want that theoretical work to have a tangible impact in other areas or fields. 

What are your interests outside of research, teaching and Caltech?

I love traveling, and being a researcher and mathematician allows me to combine work with exploring new places. Alongside my academic pursuits, I have various hobbies. I am passionate about dancing, particularly salsa, and at one point, I was even running the Caltech Salsa Club during my postdoc days. I enjoy playing chamber music; I play the viola and am currently involved in several quintets, quartets, and trios. I also participate in the Caltech Chamber music program from time to time. Music has been a fantastic way for me to connect with people, especially since I have moved countries frequently as an academic. Every time I relocate, rebuilding social circles can be challenging, but music and dancing have helped a lot. 

For over a decade, I have been involved in mathematics and science projects in Africa. Initially, it was on a voluntary basis, but now I have a position with the African Institute of Mathematical Sciences (AIMS). In particular, I have established a PhD program in data science there. I travel to Africa several times a year and have been involved in projects ranging from primary education to university-level research. Now that I am at Caltech, I am exploring ways to connect my role here with my commitment to capacity building in mathematics in Africa. 

Do you have any advice for Caltech students who want to get into research?

You should make sure you enjoy what you do. Do not try to fulfill someone else’s expectations because research is challenging, and if you are doing it for someone else and not because you are actually passionate about it, then it will be harder. For Caltech undergrads, I would advise them to collaborate a lot and not try to face challenges by themselves. That is always true in life!