I work in applied stochastic dynamics. I am interested in dynamical processes of things that evolve over time in some complex way, but with some randomness. The applied part is I’m interested in a range of applications of stochastic dynamics.

My Ph.D. was about propagating waves through a medium that has randomness. That randomness does some scattering. The question is: does the wave propagate? Does it get trapped? Different scenarios are possible, and trapping can occur. Instead of thinking of a wave that just propagates, it might get trapped because of the randomness. Propagation is not perfect anymore.

Later, I moved to applications related to optics, such as randomness that will limit or amplify the strength of a laser. Lasers are set up with a feedback mechanism to boost the power. But with some randomness – including imperfections or noise – that mechanism may be disturbed, so the lasers may not be as focused or have the large amplitudes as expected. Understanding the influence of imperfections or noise, can lead to better laser design.

Then I moved to applications related to neuroscience. How do signals propagate? How do neurons use noise to help propagate or detect signals? We construct mathematical models that enable us to predict how noise might enhance or disrupt the ability of a neuron to send or receive a signal?

The neuroscience application took me to the area of epidemiology. How does noise enhance cycles of certain diseases? In this case, the noise is the random interactions of a population. A lot of mathematical models predict a certain behavior for particular interaction rates. But fluctuations in the random interactions will yield something else. Some of that effect is seen in cycling of certain types of diseases.

More recently, I’ve gotten into uncertainty in climate dynamics, trying to understand how random fluctuations affect the predictions of climate models.

Mathematics is the great unifier. As applied mathematicians, we can look at some behavior, understand the various models that might be used to model that behavior, and boil it down to an abstract framework. Then we modify that framework depending on the dynamics we’re seeing, or the physical or biological phenomena we’re observing.

**What has been the most exciting time so far in your research life?**

I am one of those people who is always excited by the next project, so I’m most excited about a number of projects going on right now, as well as those just starting up. These include heavy tailed distributions in stochastic climate dynamics with multiple scales; we’re developing new approaches for stochastic dynamic bifurcations, including both smooth and non-smooth bifurcations. The applications are diverse, including optics, manufacturing, biology, and the environment.

I’m also just starting a project in characterizing robustness in biochemical networks.

**How did you find your way to mathematics research? **

As an undergraduate, I did a senior project exploring mathematical models in biology. And I took a number of courses at the interface of mathematics and computer science. This naturally led to interest in pursuing research in graduate school.

**What advice would you give to a college freshman who wants to be a mathematician?**

Actively look for opportunities to explore different areas of mathematics, including interfaces of mathematics with other disciplines. This will help you to get an idea of what is most interesting to you, and what isn’t. You will also get a better idea of the different types of future opportunities.

**If you could not be a mathematician, in what line of work would you be now?**

Possibly a neuropsychologist or a veterinarian.

**What three destinations are still in your travel to-do list?**

Certainly more than three, but here are some: Morocco, Indonesia, and much of South America, for different reasons – culture, nature, food, music, etc.

**If you could have dinner with any person in history, whom would you invite?**

Very difficult question! I’d prefer a brain-storming dinner with a group focused on a goal, such as those interested in increasing accessibility to higher education for all students. I’d have to do some research on the members for that group.

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