Degree Program: Applied Mathematics, Ph.D.
Department: Applied Mathematics
Undergraduate Institution: UC Santa Cruz
Graduate Institution: UC Santa Cruz
Advisor: Daniele Venturi
“As a researcher, I am constantly trying to think of new ideas. Most of them take a lot of effort to explore and oftentimes they do not work. One day, I decided to carry out an idea that had popped into my head. I quickly coded it into my computer and pressed “run.” I sat there and watched the animations appear on the screen, proving that my new idea worked even better than I had anticipated. It was such a good feeling to achieve this research breakthrough from an original idea.”
Alec Dektor is a quadruple UC Santa Cruz alumnus (B.A. math; M.A. math; M.S. scientific computing and applied mathematics; Ph.D. applied mathematics). During his time at Baskin Engineering, he published six papers—four as first author. His area of research focuses on developing new computational methods to approximate high-dimensional functions and high-dimensional partial differential equations. He begins a two-year postdoc appointment with Lawrence Berkeley National Laboratory this summer.
Describe your journey to the Baskin School of Engineering.
I came to UCSC as an undergraduate student in the B.A. math program many years ago. Within the Mathematics Department, they had a 4 + 1 program, which I opted into since I was really enjoying graduate level courses in pure mathematics.
Towards the end of the 4 +1 program, I was looking to venture out a little bit and gain new skills, so I took a class in the Applied Mathematics Department within the Baskin School of Engineering. It was the Fundamentals of Scientific Computing course taught by Professor Daniele Venturi. After the class ended, I worked with Daniele on a couple research projects. I enjoyed the research so much that I decided to expand my math academic career by joining the scientific computing and applied mathematics (SciCAM) M.S. program. After completing that program, I then joined the applied mathematics Ph.D. program. All together, my UCSC journey has been about a decade long.
What’s your area of research?
My research focuses on approximating high-dimensional functions and high-dimensional partial differential equations. For 1- and 2-D partial differential equations, there are methods that are well known and well studied. But, when you try to use those methods to approximate functions in higher dimensional spaces, which show up a lot in physics, mathematics, and engineering, those standard methods don’t really work because the computational resources you need grow incredibly fast.
Recently, many techniques have been proposed to address these problems. My research focuses on one of those techniques referred to as “tensor methods,” which allows us to address the issue of dimensionality by exploiting structure in the problem and using computational resources more wisely. My contributions have been towards a general theory of approximating partial differential equations with applications in many areas such as fluid mechanics and quantum mechanics.
What was a major research breakthrough you had during your time at Baskin Engineering?
There have been a few. The last contribution I made during my Ph.D. program was morphing a complicated function into a much simpler one to allow for easier computation. I struggled for about a year to find this transformation. And then out of nowhere one day, I decided to carry out an idea that had popped into my head. I quickly coded it into my computer and pressed “run.” I sat there and watched the animations appear on the screen, proving that my new idea worked even better than I had anticipated. It was such a good feeling to achieve this research breakthrough from an original idea.
As far as I know, I’m the first one to figure that out. One of the things I love about applied math is the reassurance you get from the computational work you’re doing. Your computer is like a little laboratory where you can run your experiments and verify theoretical results. Fast forward seven to eight months after that day, and I have a paper under review with the Journal of Computational Physics and I got to present my work at a conference in Amsterdam.
What was your favorite UCSC memory?
In the Mathematics Department, I had the chance to TA for three quarters. Because I was super passionate about the research and enjoyed teaching math concepts to undergraduate students, it was one of my most fondest memories at UCSC. Another memorable experience was being a part of the Mathematics Directed Reading Program, a mentorship program where I worked 1:1 with an undergraduate student to help them explore new mathematical topics and get introduced to research.
What’s next for you?
I start a two-year postdoc appointment at Lawrence Berkeley National Laboratory on July 3. I’m really looking forward to collaborating with new researchers and learning new things.
What advice do you have for students interested in pursuing applied mathematics graduate programs?
It’s important to not be afraid to really dig in. If you find something you’re passionate about, then fully commit to that. If it doesn’t work out, then you can always change your path, but at least you learned something along the way.
Interview Date: June 21, 2023
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