Sloan Fellowship Recipient Uses Creativity to Explore Mathematical Foundations - Profile Joe Kileel

As an early-career researcher, Joe Kileel’s projects - which have broad applications across scientific imaging, computer vision, machine learning and inverse problems - are getting noticed. Kileel is among six University of Texas at Austin recipients who recently received the prestigious 2025 Sloan Research Fellowship awarded by the Alfred P. Sloan Foundation.

Awarded annually, selected recipients are “early-career researchers whose creativity, innovation, and research accomplishments make them stand out as the next generation of leaders.”

An assistant professor of mathematics and Principal Faculty at the Oden Institute for Computational Engineering and Sciences, Kileel’s research focuses on developing computational models that exploit the underlying algebraic and geometric structure of given problems. 

Kileel specializes in tensor methods, nonconvex optimization, methods to solve polynomial systems of equations, and manifold learning. Tensor methods are used in a variety of ways, including to show the amount and direction of stress throughout an object, and in machine learning to show the values and parameters in a neural network.

Currently, he is leading two major research projects at the Oden Institute. The first focuses on developing scalable techniques for processing tensor data streams. Here the data stream could consist of high-resolution video data, statistical correlation or moment information from a different stream, discretized functions from partial differential equation (PDE) simulations, or others. 

“The scale of such data streams often requires almost immediate data compression. I’m aiming to develop methods that can do this in a provably accurate and reliable way,” Kileel explained. This work is supported through a Department of Energy (DOE) project, with co-principal investigator Per-Gunnar Martinsson, Deputy Director of the Oden Institute and professor of mathematics.

“We've worked together for the past year on the DOE funded project aimed at very rapidly and accurately compressing streams of high throughput data. More precisely, we look at ways to use randomized algorithms to efficiently compress "tensor" data arising from, e.g., simulations of complex fluid flows, or from cryo-electron microscopy,” said Martinsson.

In addition, Kileel is collaborating on developing digital twins for drug trials. Traditional drug trials are often time-consuming and costly, so the project aims to improve efficiency and safety by pulling information from a digital twin of the trial. 

Working with Karen Willcox, Oden Institute Director, and Thomas Yankeelov, lead of the Center for Computational Oncology at the Oden Institute and a professor of biomedical engineering, Kileel’s contribution includes investigating reduced ordering modeling (ROM) based on nonlinear manifolds or algebraic varieties, which would enable faster use of the digital twin. “The foundational math is more general, and ties in well with my desire to exploit underlying algebraic and geometric structure in difficult problems,” Kileel said. This research is supported by the National Science Foundation (NSF).

“At the Oden Institute, I gain a lot from collaborating with colleagues and exploring new research areas,” said Kileel.

Reflecting on the Sloan Fellowship, Kileel said, “This Fellowship in Mathematics is an honor for me. It means that senior members of the community appreciate my work. I thank my letter writers and nominators Beyond finances, the Sloan Fellowship is cool because of the list of past recipients, many of whom are big names in the field today. It kind of excites and challenges me.”  Kileel said he will use the resources to support both his research and his graduate students.

“This award for Dr. Kileel is very well deserved, as he is one of the absolute top young researchers in the field. I've been thoroughly impressed with his technical prowess and creativity,” said Martinsson.

Prior to joining UT as an assistant professor in the Department of Mathematics, Kileel completed his postdoctoral training at Princeton University under the supervision of Amit Singer. 

Looking back at the field, Kileel remarked that “methods of machine learning and more generally methods that exploit low-dimensionality in high-dimensional problems have become more widespread in applied and computational mathematics in the past 5-10 years.”

In addition to his research, Kileel currently mentors five Ph.D. students at UT (three in the Math Department and two in the Oden Institute’s CSEM program). Through his mentoring, he stresses the importance of creativity in academic research, which he hopes carries through in his teaching at UT as well. 

With the recognition of the Sloan Fellowship highlighting his potential, Kileel is set to make significant advancements in research and in guiding the next generation of applied mathematicians.