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Welcome to my research page. I am a PhD student in applied mathematics at Purdue University where I am mentored by Professor Rongjie Lai. I was very fortunate to previously have had mentors of Xiaohui Chen, Paul Atzberger, and Chris Anderson.

I study pure and applied mathematical foundations of artificial intelligence. My general areas of study are scientific machine learning, computational PDEs, Riemannian geometry, calculus of variations, variational PDEs, control theory, SDEs, physics-informed learning, and their broader relevance to the mathematics of artificial intelligence. My research attempts to bridge more classical areas of mathematics and their fundamental roles in mainstream neural archetypes. The goal of my research to understand the foundational mathematical underpinnings of how machine learning modalities exist, and to rederive these expressions with improvement, both in auxiliary quality and in computing capacity. For example, maybe the Transformer is not to be improved with computing power, but rather by reinventing the mathematics of the attention mechanism, as DeepSeek partially showed recently. My interest right now is harmonic analysis.

Please do feel free to add me on LinkedIn if you think you know me from somewhere, or please do feel free to shoot me an email. Please do not hesitate to add me if you feel we share similar mathematical interests. If you like my work, or have any interest in collaboration, please feel free to get in touch.

At UIUC, I was also affiliated with the Grainger College of Engineering through DIGIMAT, a research group focused on the interface of data science, statistical physics, and materials science. DIGIMAT is co-hosted by the National Center for Supercomputing Applications and Materials Research Lab.

I am also previously a member of Atzberger Research Group, a group focused on statistical physics, numerical analysis, scientific computation, and machine learning.

One can reach me by email. My university email is agracyk at purdue dot edu, but my permanent email is andrewgracyk at gmail dot com. Also, I receive a lot of mass email, so it is possible (but unlikely) unfamiliar email is overlooked. LinkedIn is a great place to contact me.

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An aurora borealis above two lone mountaintops in Tromso, Norway