Research Interests

I am a PhD candidate in applied mathematics in my sixth year at the University of Connecticut under the supervision of Dr. Xiaodong Yan. My research combines variational methods, differential equations, and numerical simulation to study problems arising from materials science and other related applications. My dissertation work focuses on the existence, uniqueness, qualitative properties, and parameter-dependent behavior of solutions to nonlinear free-energy models in liquid crystal science. More broadly, I am interested in how mathematics and computation can be used to describe and predict the behavior of complex physical systems.

Papers

1. T. E. St. George and A.D.W., Orthonormalization of a subset of Bernstein polynomial basis functions, The PUMP Journal of Undergraduate Research 7 (2024), 258-273, DOI https://doi.org/10.46787/pump.v7i0.3765.

Manuscripts in Preparation

1. A.D.W. and Xiaodong Yan, Polar director structure of SmAP_F phase of bent-core liquid crystals in thin planar cells with bias electric field, in preparation.

Talks

1. May 2026, Graduate Research Forum, The University of Connecticut.
2. May 2026, SIGMA Seminar, The University of Connecticut.
3. April 2026, FADE Conference, Fairfield University.
4. March 2026, Workshop in PDE and Applied Math in the Northeast Region, The University of Connecticut.
5. March 2024, Mathematics continued conference, The University of Connecticut.
6. October 2023, Geometric Analysis Student Seminar, The University of Connecticut.
7. March 2023, Geometric Analysis Student Seminar, The University of Connecticut.