- Washington University in St. Louis, Ph.D. in Mathematics
- Washington University in St. Louis, M.A. in Mathematics
- Drake University, B.S. in Mathematics
I study partial differential equations that arise in mathematical physics, particularly equations that model vibrating objects. More precisely, I study eigenvalue problems that seek to describe the vibrational frequencies of various drums and plates.
I also investigate connections between probability, specifically the expected exit times of Brownian motion paths, and a drum’s vibration frequencies.
1. Barbara Brandolini, Francesco Chiacchio, and Jeffrey Langford,
Estimates for Sums of Eigenvalues of the Free Plate via the Fourier
Transform, Communications in Pure and Applied Analysis,
(2020) 19 (1) 113-122.
2. Don Colladay, Jeffrey Langford, and Patrick McDonald, Comparison
Results, Exit Time Moments, and Eigenvalues on Riemannian Manifolds
with a Lower Ricci Curvature Bound, The Journal of Geometric Analysis,
28 (2018), no. 4, 3906-3927.
3. Barbara Brandolini, Francesco Chiacchio, Emily B. Dryden,
and Jeffrey J. Langford, Sharp Poincaré Inequalities in a Class of
Non-convex Sets, Journal of Spectral Theory, 8 (2018), no. 4, 1583-1615.