Jeffrey Langford

Educational Background

• Washington University in St. Louis, Ph.D. in Mathematics
• Washington University in St. Louis, M.A. in Mathematics
• Drake University, B.S. in Mathematics

Research interests

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.

Selected Publications

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.