Christopher Housholder — Research

Harmonic Analysis / Spectral Theory

• The Fourier Ratio on Resistance Spaces and Applications to Electrical Networks
• Fourier Ratio Bounds and Sensitivity to Sensor Placement
• The Fourier Ratio of Elliptic, Hyperelliptic, and L-Function Families

Analytic Number Theory

• Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms
• Breaking Universality in the Lower Order Terms in the 1-level and 2-level Density of Holomorphic Cusp Newforms

Combinatorics / Graph Theory / Probability

• VC-dimension of subsets of Hamming graphs
• Bounds on distinct and repeated dot product trees
• Product and Quotient Set Dominance in Finite Groups
• Random Fibonacci Tilings

Numerical Analysis / Machine Learning

• Spatial-Temporal Nonlocal Traffic Dynamics: Analytical Properties, Adaptive Kernel Formulation, and Empirical Validation
• Rethinking the Encoder--Decoder Structure for Transformer-Based Time Series Forecasting

These pages follow the corresponding manuscripts closely and use the same deliberately plain academic-web formatting as the resistance-spaces page.