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Research Projects

I separate these by what happened to the project rather than only by subject. Ongoing means I am actively working on the underlying research problem now. In Preparation means the main research phase is no longer my day-to-day focus, but a manuscript, preprint, submission, or writeup is still being prepared or circulated. Completed means the project resulted in a publication (including accepted work). Moved On means I stopped actively pursuing the project without turning it into a publication.

ONGOING

For active projects, the linked pages are intentionally problem statements: background, tools, and broad direction only.

• The Fourier Ratio on Non-Resistance Fractals
  Spectral-complexity questions beyond the resistance-space setting.
• Fourier-Reconstructible Local Attention and Compressive Memory
  Spectral complexity, localization, and recoverability for structured attention and memory objects.
• Complex Memory
  Persistent fixed-size state for sequence models under long retrieval delays.
• Nonlocal Ordered Mean Curvature with Non-Integrable Kernel — Missouri State University, Animesh Biswas.
  Rigidity and symmetry questions in the singular-kernel nonlocal setting.

IN PREPARATION

• Numerical Analysis — Scalable Interpolation — Missouri State University, Hazhar Rahmani.
  Distributed interpolation under MapReduce and finite-recurrence reconstruction.
  Scalable Interpolation under MapReduce via Finite-Recurrence Reconstruction.
• Numerical Analysis — Nonlocal Traffic Flow — Missouri State University, Animesh Biswas.
  Adaptive spatial-temporal nonlocal traffic models; journal manuscript submitted.
  Spatial-Temporal Nonlocal Traffic Dynamics: Analytical Properties, Adaptive Kernel Formulation, and Empirical Validation.
• Analytic Number Theory — SMALL REU — Williams College, Steven J. Miller.
  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.
• Harmonic Analysis — SMALL REU — Williams College, Alex Iosevich and Eyvindur Pálsson.
  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.
• Probability Theory — SMALL REU — Williams College, Steven J. Miller.
  Random Fibonacci Tilings.
• Group Theory & Combinatorics — SMALL REU — Williams College, Steven J. Miller.
  Product and Quotient Set Dominance in Finite Groups.

COMPLETED — RESULTED IN A PUBLICATION

• Geometric Combinatorics — Missouri State University, Steven Senger.
  Dot-product trees in finite point sets.
  Bounds on Distinct and Repeated Dot Product Trees.
• Combinatorics & Graph Theory — Missouri State University, Steven Senger.
  VC-dimension in Hamming graphs.
  VC-Dimension of Subsets of Hamming Graphs.
• Deep Learning — Missouri State University, Yifan Zhang.
  Encoder/decoder ablations for multivariate forecasting.
  Rethinking the Encoder-Decoder Structure for Transformer-Based Time Series Forecasting.

MOVED ON

These links are retrospective pages: background, tools, attempts, and why I stopped pursuing the problem.

• Discrete Harmonic Analysis — Missouri State University, Steven Senger.
  Finite-field time-frequency linear independence and HRT-type questions.
• Cryptographic Functions — Missouri State University, Steven Senger.
  Bent-function rigidity and minimum-distance questions over finite fields.

LAST UPDATED: September 14, 2026
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