An estimate for the Riemann–Liouville fractional integral of Lipschitz functions
An original analysis result developed into a complete manuscript, framed toward a Yau / PRIMES-level paper under close advisory supervision.
A view of the research we guide — from a first question to a defended paper — across pure mathematics, physics, chemistry and materials, biology, computer science, and applied data. Shown by field and method, never by name.
Students' identities are withheld. Every project below is described only by its field and method. No names, schools, or internal documents appear anywhere on this page.
An original analysis result developed into a complete manuscript, framed toward a Yau / PRIMES-level paper under close advisory supervision.
A structured review paper synthesizing first-order and adaptive methods, scoped and written to the extended-project assessment criteria.
An extended-MHD solver implemented and validated on a reconnection problem — a thesis, poster, and slide defense developed at a level advanced for high school.
A theoretical derivation written up as a formatted journal-style article, the argument carried through review-ready structure.
Tuning the nitrogen-intermediate pathway on a designed catalyst, with materials characterization, a written paper, and a competed regional-to-state showing.
A biodegradable adsorbent characterized and modeled with Langmuir isotherms (≈197 mg/g capacity) — a coherent three-layer poster, presentation, and analysis.
A computational target analysis linking RNA-methylation machinery to checkpoint-blockade response in lung cancer, developed through several rounds of independent review.
A constraint-based (PC-algorithm) causal-structure study over a large public health-survey corpus, evaluated against held-out predictive performance, shown as a competed poster.
A transformer-and-ensemble classifier for transit signals, evaluated with ROC and confusion-matrix analysis — slides and results competed at a regional science fair.
A segmentation pipeline trained on an urban-scenes benchmark and tuned past real-time throughput (>30 fps), written as a conference-template paper draft.
Oriented-object detection combined with a document-understanding model over a purpose-built dataset of 1,300+ technical drawings — implementation plus a paper in progress.
A pedestrian-evacuation model built from coupled social-force and floor-field rules, with original code, a poster, and a slide defense.
An end-to-end ETL over public prediction-market data with unsupervised clustering (K-Means / GMM) to profile participant behavior — model and poster drafts.
A stochastic FEM simulating rut formation under cold-climate loading, carried through successive manuscript revisions toward peer review.
We begin by finding a question that is real, tractable, and the student's own — narrow enough to finish, open enough to matter.
Then the method: the model, the experiment, or the proof, built and debugged week by week until the result holds up to scrutiny.
The work becomes an artifact — a paper, a poster, a thesis, a slide deck — written and typeset to the standard real review expects.
Finally the defense: rehearsing the questions a Grand Award judge actually asks, so the student can stand behind every line.