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Browse project ideas by Polygence mentors
Draft a Policy Solution to a Problem or Potential Problem
While research is great, a solution to a problem is even better! Is there something you notice going wrong in school or misapplied in the world of business or law? Most legal issues have multiple sides. Maybe the new use of AI raises the need for new laws. Or maybe historical Supreme Court decisions require a revision in current law based on the effects. For example, what should the Supreme Court's ethical code be? How should it be enforced? We can work to find pragmatic or theoretical fixes to a potential or current issue.
Economics, Finance, Business
Write a Research or Personal Paper
Writing and Research can take many forms at different intensities. Don't feel pressured to have 100 sources and 100 pages. Instead, work within your schedule to dive into something you *might* like. Some hot topics I find interesting are AI in law and / or business, the law and economics movement with a focus on transaction costs, the changing landscape of law firms, or how people develop a legal education. How do students at your school and in various grade levels learn about the law or business? Is it experience based, teacher / school provided in instruction, or typically through parents? Pick one and and analyze its effect, consistency, and deficiencies.
Economics, Finance, Business
Weighing a Photon's Push: Simulating How Light Slows an Atom
An atom moving toward a laser sees the light Doppler-shifted upward. Tune the laser slightly below the atomic transition and only atoms moving toward it absorb efficiently, each absorption delivering a small momentum kick opposing the motion. Repeat ten thousand times a second and a gas cools to microkelvin. This is the foundation of atomic clocks, quantum computing platforms, and the precision measurements underneath modern metrology. The student simulates it: model atoms in a velocity distribution, compute absorption probability from the Doppler-shifted detuning and natural linewidth, apply momentum kicks, and watch the distribution narrow. Then find the limits. What detuning cools fastest? Why does the temperature stop falling at a floor set by the randomness of spontaneous emission, and does the simulated floor match the Doppler limit formula? What happens with atoms that are too fast to be captured? Deliverable is a research paper reporting a measured cooling curve and a simulated Doppler limit compared against theory. Pure Python, free, no hardware. Requires comfort with probability. I built magneto-optical traps and a laser-cooled francium fountain at Lawrence Berkeley, and this is the physics those machines run on.
AI/ML, Engineering, Physics
Dating a Rock With a Radiation Detector: Reconstructing the Uranium Decay Chain From a Piece of Granite
Granite countertops, old uranium glass, and camping lantern mantles are all mildly radioactive, legally sold, and contain decay chains that have been running for billions of years. A student with a $150 detector can measure one and work backward to physics that is genuinely deep. The student measures a sample's gamma spectrum, identifies emission lines against reference tables, and reconstructs which daughter isotopes are present. Then the real question: are the chain members in secular equilibrium? If the parent's half-life vastly exceeds the daughters', every step in the chain should decay at the same rate, and measured activity ratios should reflect that. Where they do not, the student has evidence that something escaped, usually radon, which is a gas and leaks out of solid rock. Sealing a sample and watching activity climb back over days lets them measure the in-growth curve and extract radon's half-life from their own data. Deliverable is a research paper with an identified spectrum, an equilibrium analysis, and a measured half-life with uncertainty. Detector runs $120 to $250; samples are ordinary consumer goods. For a student without hardware, public spectral datasets support the identification and equilibrium work with no build. This is nuclear physics as geology and as household chemistry, and the radon result connects directly to indoor air quality, which is where most people actually encounter this science.
AI/ML, Engineering, Physics
A Spectrometer From a DVD and a Phone: Measuring What Light Is Made Of
A shard of a DVD is a diffraction grating with a known line spacing. Paired with a cardboard housing and a phone camera, it resolves spectral lines well enough to distinguish a fluorescent bulb from an LED from a sodium streetlamp, and to measure absorption through a colored solution. The student builds and calibrates the instrument against known emission lines, then uses it for an actual measurement: identifying unknown light sources, tracking absorption against concentration to test Beer's law, or characterizing how different bulbs render color. Calibration is the heart of it. Converting pixel position to wavelength, and stating how precisely, is the step that turns a craft project into an instrument. Deliverable is a research paper with a calibration curve and a resolution figure. Build cost is under $20. No programming required, though image analysis in Python strengthens it. Best fit for a student who wants to build something physical.
AI/ML, Engineering, Physics
Does a Language Model Understand Physics, or Just Recognize It? Building a Benchmark That Tells Them Apart
A model can solve a textbook problem it has effectively memorized and fail the same problem with the numbers changed. Separating genuine reasoning from pattern retrieval requires a benchmark designed to break the second one. The student builds a small evaluation set from scratch: take physics problems, then generate controlled perturbations of each one. Change the units. Change the numbers so the answer is no longer a round figure. Add an irrelevant given. Swap the unknown. Then measure how accuracy degrades across perturbation types, and whether degradation differs by topic or by model. The finding is a degradation profile the student measured, not an opinion about whether AI is smart. Deliverable is a research paper with a released benchmark. Minimal coding required; the intellectual work is in benchmark design and in defining what counts as a fair perturbation. Good fit for a strong writer who wants a rigorous project without a heavy programming lift.
AI/ML, Engineering, Physics
Do Trees Actually Cool a City? Measuring Urban Heat Islands From Free Satellite Imagery
The same neighborhood can run several degrees hotter than the one beside it, and the difference tracks how much pavement and how much canopy each has. Landsat's thermal infrared band records surface temperature across an entire metro area on a repeating cycle, and the data is free. The student pulls multi-year thermal imagery for their own city through Google Earth Engine, then tests whether temperature differences between neighborhoods hold up against ground truth: municipal tree canopy data, impervious surface maps, or census income figures where they want to push into the environmental justice angle. The real project is the statistics. How large does a canopy difference have to be before it is detectable above seasonal noise? Does the effect survive when you control for elevation or distance from water? Deliverable is a research paper with a quantified detection threshold and an honest account of confounds. Everything is free and browser-based. Some Python helps; the imagery work is the easier half.
AI/ML, Engineering, Physics
How Do You Know a Signal Is Real? Detecting a Buried Periodic Signal in Pure Noise
Dark matter searches, gravitational wave detection, and exoplanet transit surveys share a problem: the thing you are looking for is far smaller than the noise it sits in, and if you search hard enough through noise alone you will always find something. Learning when a bump is a discovery and when it is a coincidence is the central skill of experimental physics, and it is almost never taught before graduate school. The student builds a synthetic detector in Python, modeled on a resonant-cavity haloscope of the kind used to search for axions. They inject a faint periodic signal of known strength into simulated noise, then try to recover it using increasingly serious methods: a raw Fourier transform, then power spectrum averaging, then a matched filter. The core experiment is a detection-efficiency curve, sweeping signal strength downward to find where each method fails. Then the important half: run the pipeline on noise with no signal at all, many times, and count how often it reports a detection anyway. That is where the student meets false positive rates and the look-elsewhere effect, and learns why real collaborations demand five sigma. Deliverable is a research paper reporting the sensitivity limit and false-alarm rate of the student's own pipeline. Runs free in Colab, no hardware. Python required; no prior signal processing needed. I worked on the Axion Dark Matter eXperiment at Lawrence Livermore, and this is the analysis problem that experiment lives or dies on, scaled to something a student can actually finish.
AI/ML, Engineering, Physics
Measuring Special Relativity in Your Basement: Cosmic Ray Muons as Evidence for Time Dilation
Muons created about 15 kilometers up in the atmosphere live roughly 2.2 microseconds. Even at nearly light speed, classical physics says they should decay long before reaching the ground. They arrive anyway, in numbers a student can count, and the discrepancy is one of the most direct pieces of experimental evidence for time dilation available outside a particle accelerator. The student assembles a scintillator-based detector from a documented open-source design, characterizes it, and then runs real measurements: muon flux against zenith angle, against material shielding, and against altitude if a road trip or a tall building is available. The analysis is where the physics lives. From a measured flux and the known production altitude, the student calculates what survival fraction classical mechanics predicts, compares it to what they counted, and extracts the Lorentz factor their own basement data implies. Deliverable is a research paper with an uncertainty analysis, which is the part most high school physics never teaches and which distinguishes a real measurement from a demonstration. Detector cost is roughly $100 to $150. For a student without hardware access, public cosmic ray datasets support the same analysis with no build.
AI/ML, Engineering, Physics
Does Telling a Neural Network About Physics Make It Smarter? Testing Physics-Informed Learning on a Damped Pendulum
A neural network trained on data from a physical system will happily learn the dataset instead of the physics. Give it fifty noisy measurements of a swinging pendulum and it will interpolate beautifully between them, then produce nonsense the moment you ask about a time it has not seen. Physics-informed neural networks address this by adding the governing differential equation directly into the loss function, so the model is penalized not only for missing the data but for violating the physics. The student builds both versions in Tensorflow/PyTorch and runs the comparison honestly. Simulate a damped driven pendulum, sample it sparsely, add noise, and train two networks: a standard one, and one whose loss includes the residual of the equation of motion. Then test where it actually matters, by extrapolating past the training window, thinning the data until the models break, and asking how few points the physics-informed version needs to stay correct. The interesting result is usually not that one wins, but finding the regime where the advantage appears and disappears. The deliverable is a short research paper with a reproducible notebook, and the finding is a real one: a data-efficiency curve the student measured themselves. Everything runs free in Google Colab, no hardware required. Python experience helps; calculus is useful but the equation can be taken as given. This is a scaled-down version of the method I developed in my doctoral work, where the physics being enforced concerned nuclear fuel cycle facilities rather than pendulums, and the underlying question was identical.
AI/ML, Engineering, Physics