Carbon dioxide electrolysis
Electricity can turn carbon dioxide into useful chemicals. Can an electrolyzer do so with durable operation, efficient carbon use, and a favorable whole-system energy and emissions balance?
Explore all problems.
Hadwiger conjecture
A graph that needs many colors is predicted to contain a correspondingly large complete graph after edges are contracted and vertices removed.
Hubble tension
Different ways of inferring the present expansion rate of the universe give results that do not fit comfortably together. Is the mismatch in the measurements, the model, or both?
Gene regulatory grammar
Cells with similar DNA can activate very different genes. How do regulatory sequences and cellular conditions specify when, where, and how strongly a gene is used?
Value-based decision making
A choice combines what we want, what we expect, and what we remember. How does the brain turn those inputs into one action, especially when the options are uncertain?
Skolem problem
A sequence follows a fixed linear recurrence. Is there an algorithm that always decides whether any term of the sequence equals zero?
Implantable bioartificial kidney
A compact implanted device could combine blood filtration with living kidney cells. Can it provide enough continuous function to replace dialysis safely for long periods?
Hadwiger–Nelson problem
How many colors are needed to color every point of the plane so that points exactly one unit apart always have different colors?
Strange metals
In some materials, electrical transport behaves in ways that the usual picture of independently moving electron-like excitations cannot explain. What replaces that picture?
Developmental robustness
Developing organisms often produce reliable structures despite molecular noise, genetic differences, and environmental changes. How is that reliability achieved?
Cognitive control
We can switch tasks, follow a rule, and suppress a tempting response. How do brain networks coordinate that flexible control?
Quantum PCP conjecture
Can estimating a quantum system’s lowest energy remain computationally hard even when only a fixed amount of accuracy is required?
Hadamard matrix conjecture
Square matrices of plus and minus ones can have mutually orthogonal rows. The conjecture predicts one for every size divisible by four.
Atmospheric turbulence
Air contains interacting eddies over an enormous range of sizes. How can their combined effect on heat, momentum, and pollutants be predicted reliably?
Regeneration
Some animals rebuild lost body parts, while others mostly form scars. What determines whether damaged tissue can reconstruct an organized, functional structure?
All-pairs shortest paths complexity
Can exact shortest-path distances between every pair of vertices in a general weighted graph be computed in truly subcubic time?
Union-closed sets conjecture
If a finite collection of sets contains every union of two of its members, must some element occur in at least half the sets?
Quantum measurement problem
A single photon gives a left or right detector click. Quantum theory predicts the odds, but treating the detectors quantum mechanically produces a superposition of possible records. How should that state account for a definite result?
Alzheimer’s disease
Amyloid, tau, immune activity, and other changes accompany Alzheimer’s disease. How do they interact to cause neuronal dysfunction, and why does the course differ between people?
Splay tree dynamic optimality
A splay tree reorganizes itself after searches. Is its total cost always within a constant factor of the best search tree that knows all requests in advance?
Lonely runner conjecture
Runners start together on a circular track at different constant speeds. Each is predicted to eventually be well separated from all the others.
Black hole information problem
If a black hole evaporates, how is the information about what fell into it represented in what comes out? The answer must reconcile quantum evolution with gravitational calculations.
Parkinson’s disease
Parkinson’s disease affects multiple cells and systems, yet people develop it through different combinations of risks. What drives the damaging processes and their spread?
L versus NL
Can every computation that uses only logarithmic memory with nondeterministic choices be carried out using the same memory bound deterministically?