Bilingual language control
Bilingual speakers can select and switch languages. How do control strategies adapt to conversation, competing demands and language experience?
Explore all problems.
Completed-intention aftereffects
A reminder can bring back an action that is already finished. What determines whether that memory merely interrupts us or prompts a mistaken repeat?
Planar first-passage percolation fluctuations
How widely does the fastest travel time vary across a square grid with independent random edge times?
Relativistic Vlasov–Maxwell global regularity
Can smooth three-dimensional collisionless plasma equations develop a singularity from regular initial data?
Total coloring conjecture
Can every finite simple graph color its vertices and edges together using at most two colors beyond its maximum degree?
Cartan–Hadamard conjecture
Must a region in a nonpositively curved space have at least the boundary area of a Euclidean ball with the same volume?
Abundance conjecture
Does numerical nonnegativity of a minimal model’s canonical divisor guarantee a globally defined geometric map?
Bloch’s constant
What is the largest disk radius guaranteed on a one-to-one image patch of every normalized holomorphic map?
Lefschetz standard conjecture
Can a basic reversible cohomology operation on a complex algebraic variety always be reversed using algebraic cycles?
Green–Griffiths–Lang conjecture
Must all entire complex curves in a general-type projective variety lie in one proper algebraic subset?
Spore hydration
Dormant bacterial spores take up water as they restart. Does GerAB provide a water route in Bacillus subtilis?
Oxytricha genome rearrangement
Oxytricha rebuilds its working genome from scrambled DNA segments. How do RNA instructions become correctly ordered DNA joins?
De novo gene birth
New protein-coding genes can arise from DNA that did not previously encode a protein. Which ones become useful and persist through evolution?
Martian methane
A rover reports methane near the surface; an orbiter finds none. Even the reliability of the rover detections is disputed.
Planet Nine
Some distant orbits suggest an unseen planet beyond Neptune. Searches have narrowed the possibilities without finding it.
Exoplanet radius valley
Close-in small planets cluster into two size groups. Which formation and atmospheric processes produce the gap between them?
Onboard hydrogen storage
Hydrogen tanks already power cars. Can a complete storage system carry enough usable fuel while meeting the weight, space, delivery and lifetime targets together?
Superhot geothermal well integrity
Very hot geothermal wells have been drilled. Can their casing, cement and seals keep working together for a power plant’s lifetime?
Orbital cryogenic refueling
Moving cold propellant between tanks on one spacecraft has been demonstrated. Can two separate spacecraft connect and transfer it reliably in orbit?
Thermophotovoltaic efficiency
A hot surface can feed light to a cell that makes electricity. Can measured conversion exceed 50% while unused light returns to the heat source?
Positivity problem for linear recurrences
Can an algorithm decide whether an integer sequence defined by a linear recurrence never becomes negative?
Deterministic NC perfect matching
Can a deterministic parallel algorithm find a perfect matching in every general graph with polylogarithmic time and polynomially many processors?
Kannan–Lovász–Simonovits conjecture
Can local changes control the fluctuations of functions under log-concave probability laws with a constant independent of dimension?
UCT problem for nuclear C*-algebras
Does every separable nuclear C*-algebra satisfy the universal coefficient theorem relating its K-theoretic invariants?