Multilayer plastic-film sorting
Can waste-sorting systems distinguish different layered plastic films fast enough to route them for recycling?
Explore all problems.
Mobile terahertz beam management
Can narrow high-frequency wireless beams stay connected through movement and blockage without excessive tracking cost?
Membrane-distillation wetting control
Can seawater distillation membranes stay productive without letting salt water leak through their pores?
Nonthermal atmospheric water harvesting
Ultrasound can extract captured water efficiently. How can sorbent uptake and actuation stay coordinated as moisture loading and humidity change?
Microwave–optical quantum transduction
Can a practical interface transfer quantum information between microwave circuits and optical links with little loss or added noise?
Conway’s thrackle conjecture
Can a planar thrackle have more edges than vertices?
Gyárfás–Sumner conjecture
Does excluding any fixed induced tree control a graph’s coloring needs once its largest clique is bounded?
Barnette’s Hamiltonian conjecture
Does every cubic, bipartite, planar, 3-connected graph contain a cycle visiting every vertex exactly once?
Sidorenko’s conjecture
Do random graphs minimize the density of every fixed bipartite pattern among graphs of the same edge density?
Invariant subspace problem
Must every bounded linear operator on complex Hilbert space preserve a nontrivial closed subspace?
Vaught’s conjecture
Can a complete countable theory have an intermediate number of countable models?
Inverse Galois problem
Can every finite group occur as the Galois group of a finite extension of the rational numbers?
Uniform boundedness of rational torsion
Can rational torsion be bounded by abelian-variety dimension and number-field degree?
Auditory scene analysis
We can follow one voice among many. How does attention organize overlapping sounds into sources we can track?
Odor-mixture perception
A blend can smell like its ingredients or like a new odor. What determines which percept emerges?
Savings in motor adaptation
Relearning a movement adjustment can be faster than learning it first. Which memories and processes produce that advantage?
Sense of agency
We feel that our actions cause events. How do prediction and observed regularities combine to produce that feeling?
Body ownership
Vision and touch can make a rubber hand feel like your own. Which circuit processes produce this bodily attribution?
Awake hippocampal replay
While an animal pauses, its brain can rapidly replay activity associated with routes. What does that replay causally accomplish?
Compositional cognitive maps
A familiar room or obstacle can be reused in a new layout. How does the brain combine known parts into a useful map?
Event segmentation
Continuous activity feels divided into events. How do prediction and knowledge determine where one event ends and another begins?
Metacognition
Choosing an answer and judging whether it is right are different tasks. Which brain computations produce that second judgment?
Aphantasia
Some people cannot voluntarily picture a scene. Which neural differences explain lifelong absence of visual imagery?
Spontaneous thought
Thoughts arise and change direction without a new instruction. Which processes initiate and switch these self-generated episodes?