Problems
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How large can a measurable A ⊆ [0,R]^2 be while avoiding the vertices of upward-oriented axis-aligned right triangles of area 1/2? At most O_c(R^2/(log R)^c), with a matching-shaped lower bound construction.
Does every lattice of density above one admit a Gabor frame with a nice window? No. For every dimension d > 1 there are explicit criteria on lattices Λ ⊂ R^2d with D(Λ) > 1 such that no function with continuous Zak transform generates a…
Near-optimal density thresholds forcing a measurable set in R^d to contain all sufficiently large similar copies of every n-point configuration, answering a question from the Euclidean density theorem literature up to logarithmic factors.
After L^2 normalization, stable phase retrieval holds over the L^2-spans of independent real-valued centered random variables exactly when all but possibly one coordinate satisfies a uniform two-sided L^1 bound. This confirms the…
The dissipative barrier method suppresses spectral pollution when a differential operator is truncated, but can it hide genuine spectral points? Known as the graveyard problem, the question stayed open in dimension two and above for more…
Davis, Figiel, Johnson and Pełczyński showed their interpolation space admits a Schauder basis when the range space has a shrinking one. Can the DFJP space always be chosen with a basis whenever the range space has a basis? The paper…
The Elton–Odell theorem gives, in every infinite-dimensional normed space, a unit-sphere sequence with mutual distances at least 1+ε. Over C, identifying vectors differing by a unimodular scalar gives a toroidal distance. Does every…