Problems

Among all nonconstant monic polynomials f whose roots lie in [-1, 1], determine inf_f |x ∈ R : |f(x)| < 1|.

Are ICC property (T) groups remembered by their von Neumann algebras - if L(Γ) ≅ L(Λ) for such groups, must Γ ≅ Λ? A counterexample refutes Connes' conjecture that these groups are uniquely determined by their group von Neumann algebras.

For triangular arrays of nodes a_i^n∈[-1,1] let L^nf be the Lagrange interpolation polynomials of a continuous f, with fundamental polynomials p_i^n. Is there a choice of nodes such that for every continuous f there is some x where…

Let L^nf be the Lagrange interpolation polynomials of a continuous f on the Chebyshev nodes. Prove that, for any closed A⊆ [-1,1], there exists a continuous function f such that A is the set of limit points of L^nf(x).

Is there an entire non-zero function f:C→ C such that, for any infinite sequence n_1<n_2<…, the set z: f^(n_k)(z)=0 for some k≥ 1 is everywhere dense? The literal question is trivial for polynomials, so the claims address the…

Let n_1<n_2<… be a lacunary sequence of integers and f∈ L^2([0,1]) with nth Fourier partial sum f_n. Is there an absolute constant C>0 such that if | f-f_n|_2 ≪ (logloglog n)^-C then 1/N∑_k≤ Nf(α n_k)→∫_0^1 f for almost every α? A preprint…

Must every sufficiently large node set admit bounded labels that force any polynomial fitting almost all labels at degree below (1+ε)n to have arbitrarily large uniform norm? Claimed via Beurling density for Bernstein spaces.