20 problems.
- Jordan canonical form of an upper-triangular \(3\times3\) matrix
- The integral \(\int_0^\infty x^{50}/(x^{100}+1)\,dx\)
- A strict distance contraction on a compact metric space has a unique fixed point
- Triviality of a group with mutually exponentiating conjugation relations
- Monotone positive coefficients exclude polynomial roots from the unit disk
- A differential inequality forces positivity on the positive half-line
- Determinant of \(X\mapsto(AX+XA)/2\) on \(M_3(\mathbb R)\)
- Divisibility of the central binomial coefficient by two and four
- Absolute convergence of all derivatives of \(\sum z^n/n^{\log n}\)
- Limsup growth of a finite sum of complex power sequences
- Entire functions of the form \(e^x(s(y)+it(y))\)
- Irreducibility over \(\mathbb Q\) of four quadratic and cubic polynomials
- Vanishing Fourier sine coefficients of a continuous function on \([0,\pi]\)
- Equality of the kernels of \(A\) and \(A^T\) under a nonnegative quadratic form
- Every disk-holomorphic function is bounded along some sequence approaching the boundary
- Sums of nilpotent matrices and invertibility of \(I-A\)
- The complement of a regular level curve in \(\mathbb R^3\) is path connected
- A quadratic integral functional attains its maximum on a unit Lipschitz ball
- A fixed-point-free prime-order rational representation has dimension divisible by \(p-1\)
- Local invertibility of the matrix-squaring map at \(I_2\) and \(\operatorname{diag}(1,-1)\)