Discover86,978Open Problems in Mathematics

Dekinga, Shadrin, and Verlinde prove Artemev’s conjecture linking resonance transformations for (2,2p+1) minimal strings to the x-y swap in topological recursion.

Renzo Bruera and Xavier Cabré establish interior and global regularity estimates for stable MEMS-type elliptic solutions through dimension six, with counterexamples known from dimension seven onward.

The manuscript derives the four-point SU(2) AGT correspondence with four fundamental hypermultiplets at generic beta from an all-level factorization of Selberg averages.

A preprint proves that the stiffness of the spontaneously broken continuous symmetry equals its Gaussian variational value in quantum geometric nesting models.

The manuscript proves rationality and q-reciprocity for the q-Ehrhart series of hyperplane slices of cubes, confirming the Reiner–Rhoades conjecture for these polytopes.

The preprint proves that the maximum number of queens on an n-by-n board with no queen attacking more than one other is floor(4n/3) for n at least 6 and n for smaller boards.

A newly posted counterexample shows that some finite lattices admit no dot-algebra representation of their top element from algebraically non-cancelling intersections.

For sufficiently large t, the preprint claims the Erdős–Gallai edge threshold is sharp for forcing t consecutive even cycle lengths and gives the equality structure.

For every r at least 2, a manuscript constructs powers of bipartite graphs whose chromatic number is quadratic in clique number, settling the cited open problem for squares.

A preprint determines boxicity and threshold dimension for zero-divisor graphs of reduced rings and principal-ideal-domain quotients, answering two recently posed questions.