5 problems

Let a general Calabi–Yau threefold be given, and let a chamber of its BPS moduli space be fixed. A crystal model is a crystal whose melting configurations encode the BPS states in…

Let $\Gamma$ be a binary dihedral, tetrahedral, octahedral, or icosahedral subgroup of $\operatorname{SU}(2)$, and let the corresponding affine Dynkin diagram have rank parameter…

Three-dimensional quantum crystal melting conjecture. The three-dimensional quantum crystal melting model is integrable and has the same mass gap as its one- and two-dimensional co…

Let $\Omega(n)$ be the degeneracy of the unrestricted crystal model and let $\Omega_N(n)$ be the degeneracy when the crystal is restricted to a box whose first row has length at mo…

The crystal parameters $q_0,q_a,q_b,q_c$ and the string parameters $q_s,Q_A,Q_B,Q_C$ are related by an identification depending on the pyramid length $n$, and the corresponding gen…