We show that the big quantum cohomology of the symplectic isotropic Grassmanian IG(2,6) is generically semisimple, whereas its small quantum cohomology is known to be non-semisimple. This gives yet another case where Dubrovin's conjecture holds and …
We introduce gamma structures on regular hypergeometric $D$-modules in dimension $1$ as special one-parametric systems of solutions on the compact subtorus. We note that a balanced gamma product is in the Paley–Wiener class and show that the …
We introduce a new family of directed, multi-state bootstrap percolation models that naturally occur as the “convolution” of classical bootstrap percolation models as well as generalized $k$-cross models studied by Gravner, Holroyd, Liggett, and the …
For stability conditions on K3 surfaces, we study moduli stacks of semistable objects with Donaldson–Thomas type invariants, introduced by Joyce, and mock theta functions, introduced by Ramanujan. In particular, we will show invariance of moduli …
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation $\Delta …
We consider associative algebras presented by a finite set of generators and relations of special form: each generator is annihilated by some polynomial, and the sum of generators is zero. The growth of this algebra in dependence on the degrees of …
We consider algebras $e\_i\Pi\_\lambda(Q) e\_i$ obtained from deformed preprojective algebra of affine type $\Pi\_\lambda(Q)$ and an idempotent $e\_i$ for certain concrete value of the vector $\lambda$ which corresponds to the traces of $-1\in …
We consider the algebras $e\_i\Pi\_\lambda(Q)e\_i$, where $\Pi\_\lambda(Q)$ is the deformed preprojective algebra of weight $\lambda$ and $i$ is some vertex of $Q$, in the case where $Q$ is an extended Dynkin diagram and $\lambda$ lies on the …