Classification of Zamolodchikov periodic cluster algebras

COMPOSITIO MATHEMATICA Cluster algebras via cluster categories with infinite-dimensional morphism spaces

Small Lefschetz fibrations on the BMY line

We give explicit positive factorizations for a genus-19 Lefschetz fibration over the torus and a family of genus-4 Lefschetz fibrations over a genus-2 surface. All these examples have only three nodes, and their total spaces are symplectic 4-manifolds of general type on the Bogomolov-Miyaoka-Yau line. In the course of...

Homomesy of Tropical $T$-systems: Finite Type

In 2007, Fomin and Zelevinsky introduced the bipartite belt, a sequence of bipartite cluster mutations whose exchange relations form a discrete dynamical system. For each Dynkin diagram, this system is periodic, as a special case of Zamolodchikov periodicity. In the associated tropical dynamics, every mutation along th...

Categorification and mirror symmetry for Grassmannians

The homogeneous coordinate ring C[Gr(k,n)]$\mathbb {C}[\operatorname{Gr}(k,n)]$ of the Grassmannian is a cluster algebra, with an additive categorification CMC$\operatorname{CM}C$ . In particular, every M$M$ in CMC$\operatorname{CM}C$ has a cluster character ΨM∈C[Gr(k,n)]$\Psi _M\in \mathbb {C}[\operatorname{Gr}(k,n)]$...

Presymplectic BV-AKSZ and constrained DGCAs

The AKSZ construction encodes the Batalin-Vilkovisky formulation of a topological field theory in terms of finite-dimensional geometric data. There are at least two ways to extend this approach to nontopological gauge theories. The first, due to Costello, replaces the spacetime exterior algebra with a more general DGCA...

On the Peirce spectral rigidity of decorated incidence algebras

The multiplication operator of an idempotent in a metrized commutative nonassociative algebra is a self-adjoint linear endomorphism whose spectrum reflects the algebraic and geometric structure encoded in the algebra. Although for general algebras the spectra of idempotents can behave arbitrarily, for the most interest...