The links between the theory of cluster algebras [19],[20],[6],[22] and functional identities for
the Rogers dilogarithm first became apparent through Fomin-Zelevinsky's proof [21] of …

We define a new type of Hall algebras associated eg with quivers with polynomial potentials.
The main difference with the conventional definition is that we use cohomology of the stack …

We show that the meromorphic Jacobi form that counts the quarter-BPS states in N= 4 string
theories can be canonically decomposed as a sum of a mock Jacobi form and an Appell …

We develop a theory of Bridgeland stability conditions and moduli spaces of semistable
objects for a family of varieties. Our approach is based on and generalizes previous work by …

We explore the relationship between four-dimensional N=2 quantum field theories and their
associated BPS quivers. For a wide class of theories including super-Yang-Mills theories …

Borisov and Joyce constructed a real virtual cycle on compact moduli spaces of stable
sheaves on Calabi–Yau 4-folds, using derived differential geometry. We construct an …

We study the BPS spectra of N= 2 N= 2 complete quantum field theories in four dimensions.
For examples that can be described by a pair of M5 branes on a punctured Riemann surface …

Given a smooth complex threefold X, we define the virtual motive Hilb^n(X)_vir of the Hilbert
scheme of n points on X. In the case when X is Calabi–Yau, Hilb^n(X)_vir gives a motivic …

We study the virtual geometry of the moduli spaces of curves and sheaves on K 3 surfaces in
primitive classes. Equivalences relating the reduced Gromov–Witten invariants of K 3 …

To any quiver with relations we associate a consistent scattering diagram taking values in
the motivic Hall algebra of its category of representations. We show that the chamber …