Related papers: Categorified canonical bases and framed BPS states
Canonical principal parameters are introduced for surfaces in $\mathbb R^3$ without umbilical points. It is proved that in these parameters the surface is determined (up to position in space) by a pair of invariants satisfying a partial…
A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…
We construct three sequences of regular surfaces of general type with unbounded numerical invariants whose canonical map is 2-to-1 onto a canonically embedded surface. Only sporadic examples of surfaces with these properties were previously…
We classify completely the surfaces of general type whose canonical map is 3-to-1 onto a surface of minimal degree in projective space. These surfaces fall into 5 distinct classes and we give explicit examples belonging to each of these…
A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition. This includes representations of the skein algebra of the surface. We…
We analyze in full-detail the geometric structure of the covariant phase space (CPS) of any local field theory defined over a space-time with boundary. To this end, we introduce a new frame: the "relative bicomplex framework". It is the…
Following our previous work [18], we introduce the notions of partial seed homomorphisms and partial ideal rooted cluster morphisms. Related to the theory of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras of a…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
We are interested in the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a triangulated marked surface $\mathbf{S}$ (without punctures). We prove that the spherical twist group ST of $\mathcal{D}$ is…
We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level $\mathrm{K}$, and its generalization. In particular, we put these theories on a flat (2+1) dimensional torus…
We define an algebra on the space of BPS states in theories with extended supersymmetry. We show that the algebra of perturbative BPS states in toroidal compactification of the heterotic string is closely related to a generalized Kac-Moody…
For a triangulated category A with a 2-periodic dg-enhancement and a triangulated oriented marked surface S we introduce a dg-category F(S,A) parametrizing systems of exact triangles in A labelled by triangles of S. Our main result is that…
A universal geometric cluster algebra over an exchange matrix B is a universal object in the category of geometric cluster algebras over B related by coefficient specializations. (Following an earlier paper on universal geometric cluster…
We study the Ginzburg dg algebra $\Gamma_\mathbf{T}$ associated to the quiver with potential arising from a triangulation $\mathbf{T}$ of a decorated marked surface $\mathbf{S}_\bigtriangleup$, in the sense of Qiu. We show that there is a…
We study experimentally what is arguably the simplest yet non-trivial colloidal system: two-dimensional clusters of 6 spherical particles bound by depletion interactions. These clusters have multiple, degenerate ground states whose…
We prove a version of quantum geometric Langlands conjecture in characteristic $p$. Namely, we construct an equivalence of certain localizations of derived categories of twisted crystalline $\mathcal D$-modules on the stack of rank $N$…
We develop a bar involution and canonical basis for every morphism space of the oriented skein category through a diagrammatic approach. In particular, our construction gives rise to Kazhdan-Lusztig type bases on quantized walled Brauer…
Vector spaces of (framed) BPS states of Lagrangian four-dimensional N=2 field theories can be defined in semiclassical chambers in terms of the $L^2$-cohomology of Dirac-like operators on monopole moduli spaces. This was spelled out…
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We…
Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool,…