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Quiver algebras as Fukaya categories
(Mathematical Sciences PublishersGeometry & Topology, 2015-10-20)
We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasiprojective 3–folds associated to meromorphic quadratic ...
The 1-2 model
(American Mathematical SocietyIn the Tradition of Ahlfors–Bers, VII, 2017)
The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was ...
Variation of Gieseker moduli spaces via quiver GIT
(Mathematical Sciences PublishersGeometry & Topology, 2016)
We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds ...
Polynomials and models of type theory
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsMagdalene College, 2015-06-30)
This thesis studies the structure of categories of polynomials, the diagrams that represent polynomial functors. Specifically, we construct new models of intensional dependent type theory based on these categories.
Firstly, ...
Potential automorphy and the Leopoldt conjecture
(Johns Hopkins University PressAmerican Journal of Mathematics, 2017-10-01)
We study in this paper Hida's p-adic Hecke algebra for GL_n over a CM field F. Hida has made a conjecture about the dimension of these Hecke algebras, which he calls the non-abelian Leopoldt conjecture, and shown that his ...
Critical Surface of the Hexagonal Polygon Model
(SpringerJournal of Statistical Physics, 2016-05-01)
The hexagonal polygon model arises in a natural way via a transformation of the 1-2 model on the hexagonal lattice, and it is related to the high temperature expansion of the Ising model. There are three types of edge, and ...
Quantifying separability in virtually special groups
(Mathematical Society PublishingPacific Journal of Mathematics, 2016)
We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if G is a virtually compact special hyperbolic group, and Q ≤ G is a K-quasiconvex ...
Cubulating hyperbolic free-by-cyclic groups: the irreducible case
(Duke University PressDuke Mathematical Journal, 2016)
Let V be a fi nite graph and let ∅ : V → V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a ...
D-modules on rigid analytic spaces I
(De GruyterJournal für die reine und angewandte Mathematik, 2016)
We introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small ...