Related papers: Betti Spectral Gluing
We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this…
Given a topological modular functor $\mathcal{V}$ in the sense of Walker \cite{Walker}, we construct vector bundles over $\bar{\mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction…
In this paper we provide an explicit construction of a $distinctive$ multiple Dirichlet series associated to products of quadratic Dirichlet L-series, which we believe should be tightly connected to a generalized metaplectic Whittaker…
We study the homological properties of $\Delta_{\mathbf{r}}(n_1, \dots, n_e)$, a simplicial complex formed by sequentially gluing complete graphs along $(r_i-1)$-simplices. This construction generates precisely the chordal clique complexes,…
This is a survey of various results about spectral covers and their relationship to Higgs bundles. To a G-principal Higgs bundle on a variety S corresponds a cameral cover \widetilde{S} of S (a W-Galois cover, where W is the Weyl group of…
We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and…
We concentrate on a treatment of a Higgs-Coulomb duality as an absence of manifest phase transition between ordered and disordered phases of 2d $\mathcal{N}=(2,2)$ theories. We consider these examples of QFTs in the Schr\"odinger picture…
We associate a monoidal category $\mathcal{H}_B$, defined in terms of planar diagrams, to any graded Frobenius superalgebra $B$. This category acts naturally on modules over the wreath product algebras associated to $B$. To $B$ we also…
We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra…
We consider two problems associated to the space of Riemann surfaces that are closely related to string theory. We first consider the problem of existence of heterotic-string and type-II-superstring field theory vertices in the product of…
We construct rational models for classifying spaces of self-equivalences of bundles over simply connected finite CW-complexes relative to a given simply connected subcomplex. Via work of Berglund-Madsen and Krannich this specializes to…
Hessenberg varieties are a family of subvarieties of the flag variety, including the Springer fibers, the Peterson variety, and the entire flag variety itself. The seminal example arises from a problem in numerical analysis and consists for…
In this article, we study the Dirac spectrum of typical hyperbolic surfaces of finite area, equipped with a nontrivial spin structure (so that the Dirac spectrum is discrete). For random Weil-Petersson surfaces of large genus $g$ with…
Given a smooth genus two curve $C$, the moduli space SU$_C(3)$ of rank three semi-stable vector bundles on $C$ with trivial determinant is a double cover in $\mathbb{P}^8$ branched over a sextic hypersurface, whose projective dual is the…
Let G be an algebraic group over an algebraically closed field of positive characteristic such that its neutral connected component is a unipotent group. We consider a certain class of closed idempotents in the braided monoidal category…
In this article we give an explicit description of the Hitchin fiber of SU(1,2) Higgs bundles $(L,F,\gamma,\beta)$ over a compact Riemann surface $X$ of genus $\ge 2$ with $q=\gamma\circ\beta$ having simple zeros and Toledo invariant…
We extend several $g$-type theorems for connected, orientable homology manifolds without boundary to manifolds with boundary. As applications of these results we obtain K\"uhnel-type bounds on the Betti numbers as well as on certain…
Every four-dimensional ${\cal N}=2$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected…
Given a generic ray of Higgs bundles $(\overline{\partial}_E, t\varphi)$, we describe the corresponding family of hermitian metrics $h_t$ solving Hitchin's equations via gluing methods. In the process, we construct a family of approximate…
This paper builds on our previous work in which we showed that, for all connected semisimple linear Lie groups $G$ acting on a non-compactly causal symmetric space $M = G/H$, every irreducible unitary representation of $G$ can be realized…