Related papers: A GLSM view on Homological Projective Duality
We give a geometric realization of the symmetric algebra of the tensor space $C^n \bigotimes C^m$ together with the action of the dual pair $(gl_n, gl_m)$ in terms of lagrangian cycles in the cotangent bundles of certain varieties. We…
Suppose $G$ is a connected complex Lie group and $\Gamma$ is a discrete subgroup such that $X := G/\Gamma$ is K\"ahler and the codimension of the top non--vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or…
Two Higgs-doublet models usually consider an ad-hoc $\mathbb{Z}_2$ discrete symmetry to avoid flavor changing neutral currents. We consider a new class of two Higgs-doublet models where $\mathbb{Z}_2$ is enlarged to the symmetry group…
We construct a categorification of the maximal commutative subalgebra of the type $A$ Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to the…
Let $X$ be a smooth irreducible nondegenerate projective variety and let $X^*$ denote its dual variety. It is well known that $\sigma_2(X)^*$, the dual of the 2-secant variety of $X$, is a component of the singular locus of $X^*$. The locus…
Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…
We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of…
Given a sufficiently positive embedding $X\subset\mathbb{P}^N$ of a smooth projective variety $X$, we consider its secant variety $\Sigma$ that comes equipped with the embedding $\Sigma\subset\mathbb{P}^N$ by its construction. In this…
In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…
In this thesis we review some results on the generalization of the gauge/gravity duality to new cases by using T-duality and by including fundamental matter, finding applications to condensed matter physics. First, we construct new…
We study the consistency of two Higgs doublet models in light of the new bosonic particle discovery at the LHC. We work within a general setup that we call the 2HDM-X, in which the quarks couple to both scalar doublets with aligned…
The Segre cubic and Castelnuovo-Richmond quartic are two projectively dual hypersurfaces in $\mathbb{P}^4$, with a long and rich history starting in the 19th century. We will explain how Kuznetsov's theory of homological projective duality…
In the first part of this paper the projective dimension of the structural modules in the BGG category $\mathcal{O}$ is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an…
Following the work of Burger, Iozzi and Wienhard for representations, in this paper we introduce the notion of maximal measurable cocycles of a surface group. More precisely, let $\mathbf{G}$ be a semisimple algebraic $\mathbb{R}$-group…
We investigate toric GLSMs as models for tachyon condensation in type II strings on space-time non-supersymmetric orbifold singularities. The A-model correlators in these theories satisfy a set of relations related to the topology of the…
In previous work, we have constructed diagrammatic idempotents in an affine extension of the Temperley-Lieb category, which describe extremal weight projectors for sl(2), and which categorify Chebyshev polynomials of the first kind. In this…
In Part I, we extend our analysis in [arXiv:0807.1107], and show that a mathematically conjectured geometric Langlands duality for complex surfaces in [1], and its generalizations -- which relate some cohomology of the moduli space of…
We study the idea of the Higgs as a pseudo-Goldstone boson within the framework of partial supersymmetry in Randall-Sundrum scenarios and their CFT duals. The Higgs and third generation of the MSSM are composites arising from a strongly…
In the context of Composite Higgs Models we consider the realisation of an extended Higgs sector with two Higgs doublets arising as pseudo Nambu-Goldstone bosons from a $\textrm{SO}(6) \to \textrm{SO}(4) \times \textrm{SO}(2)$ breaking. The…
We consider a composite Higgs model embedded into a Grand Unified Theory(GUT) based on the E_6 gauge group. The phenomenological viability of this E_6 inspired composite Higgs model (E6CHM) implies that standard model (SM) elementary…