Related papers: Parabolic refined invariants and Macdonald polynom…
In this thesis, we explore two approaches to string phenomenology. In the first half of the work, we investigate M-theory compactifications on spaces with co-dimension four, orbifold singularities. We construct M-theory on C^2/Z_N by…
We introduce in this paper a hypercohomology version of the resonance varieties and obtain some relations to the characteristic varieties of rank one local systems on a smooth quasi-projective complex variety $M$, see Theorem (3.1) and…
The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are…
Superconducting cosmic strings (SCSs) have received revived interests recently. In this paper we treat closed SCSs as oriented knotted line defects, and concentrate on their topology by studying the Hopf topological invariant. This…
We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on…
We study the resurgent structures of Wilson loops in refined topological string theory. We argue that the Borel singularities should be integral periods, and that the associated Stokes constants are refined Donaldson-Thomas invariants, just…
We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…
Every Riemann surface with genus $g$ and $n$ punctures admits a hyperbolic metric, if $2g-2+n>0$. Such a surface can be decomposed into pairs of pants whose boundaries are geodesics. We construct a string field theory for closed bosonic…
The concept of concrete regularity structure gives the algebraic backbone of the operations involved in the local expansions used in the regularity structure approach to singular stochastic partial differential equations. The spaces and the…
We propose a refinement of the Kontsevich-Soibelman operator for a class of ``special'' 4d $\mathcal{N}=2$ superconformal field theories characterized by the following conditions: (1) their Coulomb branch admits a source/sink chamber, i.e.,…
Lagrangian formalism on graded manifolds is phrased in terms of the Grassmann-graded variational bicomplex, generalizing the familiar variational bicomplex for even Lagrangian systems on fiber bundles.
This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2,C) representations of a surface group. Specifically, we find an asymptotic correspondence between the…
An extended class of N=2 locally supersymmetric invariants with higher-derivative couplings based on full superspace integrals, is constructed. These invariants may depend on unrestricted chiral supermultiplets, on vector supermultiplets…
For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general…
We study properties of the recently established refined topological recursion for some simple spectral curves associated to quadratic differentials. We prove explicit formulas for the free energy and Voros coefficients of the corresponding…
We primarily investigate the properties of characteristic polynomials of semimatroids. In particular, we provide a combinatorial interpretation of their coefficients, generalizing the Whitney's Broken Circuit Theorem. We also prove that the…
We conjecture closed-form expressions for the Macdonald limits of the superconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas (AD) theories in terms of certain simple deformations of Macdonald polynomials. As checks…
Multi-dimensional continuous local martingales, enhanced with their stochastic area process, give rise to geometric rough paths with a.s. finite homogenous p-variation, p>2. Here we go one step further and establish quantitative bounds of…
This paper provides some technical results needed in "Formalism for Relative Gromov-Witten Invariants." We study line-bundles on the moduli stacks of relative stable and rubber maps that are used to define relative Gromov-Witten invariants…
We develop a gauge theory or theory of bundles and connections on them at the level of braids and tangles. Extending recent algebraic work, we provide now a fully diagrammatic treatment of principal bundles, a theory of global gauge…