Related papers: Galois conjugates of String-net Model

The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…

We extend the study of the condensed Galois category of a scheme introduced by Barwick, Glasman and Haine in their work on Exodromy. We elaborate its connection to Lurie's work on Ultracategories and provide a description in terms of…

The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…

Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential…

A fundamental theorem of Katz \cite{Katz87} determines the differential Galois groups of rank $n$ connections on algebraic curves with slope $r/n$ at a singularity, where $\gcd(r,n)=1$. We extend this result to $G$-connections, where $G$ is…

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined…

In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew…

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…

The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Gamma, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum…

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and…

This paper investigates the principal minors of a parameterized Hermitian Laplacian matrix for oriented graphs. Particularly, we focus on the properties of the matrix for parameters chosen as Galois conjugates of a primitive $p$th root of…

We examine a moduli problem for real and quaternionic vector bundles on a smooth complex projective curve with a fixed real structure, and we give a gauge-theoretic construction of moduli spaces for semi-stable such bundles with fixed…

Let $p$ be a fixed odd prime, and let $K$ be a finite extension of $\mathbb{Q}_p$ with ring of integers $\mathcal{O}_K$. The Emerton-Gee stack for $\mathrm{GL}_2$ is a stack of $(\varphi, \Gamma)$-modules. The stack, denoted…

We introduce the adjoint homological Selmer module for an SL$_2$-representation of a knot group, which may be seen as a knot theoretic analogue of the dual adjoint Selmer module for a Galois representation. We then show finitely generated…

Let $K$ be a number field and $G$ a finite abelian group. We study the asymptotic behaviour of the number of tamely ramified $G$-extensions of $K$ with ring of integers of fixed realisable class as a Galois module.

Although free-fermion systems are considered exactly solvable, they generically do not admit closed expressions for nonlocal quantities such as topological string correlations or entanglement measures. We derive closed expressions for such…

Using bulk gapless topological superconductors in both 1d and 2d as free fermion model examples, we demonstrate the power of subsystem correlation spectrum (the spectrum of correlation matrix), or equivalently the entanglement spectrum for…

We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly…

We extend the theory of tautological classes on moduli spaces of stable curves to the more general setting of moduli spaces of admissible Galois covers of curves, introducing the so-called H-tautological ring. The main new feature is the…

Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…