Related papers: The Multiplication on BP

The entanglement between two parts of a many-body system can be characterized in detail by the entanglement spectrum. Focusing on gapped phases of one-dimensional systems, we show how this spectrum is dominated by contributions from the…

Bielliptic and quasi-bielliptic surfaces form one of the four classes of minimal smooth projective surfaces of Kodaira dimension $0$. In this article, we determine the automorphism schemes of these surfaces over algebraically closed fields…

The separability tensor element of a separable extension of noncommutative rings is an idempotent when viewed in the correct endomorphism ring; so one speaks of a separability idempotent, as one usually does for separable algebras. It is…

I review my work together with Piljin Yi on the spectrum of BPS-saturated states in N = 2 supersymmetric Yang-Mills theories. In an M-theory description, such states are realized as certain two-brane configurations. We first show how the…

In this work, we point out that the Q/U Stokes parameters and E/B mode polarizations are the four components of a unique quaternion, which describes at the same time the directions and the parity states of spherical linear polarizations. We…

In this paper, we introduce an algebraic-topological invariant for commutative pm-rings, termed the spectral fundamental group, which is denoted by $\pi_{k}^{alg}(A)$. This group is defined via homotopy classes of loops within the space of…

We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…

Let $(X,E_X)$ and $(V,E_V)$ be finite connected graphs without loops. We assume that $V$ has two distinguished vertices $a,b$ and an automorphism $\gamma$ which exchanges $a$ and~$b$. The $V$-edge substitution of $X$ is the graph $X[V]$…

We describe a structure on a commutative ring (pre)cyclotomic spectrum $R$ that gives rise to a (pre)cyclotomic structure on topological Hochschild homology ($THH$) relative to its underlying commutative ring spectrum. This lets us…

Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this…

Bound states in the continuum (BICs) and exceptional points (EPs) are unique singularities of non-Hermitian systems. BICs demonstrate enhancement of the electromagnetic field at the nanoscale, while EPs exhibit high sensitivity to small…

Let p be a prime. The Smith-Toda complex V(k) is a finite spectrum whose BP-homology is isomorphic to BP_*/(p,v_1,...,v_k). For example, V(-1) is the sphere spectrum and V(0) the mod p Moore spectrum. In this paper we show that if p > 5,…

The circular Bragg phenomenon is the circular-polarization-state-selective reflection of light in a spectral regime called the circular Bragg regime. In continuation of an expository review on this phenomenon published in 2014, an album of…

We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dimensions. In particular we identify N=1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces…

Let $BPU(n)$ be the classifying space of the projective unitary group $PU(n)$. We determine the integral cohomology ring of $BPU(4)$, and the Steenrod algebra structure of its mod $2$ cohomology.

We compute the five point world sheet scattering amplitude of a symmetric closed string Ramond-Ramond , a transverse scalar field, a world volume gauge field and a real tachyon in both world volume and transverse directions of brane in type…

Given a Boolean algebra B and an embedding e:B -> P(N)/fin we consider the possibility of extending each or some automorphism of B to the whole P(N)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras…

We address some questions concerning indecomposable polynomials and their spectrum. How does the spectrum behave via reduction or specialization, or via a more general ring morphism? Are the indecomposability properties equivalent over a…

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

We present a 1-loop toroidal membrane winding sum reproducing the conjectured $M$-theory, four-graviton, eight derivative, $R^4$ amplitude. The $U$-duality and toroidal membrane world-volume modular groups appear as a Howe dual pair in a…