相关论文: Recent Developments in Line Bundle Cohomology and …

I show that holographic calculations of entanglement entropy in the context of AdS bulk space modified by wormhole geometries provide the expected entanglement magnitude. This arises in the context of string theory by means of additional…

This is a pedagogical review article surveying the various approaches towards understanding gauge coupling unification within string theory. As is well known, one of the major problems confronting string phenomenology has been an apparent…

The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of 2-dimensional sigma models as…

We investigate orbifold compactifications of the heterotic string, addressing in detail their construction, classification and phenomenological potential. We present a strategy to search for models resembling the minimal supersymmetric…

The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…

The persistent homology with coefficients in a field F coincides with the same for cohomology because of duality. We propose an implementation of a recently introduced algorithm for persistent cohomology that attaches annotation vectors…

We prove `twisted' versions of Kirchhoff's network theorem and Kirchhoff's matrix-tree theorem on connected finite graphs. Twisting here refers to chains with coefficients in a flat unitary line bundle.

Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively…

In this paper we construct various non-trivial and non-tautological cohomology classes on compactified and uncompactified strata of curves with a differential, by using the geometry of the boundary stratification of the moduli space of…

I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…

It has been shown recently that the geometry of D-branes in general topologically twisted (2,2) sigma-models can be described in the language of generalized complex structures. On general grounds such D-branes (called generalized complex…

In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the contributing components which depends on…

The Ricci curvature equations are a central subject of study in geometry. However, in the smooth real case, their linear analysis is often confined to settings in which the background metric is Einstein. In this paper, we establish…

I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a…

The covariant canonical method of quantization based on the De Donder-Weyl covariant canonical formalism is used to formulate a world-sheet covariant quantization of bosonic strings. To provide the consistency with the standard…

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…

This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.

At the present time, string theory (and its generalizations) remain relatively abstruse subjects to the particle phenomenologist and experimentalist. Yet, striking developments of the last two years offer hope that a fundamental…

The main goal of string phenomenology is to find realistic models of particle physics and cosmology within string theory. Dark bubble cosmology is an alternative to string compactifications, where our universe lives on a bubble expanding in…

In this paper we view the sigma-model couplings of appropriate vertex operators describing the interaction of string matter with a certain type of string solitons (0-branes) as the quantum phase space of a point particle. The sigma-model is…