相关论文: A-Genus and the Sigma Model
In this paper we present a new approach to construct the set of numerical semigroups with a fixed genus. Our methodology is based on the construction of the set of numerical semigroups with fixed Frobenius number and genus. An equivalence…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
This paper examines two cosmological models of quantum gravity (from string theory and loop quantum gravity) to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical…
The space-time foliation Sigma compatible with the gravitational field g on a 4-manifold M determines a fibration pi of M, pi : M -> N is a surjective submersion over the 1-dimensional leaves space N. M is then written as a disjoint union…
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…
These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of…
Given a field with a set of discrete valuations $V$, we show how the genus of a division algebra over the field is related to the genus of the residue algebras at various valuations in $V$ and the ramification data. When the division…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
N = 2 supersymmetry in four space-time dimensions is intimately related to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On the…
These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group…
We introduce a classical fractional particle model in $\mathbb{R}^{n}$, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum…
A new class of cylindrically symmetric inhomogeneous string cosmological models is investigated. To get the deterministic solution, it has been assumed that the expansion ($\theta$) in the model is proportional to the eigen value…
We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the…
Let $K$ be a global function field of characteristic $p$, and let $\Gamma$ be a finite-index subgroup of an arithmetic group defined with respect to $K$ and such that any torsion element of $\Gamma$ is a $p$-torsion element. We define…
We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field…
These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory. The lectures consist of four sections, each dealing with a different soliton. We start with…
In this letter we apply the methods of our previous paper hep-th/0108045 to noncommutative fermions. We show that the fermions form a spin-1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations…
Various aspects of non-linear sigma models with an $SU(N)\times U(1)$ symmetric target space are considered. In the case $N=2$, three-dimensional topological defects are discussed which are relevant for frustrated magnetic systems and which…
In this paper, we investigate Weng zeta functions associated with curves of genus 2 over finite fields. Building upon Weng's framework for non-abelian zeta functions, we establish that, as the rank n tends to infinity, the Riemann…
Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary…