A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Review of instantons in noncommutative gauge theories across 4, 6, and 8 dimensions.
The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.
The paper applies potential theory to conformal geometry, proving theorems and dimension estimates.
Estimates the rational homological dimension of Riemann surfaces with boundary and marked points.
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
Survey on GKM theory in low dimensions, highlighting combinatorics-geometry interplay.
Study on Hodge theory for almost complex manifolds.
Develops trace class operators and inverse Laplacian theory for infinite dimensions.
We consider several diffeomorphism invariant field theories of 2- and 3-forms in six dimensions. They all share the same kinetic term , but differ in the potential term that is added. The theory with no potential term is topological - it describes no propagating degrees of freedom. We show that the theory co…
New theory explains how chaotic training improves neural network generalization.
We present a proof of Milnor conjecture in dimension 3 based on Cheeger-Colding theory on limit spaces of manifolds with Ricci curvature bounded below. It is different from [Liu] that relies on minimal surface theory.
We introduce dynamic asymptotic dimension, a notion of dimension for actions of discrete groups on locally compact spaces, and more generally for locally compact étale groupoids. We study our notion for minimal actions of the integer group, its relation with conditions used by Bartels, Lück, and Reich in the context of…
This paper studies the Yang--Mills ASD equation over the cylinder as a non-linear evolution equation. We consider a dynamical system consisting of bounded orbits of this evolution equation. This system contains many chaotic orbits, and moreover it becomes an infinite dimensional and infinite entropy system. We study th…
We define an extended field theory in dimensions , that takes the form of a `quasi 2-functor' with values in a strict 2-category , defined as the `completion of a partial 2-category' , notions which we define. Our construction extends Wehrheim and Woodward's Floer Field th…
Analyzes Kodaira-Iitaka dimension and multiplicity using intersection theory.
We review the relations between (twisted) supersymmetric gauge theories in four dimensions and moduli problems in four-dimensional topology, and we study in detail the non-abelian monopole equations from this point of view. The relevance of exact results in N=1 and N=2 supersymmetric gauge theories to the computation o…
Theory of symplectic reduction in infinite dimensions developed.
We present an approach to cohomological dimension theory based on infinite symmetric products and on the general theory of dimension called the extension dimension. The notion of the extension dimension $\ExD(X)$ was introduced by A.N.Dranishnikov \cite {D} in the context of compact spaces and CW complexes. This pa…
Study skein modules via gauge theory, finding non-TQFT dimensions.
Generalized Fáry's theorem to higher dimensions.
Study permeable sets and their dimensions, with applications to fractals.
Paper shows string cobordism at 24 dims can be determined by elliptic genus.
We extend the Nielsen theory of coincidence sets to equalizer sets, the points where a given set of (more than 2) mappings agree. On manifolds, this theory is interesting only for maps between spaces of different dimension, and our results hold for sets of k maps on compact manifolds from dimension (k-1)n to dimension …
The equations of motion and the Bianchi identity of the C-field in M-theory are encoded in terms of the signature operator. We then reformulate the topological part of the action in M-theory using the signature, which leads to connections to the geometry of the underlying manifold, including positive scalar curvature. …
Enhances conformal geometry in higher dimensions with infinite-dimensional algebra.
We expand Topological Field Theory on some special CW-complexes (brane complexes). This Brane Topological Field Theory one-to-one corresponds to infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser dimension. We define general and regular Hurwitz numbers of brane complexes and prove that they ge…
Connected space of Dirac-minimal metrics in 2 and 4 dimensions.
Extends Arnold's linking theory to higher dimensions and submanifolds.
We give a brief overview of the theory of complex dimensions of real (archimedean) fractal strings via an illustrative example, the ordinary Cantor string, and a detailed survey of the theory of p-adic (nonarchimedean) fractal strings and their complex dimensions. Moreover, we present an explicit volume formula for the…
Extends Heegaard Floer theory to surfaces of dimension one.
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
The paper analyzes arbitrage theory in a fluctuating market of stochastic dimension.
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
We present a Donaldson-Witten type field theory in eight dimensions on manifolds with holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
The paper explores Kaluza-Klein theories without assuming a fibration structure.
The study examines higher-order modern portfolio theory with complex critical points and feasible portfolio variety.
We study knots in 3d Chern-Simons theory with complex gauge group , in the context of its relation with 3d theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d theory, which is compactified on a 3-manifold . …
Extends potential theory to Carnot groups, estimating Hausdorff dimension.
New index theory proves Gromov's dihedral conjectures.
This work has its origins in an attempt to describe systematically the integrable geometries and gauge theories in dimensions one to four related to twistor theory. In each such dimension, there is a nondegenerate integrable geometric structure, governed by a nonlinear integrable differential equation, and each solutio…
The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold…
It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we attempt to verify this directly by analyzing the equations and counting their solut…
New theory shows deep networks adapt to data's intrinsic dimensionality even when data isn't on a low-dimensional manifold.
Develops infinite-dimensional Kempf-Ness theory for complexification-free groups.
Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to gluings of higher dimensional simplices. It is generally assumed that GFT graphs are always dual to pseudo manifolds. In this paper we prove that already in dimension three (and in all higher dimensions), this is not true due…
New theory captures framing anomaly in gauge theory.
A surface functional theory for p-dimensional extended objects, the p-branes, was proposed in previous papers. The field equations for toroidal p-branes was exactly solved in dimensions, yielding equally spaced mass-squared spectrum with massless states. In this paper, we obtain the asymptotic distribution of m…