arXiv research

Explains alternating knots for a concise encyclopedia.

Explains Turaev surfaces for knot theory.

Survey on spatial graphs with few vertices and edges.

Review of invariants for spatial graphs.

Higher topos theory applied to physics.

Short survey to be published at the Encyclopedia of Mathematical Physics.

This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics

This is an overview article on the Kontsevich integral written for the Encyclopedia of Mathematical Physics, to be published by Elsevier.

This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.

This encyclopedia article briefly reviews without proofs some of the main results in cotangent bundle reduction. The article recalls most the necessary prerequisites to understand the main results.

This encyclopedia article briefly reviews without proofs some of the main results in symplectic reduction. The article recalls most the necessary prerequisites to understand the main results, namely, group actions, momentum maps, and coadjoint orbits, among others.

This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.

This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.

This note is an expanded and updated version of our entry with the same title for the 2006 Encyclopedia of Mathematical Physics. We give a brief overview of graded Poisson algebras, their main properties and their main applications, in the contexts of super differentiable and of derived algebraic geometry.

Quantum character varieties unify four construction methods.

This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometric and topological structure of collapsed/non-collapsed regions in Riemannian manifold under various curvature assumptions. Numerous applicat…

The paper connects three integer sequences to a knot polynomial.

We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have solved many longstanding open problems and conjectures; for more on this, see th…

Survey on advanced gauge theory concepts.

A concise review of recent few-shot meta-learning methods.

Bayesian interpolants explain neural network inferences concisely.

Overview of 3D TQFTs and 3-manifold invariants.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

This article reviews $\infty$-bundles and their applications in geometry and physics.

This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.

We give a concise proof that large classes of optimal (constant curvature or Einstein) pseudo-Riemannian metrics are maximally symmetric within their conformal class.

We give a precise and concise formulation of the orientifold construction in Type II superstring theory. Our results include anomaly cancellation on the worldsheet and a spacetime computation of the background Ramond-Ramond charge.

Defines linking number and Milnor invariants, their properties.

AWD distills neural network info into interpretable wavelets.

Introduces string structures linking to loop spaces.

GRACE generates concise explanations for neural networks on tabular data.

We prove that the homotopy class of a Morin mapping f: P^p --> Q^q with p-q odd contains a cusp mapping. This affirmatively solves a strengthened version of the Chess conjecture [DS Chess, A note on the classes [S_1^k(f)], Proc. Symp. Pure Math., 40 (1983) 221-224] and [VI Arnol'd, VA Vasil'ev, VV Goryunov, OV Lyashenk…

We define covariant Lie derivatives acting on vector-valued forms on Lie algebroids and study their properties. This allows us to obtain a concise formula for the Frölicher-Nijenhuis bracket on Lie algebroids.

We give a concise proof of a classification of lens spaces up to orientation-preserving homeomorphisms. The chief ingredient in our proof is a study of the Alexander polynomial of ` symmetric' links in $S^3$.

A method for concise fuzzy system modeling using ESSC-SL-CTSK-FS.

Proof given for SGD convergence in a concise manner.

ConCuR generates high-quality CUDA kernels with concise reasoning traces.

We develop the theory of Berezin-Toeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de Monvel-Guillemin theory, that we simplify in several ways to obtain a concise exposition. A comparison with the spin-c Dirac quantization is also included.

We give a concise introduction to the Farrell-Jones Conjecture in algebraic $K$-theory and to some of its applications. We survey the current status of the conjecture, and we illustrate the two main tools that are used to attack it: controlled algebra and trace methods.

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary con…

It is classical that given any Seifert structure on N, Reidemeister-Schreier's algorithm produces a presentation of all index 2 subgroups of the fundamental group of N, described as the fundamental group of some Seifert manifolds. The new result of this article is concise formulas that gather all possible cases.

After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary results from Riemannian geometry are proven using these generalizations. In particul…

We generalise the hyper-Kahler/quaternionic Kahler (HK/QK) correspondence to include para-geometries, and present a new concise proof that the target manifold of the HK/QK correspondence is quaternionic Kahler. As an application, we construct one-parameter deformations of the temporal and Euclidean supergravity c-map m…

Defines a filtration on variational bicomplex for concise functional form conditions.

A theory linking invariants, Floer homologies, and Higgs bundles.

The Klein-Grifone approach to global Finsler geometry is adopted. A global existence and uniqueness theorem for Chern connection is formulated and proved. The torsion and curvature tensors of Chern connection are derived. Some properties and the Bianchi identities for this connection are investigated. A concise compari…

GPflow is a Gaussian process library that uses TensorFlow for its core computations and Python for its front end. The distinguishing features of GPflow are that it uses variational inference as the primary approximation method, provides concise code through the use of automatic differentiation, has been engineered with…

A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel tran…