Thurston's influence on French math traced and problems solved.
problem Major problems in French math traced back to Thurston.
method Overview and survey of Thurston's influence and results.
result French math problems rooted in Thurston's work.
On-device research index
arXiv research
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.
169,291 papers · 148 categories
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48 results for “mathematical survey”
Survey article on Kahler-Einstein metrics and algebraic geometry.
problem Understanding Kahler-Einstein metrics in algebraic geometry.
method Not specified in the abstract, likely involves mathematical analysis and algebraic geometry techniques.
result Discussion of recent developments and challenges in the field.
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematical Foundations of Quantum Field Theory and Perturbative String Theory".
Survey of Baum-Connes conjecture history and methods.
problem Baum-Connes conjecture in mathematics.
method History and methods of the conjecture.
result Current status of the conjecture.
The paper surveys mathematical results on filtration enlargement with financial examples.
problem Mathematical finance applications of filtration enlargement theory.
method Exhaustive survey and interpretation of key results from literature.
result Provides a compendium of known mathematical results for mathematical finance researchers.
Survey on two-numbers and their applications in mathematics.
problem Understanding the geometric properties of connected Riemannian manifolds.
method Review of existing literature and open problems.
result Two-numbers are closely related to various mathematical areas.
This paper surveys and classifies attribute-aware CF models.
problem Rating prediction with user and item attributes.
method Mathematical classification of attribute-aware CF models into four categories.
result Comprehensive comparison of effectiveness among different categories.
Survey on new Ricci flow techniques.
problem None explicitly stated.
method None explicitly stated.
result None explicitly stated.
Survey article on recent Kähler geometry and exceptional holonomy.
problem Exploring recent advancements in Kähler geometry and exceptional holonomy.
method Not specified in the abstract, likely a review of existing research.
result Not specified in the abstract, likely a summary of recent findings.
Survey of three graph curvature notions and their Riemannian geometry parallels.
problem Exploring and comparing different curvature notions on graphs.
method Definition and motivation of combinatorial, Bakry-Émery, and Ollivier's Ricci curvatures.
result Comparison of discrete and Riemannian geometric curvature concepts.
Survey on AI math foundations, focusing on neural networks.
problem Lack of rigorous mathematical foundation for AI.
method Survey and discussion of theoretical directions in AI.
result Discussion of open problems in AI math.
Short survey to be published at the Encyclopedia of Mathematical Physics.
We give a brief survey on aspects of the local index theory as developed from the mathematical works of V. K. Patodi. It is dedicated to the 70th anniversary of Patodi.
Survey of gradient boosting algorithms and their applications.
problem Improving machine learning models through boosting techniques.
method Detailed mathematical frameworks of gradient boosting algorithms.
result Illustration of gradient boosting's role in model optimization and ranking.
Higher Gauge Theoryhep-th
Survey on advanced gauge theory concepts.
problem Understanding higher gauge theory structures.
method Introduction to higher structures and connections on higher principal bundles.
result Summarized applications and principles of higher gauge theories.
Survey of contact homology for contact manifolds.
problem Understanding contact manifolds through homology.
method Holomorphic curves invariants.
result Useful for students and young mathematicians.
Survey on strong convergence in random matrices and its applications.
problem Understanding convergence of random matrices to operators.
method Analysis of operator norms of noncommutative polynomials.
result New insights and applications in random graphs, geometry, and operator algebras.
This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our…
Geometry and the Quantumhep-th
Survey of work on quantum geometry and gravity.
problem How geometry emerges from quantum formalism.
method Developed a slightly noncommutative structure and spectral model of gravity.
result Model fits with experimental knowledge of gravity and matter.
Discrete Coxeter groupsmath.GT
Survey on Coxeter groups for Lie group examples.
problem Understanding Coxeter groups and their applications.
method Constructing discrete subgroups of Lie groups using Coxeter groups.
result Coxeter groups provide new examples in discrete subgroups of Lie groups.
Survey on modeling event sequences through temporal processes.
problem Modeling phenomena with sequences of events over continuous time.
method Probabilistic models based on point processes, categorized into simple, marked, and spatio-temporal.
result Analysis of existing approaches and their applicability to prediction and modeling.
This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
Survey revisits Bachelier and Dupire, highlighting optimal transport's role.
problem Finding arbitrage-free models calibrated to volatility surfaces.
method Revisits mathematical finance principles, uses optimal transport results.
result Optimal transport provides rigorous foundations for Dupire's model.
Survey on geometry and topology of maximal antipodal sets.
problem Maximal antipodal sets on Riemannian manifolds.
method Comprehensive survey of existing research.
result Relation to various mathematical areas.
This survey reviews Heterogeneous Representation Learning (HRL) for diverse data types.
problem Challenges in learning from heterogeneous data types.
method Unified learning framework for modeling various learning settings.
result Unified mathematical framework for multi-view, transfer, privileged, and multi-task learning.
This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.
Geometry of -minimal surfaces in math.DG
Survey on geometric properties of special minimal surfaces.
problem Understanding -minimal surfaces in .
method Systematic geometric study of -minimal surfaces.
result Fundamental results in the theory of -minimal surfaces.
The abstract discusses open problems in isoparametric theory.
problem Open problems in isoparametric theory.
method Survey and propose open problems.
result Discussion of open problems in isoparametric theory.
This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.
This survey was compiled from lectures and problem sessions at the International Conference on Geometric Topology at the Mathematical Research and Conference Center in Bedlewo, Poland in July 2005.
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 of mathematical foundations for reinforcement learning.
problem Design and analysis of modern reinforcement learning algorithms.
method Organizes mathematical structures from probability, optimization, and operator theory.
result Unified mathematical entry point for researchers in various fields.
Signatures simplify analysis of evolving data streams.
problem Understanding and analyzing irregular, non-stationary data streams.
method Mathematical signatures reduce noise and preserve key information.
result Signatures manage the exponential scaling of data complexity.
Survey of weak form's role in equation learning, parameter estimation, and coarse graining.
problem Noise robustness, accuracy, and computational efficiency in weak form applications.
method Survey and recent developments in weak form versions of equation learning, parameter estimation, and coarse graining.
result Surprising noise robustness, accuracy, and computational efficiency in weak form applications.
Survey on nonlinear parabolic equations in finance.
problem Nonlinear extensions of the Black-Scholes theory.
method Qualitative and numerical analysis of nonlinear parabolic equations.
result Existence and uniqueness of solutions to nonlinear parabolic equations.
Survey on Gaussian processes and their deep variants.
problem Limitations of Gaussian processes and their derivatives.
method Comprehensive review of existing methods and research themes.
result Advancements in Deep Gaussian Processes over the past decade.
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathematics in 1994 by Gelfand, Kapranov and Zelevinski. Some traces of amoebas were appearing from time to time, even before the formal introduct…
Towards the global vision of engagement of Generation Z at the workplace: Mathematical modelingecon.GN
Mathematical models reveal key factors for engaging Gen Z at work.
problem Understanding and improving engagement of Generation Z employees.
method Correlation and cluster analyses on engagement surveys.
result Clear responsibilities and challenging work are essential for Gen Z employees.
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.
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in this field and highlights some applications in mathematical physics.
In this survey, a short introduction in the recent discovery of log-normally distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to empirical trend data…
Survey of kernels, RKHS, and their applications in machine learning.
problem Understanding kernels and their applications in machine learning.
method Review of historical context, mathematical definitions, and practical applications of kernels.
result Comprehensive overview of kernels, RKHS, and their applications.
Survey on inverse exponential Radon transform methods.
problem Analytical methods for inverse exponential Radon transform.
method Derivation of classical inversion formula, finite Hilbert transform, exact reconstruction from partial measurements, diverging-beam data.
result Exact reconstruction from 180 degree data using finite Hilbert transform.
Surveying mean curvature flow on solvmanifolds, focusing on translating solutions.
problem Understanding translating solutions on solvmanifolds.
method Exploration of mean curvature flow, introduction of translating solutions, discussion of solvmanifolds.
result Equations describing translating solutions on the family of 3D solvmanifolds.
Quantum character varietiesmath.QA
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lectures the authors gave at the Fields Institute in the Thematic Program of Calabi-Yau Varieties in the fall of 2013.
The survey we are presenting is over 22 years old but it has still some ideas which where never published (except in Polish). This survey is the base of the third Chapter of my book: KNOTS: From combinatorics of knot diagrams to combinatorial topology based on knots, which is still in preparation (but compare http://ar…
We discuss classical gravitational aspects of the AdS/CFT correspondence, with the aim of obtaining a rigorous (mathematical) understanding of the semi-classical limit of the gravitational partition function. The paper surveys recent progress in the area, together with a selection of new results and open problems.