Survey on new Ricci flow techniques.
problem None explicitly stated.
method None explicitly stated.
result None explicitly stated.
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48 results for “recent developments”
Survey on DDVV-type inequalities, their history, and recent developments.
problem None explicitly stated; focuses on surveying existing work.
method None explicitly stated; focuses on surveying existing work.
result Survey of DDVV-type inequalities and their history and recent developments.
Recent developments in Seiberg-Witten theory and relations with Complex Geometry.
This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
Survey on broken ray transforms and open problems.
problem Understanding broken ray transforms and their applications.
method Survey of recent developments and open problems.
result Discussion of open problems in broken ray transforms.
This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
Survey of recent metric geometry in Kähler metrics space.
problem Understanding the metric geometry of Kähler metrics space.
method Survey and highlighting of recent results.
result Highlighting of open problems in the field.
Survey of recent measures of association, including a new coefficient.
problem Exploring new measures of association in statistics.
method Survey and introduction of a new correlation coefficient.
result Proposed a new extension of the correlation coefficient to standard Borel spaces.
On astheno-Kähler manifoldsmath.DG
Survey of astheno-Kähler manifolds and their challenges.
problem Understanding astheno-Kähler manifolds and their existence.
method Review of classical findings and recent developments.
result Challenges in the existence of astheno-Kähler manifolds.
Some recent developments on isometric immersions via compensated compactness and gauge transformsmath.AP
Survey on recent developments in isometric immersions using PDE techniques.
problem Analyzing isometric immersions with low Sobolev regularity.
method Compensated compactness and Coulomb-Uhlenbeck gauges.
result Weak continuity and stability of Gauss-Codazzi-Ricci equations.
Stringy orbifoldsmath.AG
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.
This is a very brief report on recent developments on the Dirichlet problem for the minimal surface system and minimal cones in Euclidean spaces. We shall mainly focus on two directions: (1) Further systematic developments after Lawson-Osserman's paper \cite{l-o} on the Dirichlet problem for minimal graphs of high codi…
Satellite imagery helps assess sustainable development with machine learning.
problem Lack of ground data on sustainable development outcomes.
method Combining satellite imagery with machine learning to model outcomes.
result Machine learning models perform well across multiple sustainable development domains.
Study on insurance risk management and sustainable development.
problem Lack of attention to non-climate change aspects of sustainable development in insurance.
method Analysis of recent developments and legislative initiatives in insurance risk management.
result Strategies for small- and medium-sized enterprises to manage sustainable development risks.
In this note, we give a brief survey on some recent developments of biharmonic submanifolds. After reviewing some recent progress on Chen's biharmonic conjecture, the Generalized Chen's conjecture on biharmonic submanifolds of non-positively curved manifolds, and some classifications of biharmonic submanifolds of spher…
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type submanifolds was published in [40]. A detailed survey of the results, up to 1996, on t…
We review some recent results on the mean curvature flows of Lagrangian submanifolds from the perspective of geometric partial differential equations. These include global existence and convergence results, characterizations of first-time singularities, and constructions of self-similar solutions.
This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine learning, whose early development was so deeply influenced by two remarkable groups at …
Surveying recent work on Kähler metrics and algebraic variety stability.
problem Understanding canonical Kähler metrics on algebraic varieties.
method Analyzing recent developments in algebraic geometry.
result Relation between canonical Kähler metrics and stability in algebraic geometry.
Recent developments link Steklov eigenvalues to manifold geometry.
problem Steklov eigenvalues and eigenfunctions on compact Riemannian manifolds.
method Analytical and geometric approaches, including isoperimetric bounds, stability analysis, optimisation, and discretization.
result Connections between Steklov eigenvalues and manifold geometry, including optimisation and isospectrality.
The Novikov Conjecturemath.GT
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
The h-principle helps solve complex geometric problems.
problem Solving complex geometric problems using the h-principle.
method Developed from the Oka-Grauert principle and Gromov's theory, the h-principle is applied to Oka manifolds and maps.
result Recent developments and applications of the h-principle in complex analysis and geometry.
In recent years, there are many progress made in Kähler geometry. In particular, the topics related to the problems of the existence and uniqueness of extremal Kähler metrics, as well as obstructions to the existence of such metrics in general Kähler manifold. In this talk, we will report some recent developments in th…
RandNLA uses randomness for matrix problems in machine learning.
problem Matrix problems in machine learning.
method Randomized Numerical Linear Algebra.
result New challenges in RandNLA due to hardware trends and advances in ML.
This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results about symmetries of spatial graphs. In both cases we consider spatial graphs in as well as in other -manifolds.
In traditional generative modeling, good data representation is very often a base for a good machine learning model. It can be linked to good representations encoding more explanatory factors that are hidden in the original data. With the invention of Generative Adversarial Networks (GANs), a subclass of generative mod…
We review recent developments in the theory of Thompson group representations related to knot theory.
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative prop…
Survey on factor models and their applications in econometrics.
problem Estimating low-rank structures in high-dimensional models.
method Low-rank recovery techniques for factor model estimation.
result New insights into factor model applications in econometrics.
Survey of recent developments in symmetric reductions and controls for Hamiltonian systems.
problem Understanding the internal relationships of geometric structures and controls in Hamiltonian systems with symmetry.
method Survey and introduction of recent developments in controlled Hamiltonian systems with symmetry.
result Reveals the relationships between geometric structures, nonholonomic constraints, dynamical vector fields, and controls.
This contribution to the CPT'13 meeting briefly introduces Lorentz and CPT violation and outlines two recent developments in the field.
This paper overviews recent developments in the classification up to quasi-isometry of finitely generated groups, and more specifically of relatively hyperbolic groups.
We give an overview over the higher torsion invariants of Bismut-Lott, Igusa-Klein and Dwyer-Weiss-Williams, including some more or less recent developments.
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances of the blockmodel, such as non-assortative networks and overlapping communities. …
In this paper we survey the recent developments of the Ricci flows on complete noncompact Kähler manifolds and their applications in geometry.
Several rigidity problems in toric topology are addressed in \cite{ma-su08}. In this paper, we survey results on those problems including recent development.
We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.
This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)
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.
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, …
Algebraic integral geometrymath.DG
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
This survey starts with the historical landmarks leading to the study of principal configurations on surfaces, their structural stability and further generalizations. Here it is pointed out that in the work of Monge, 1796, are found elements of the qualitative theory of differential equations (QTDE), founded by Poincar…
In the lecture notes, the author will survey the development of conformal geometry on four dimensional manifolds. The topic she chooses is one on which she has been involved in the past twenty or more years: the study of the integral conformal invariants on 4-manifolds and geometric applications. The development was he…
With the availability of large databases and recent improvements in deep learning methodology, the performance of AI systems is reaching or even exceeding the human level on an increasing number of complex tasks. Impressive examples of this development can be found in domains such as image classification, sentiment ana…