Survey of recent austere submanifold results.
problem Understanding austere submanifolds.
method Review of existing papers [24,25].
result Recent progress in the field of austere submanifolds.
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.
168,742 papers · 148 categories
Trend · papers per month
48 results for “recentering”
Survey on new Ricci flow techniques.
problem None explicitly stated.
method None explicitly stated.
result None explicitly stated.
Higgs bundles used in new applications.
problem None explicitly stated in the abstract.
method Overview of recent applications.
result Applications of Higgs bundles.
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…
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.
Survey of recent Kleinian representation convergence results.
problem Kleinian representation convergence
method Survey and analysis of recent results following Thurston's theorems
result Survey of recent and less recent results on convergence of Kleinian representations
Review of recent G₂-structures on 7D manifolds.
problem Constructing examples of closed G₂-structures.
method Discussion of recent results and examples.
result Review of recent findings on G₂-structures.
This is a mainly expository article honoring my recently deceased friend and collaborator Krzysztof Galicki who died after a tragic hiking accident. I give a review of our recent work in Sasakian geometry. A few new results are also presented.
Survey of recent scalar curvature results on open 3-manifolds.
problem None explicitly stated; focuses on recent results.
method Survey and review of existing research.
result Recent findings on scalar curvature in open 3-manifolds.
Survey of recent developments in racks and quandles.
problem Understanding recent advancements in algebraic theory of racks and quandles.
method Report on representation theory of quandles and ring theoretic approach.
result Presentation of recent elements in quandle theory.
Recent developments in Seiberg-Witten theory and relations with Complex Geometry.
Survey of recent progress in Sasakian geometry.
problem Topological properties and existence of Sasakian structures.
method Review of recent research findings.
result Recent progress in Sasakian geometry.
Weil-Petersson perspectivesmath.DG
We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichmüller spaces. For recent progress on and the understanding of infinite dimensional Teichmüller spaces the reader is directed to the recent work of Teo-Takhtajan. As part of the highlight, we also present possible…
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
A concise review of recent few-shot meta-learning methods.
problem Mimicking human fast adaptation to new concepts based on prior knowledge.
method Categorized into four branches based on technical characteristics.
result Current challenges and future prospects identified.
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…
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.
Until recently, research on artificial neural networks was largely restricted to systems with only two types of variable: Neural activities that represent the current or recent input and weights that learn to capture regularities among inputs, outputs and payoffs. There is no good reason for this restriction. Synapses …
We give a short review of recent progress on the positive energy theorem in general relativity, especially for spacetimes with nonzero cosmological constant.
Counterexample disproves recent Penrose conjecture variant.
problem A variant of the Penrose conjecture.
method Provided a counterexample.
result The conjectured variant of the Penrose inequality is false.
In this note we give an overview of some of our recent work on Anosov representations of discrete groups into higher rank semisimple Lie groups.
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.
Interactive Machine Learning (IML) is an iterative learning process that tightly couples a human with a machine learner, which is widely used by researchers and practitioners to effectively solve a wide variety of real-world application problems. Although recent years have witnessed the proliferation of IML in the fiel…
The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.
The recent, remarkable growth of machine learning has led to intense interest in the privacy of the data on which machine learning relies, and to new techniques for preserving privacy. However, older ideas about privacy may well remain valid and useful. This note reviews two recent works on privacy in the light of the …
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.
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.
By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.
Some recent work in Frechet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Frechet manifolds that could be represented as projective limits of Banach manifolds. This led to …
Intro to Poisson geometry, focusing on basics and recent tools.
problem Understanding Poisson structures and their applications.
method Exercises leading to conclusions on foundational and recent topics.
result Introduction to Poisson geometry basics and recent developments.
This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.
Simplified proof of a recent inequality for closed hypersurfaces.
problem Proving an inequality for closed hypersurfaces in manifolds with nonnegative Ricci curvature.
method Simple proof of a recent result by Agostiniani, Fogagnolo, and Mazzieri.
result A simplified proof of the inequality for closed hypersurfaces.
This paper reviews recent advances in Gaussian process regression methods.
problem Handling uncertainties and scalability in large-scale systems with sparse data.
method Factorised Gaussian process methods, including hierarchical off-diagonal low-rank approximation and GP with Kronecker structures.
result These methods provide scalable solutions with inherent uncertainty assessment.
Survey of recent results on homogeneous finite-dimensional spaces.
problem Understanding properties of homogeneous finite-dimensional spaces.
method Discussion of recent results and unsolved problems.
result Discussion of recent results and unsolved problems.
Mondino and Naber recently proved that finite dimensional spaces are rectifiable. Here we show that the push-forward of the reference measure under the charts built by them is absolutely continuous with respect to the Lebesgue measure. This result, read in conjunction with another recent work of us, has relev…
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.
Ricci solitons are natural generalizations of Einstein metrics. They are also special solutions to Hamilton's Ricci flow and play important roles in the singularity study of the Ricci flow. In this paper, we survey some of the recent progress on Ricci solitons.
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We first present a series of new regret guarantees that hold at any time and under …
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.
Survey of algebraic structures for singular knots.
problem Invariants of singular knots using quandle-like structures.
method Exploration of singquandles, psyquandles, and their invariants.
result Enhancements to the singquandle counting invariant and new polynomial invariants.
Summarizes key algorithmic trading problems and recent advances.
problem Optimal execution, placement, and price impact in algorithmic trading.
method Discusses recent advances in algorithmic trading using Machine Learning techniques.
result Recent progress in algorithmic trading includes the use of Deep Learning, Reinforcement Learning, and Generative Adversarial Networks.
Surveying recent progress on flows of -structures on 7-manifolds.
problem Preserving metrics while modifying -structures on 7-manifolds.
method Heat flows and other approaches in terms of -forms, octonions, vector fields, and geometric structures.
result Comparison of different perspectives on -structure flows.
Researchers prove mirror symmetry for certain non-compact Calabi-Yau surfaces.
problem Proving mirror symmetry for non-compact Calabi-Yau surfaces.
method Surveying recent works on Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del Pezzo surfaces.
result All gravitational instantons can be compactified to weak del Pezzo surfaces.
We review recent probabilistic results on covariant Schrödinger operators on vector bundles over (possibly locally infinite) weighted graphs, and explain applications like semiclassical limits. We also clarify the relationship between these results and their formal analogues on smooth (possibly noncompact) Riemannian m…
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.
Abstract reviews recent Lagrangian analysis on immersions into higher dimensions.
problem Analyzing Lagrangians on immersions into higher dimensions.
method Reviews recent progress on Lagrangians on immersions with first and second fundamental forms and their derivatives.
result Recent progress in the analysis of Lagrangians on immersions into higher dimensions.