Related papers: Multidimensional L2 conjecture: a survey
We first give a complete, albeit brief, review of the discovery of mirror symmetry in $N=2$ string/conformal field theory. In particular, we describe the naturality arguments which led to the initial mirror symmetry conjectures and the…
Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is…
In this chapter, we survey some recent developments in the field of geophysical inversion. We aim to provide an accessible general introduction to the breadth of current research, rather than focussing in depth on particular topics. In…
Multi-object spectroscopy has been a key technique contributing to the current era of 'precision cosmology'. From the first exploratory surveys of the large-scale structure and evolution of the universe to the current generation of superbly…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
A review is given of recent research on two-dimensional gauge theories, with particular emphasis on the equivalence between these theories and certain string theories with a two-dimensional target space. Some related open problems are…
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
We prove the $l^2$ Decoupling Conjecture for compact hypersurfaces with positive definite second fundamental form and also for the cone. This has a wide range of important consequences. One of them is the validity of the Discrete…
This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this…
Several results about the union-closed sets conjecture are presented.
Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is…
In this paper we study the convergence of multiple Dirichlet L-series. In particular we give an integral representation of the series in the region of convergence by using Abel's summation formula. A certain generalized result is also…
This survey presents a comprehensive analysis of the phenomenon of hallucination in multimodal large language models (MLLMs), also known as Large Vision-Language Models (LVLMs), which have demonstrated significant advancements and…
I provide a summary of the theoretical talks in Hard Probes 2012 together with some personal thoughts about the present and the future of the field.
I review the recent theoretical progress towards the computation of jet observables at two loops in QCD.
This survey is on recent advancements in the intersection of physical modeling and machine learning. We focus on the modeling of nonlinear systems which are closer to electric motors. Survey on motor control and fault detection in operation…
We review recent developments in two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories focusing on the implementation and applications of localization techniques.
Cross-lingual alignment, the meaningful similarity of representations across languages in multilingual language models, has been an active field of research in recent years. We survey the literature of techniques to improve cross-lingual…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
This is a survey on spectral theory of dynamical systems.