Related papers: Lecture notes on differential calculus on RCD spac…
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete…
The aim of these notes is to give a introduction to the ideas and techniques of handling rational curves on varieties. The main emphasis is on varieties with many rational curves which are the higher dimensional analogs of rational curves…
Room acoustics is commonly regarded and studied as an applied subdiscipline of engineering acoustics. It is likely for this reason that many textbooks and lecture notes on the topic provide a too brief, unsystematic, and incomplete physical…
We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…
Recent research has led to the development of MCMC algorithms with likelihood-informed proposals when targeting posterior distributions supported on discrete state spaces. Our work is placed within this field and puts forward a new MCMC…
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical…
Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…
The past decade has witnessed two important new developments in the study of linear series on algebraic varieties. First, vector bundles have emerged as powerful tools for analyzing linear series on curves and surfaces. More recently, the…
The previous decade has brought a remarkable increase of the interest in applications that deal with querying and mining of time series data. Many of the research efforts in this context have focused on introducing new representation…
These are lecture notes on the rigidity of submanifolds of projective space "resembling" compact Hermitian symmetric spaces in their homogeneous embeddings. Recent results are surveyed, along with their classical predecessors. The notes…
This paper gives a short introduction into the metric theory of spaces with dilations.
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…
These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…
Distance metric learning has attracted much attention in recent years, where the goal is to learn a distance metric based on user feedback. Conventional approaches to metric learning mainly focus on learning the Mahalanobis distance metric…
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future…
Deep metric learning papers from the past four years have consistently claimed great advances in accuracy, often more than doubling the performance of decade-old methods. In this paper, we take a closer look at the field to see if this is…
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
These Lecture notes give an introduction to Regge calculus as a discrete model of General Relativity.
These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.