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This works deals with the formal mathematical structure of so called Grassmann Numbers applied to Theoretical Physics, which is a basic concept on Berezin integration. To achieve this purpose we make use of some constructions from relative…
This is a brief review of my work on the correspondence between four-dimensional $\mathcal{N} = 1$ supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
We propose a theory of the dynamics of polymers in dilute solution, in which the popular Zimm and Rouse models are limiting cases of infinitely large and small draining parameter. The equation of motion for the polymer segments beads) is…
Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.
In a recent article on stretched polymers in a poor solvent by Grassberger and Hsu \cite{grassberger2002a-a} questions were raised as to the conclusions that can be drawn from currently proposed scaling theory for a single polymer in…
A small amount of polymer additives can cause substantial reduction in the energy dissipation and friction loss of turbulent flow. The problem of polymer-induced drag reduction has attracted continuous attention over the seven decades since…
We review the achievements of the theory of polarization bremsstrahlung of relativistic particles, including the case when both colliders have internal structure. The main features which the relativistic effects bring into the problem are…
We discuss the numerical implementation of two related representations of fermionic density matrices which have been introduced in Annals of Physics 370, 12 (2016). In both of them, the density matrix is expanded in a basis of Bargmann…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…
In this article, we derived some consequences to the symmetrization process developed in \cite{Deng23}. This consists a geometric derivation of part of the properties which uniquely determines the Kazhdan-Lusztig polynomials of type $A_n$…
The purpose of this paper is to provide a both comprehensive and summarizing account on recent results about analysis and geometry on configuration spaces $\Gamma_X$ over Riemannian manifolds $X$. Particular emphasis is given to a complete…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.
We study different representation theorems for various reducts of Heyting polyadic algebras. Superamalgamation is proved for several (natural reducts) and our results are compared to the finitizability problem in classical algebraic logic…
We use the method of dimensional reduction to show that a branching polymer with excluded volume interaction confined between two flat plates has, in the thermodynamic limit, a confinement free energy and density profile that is the same as…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
This manuscript treats the diverse applications of bricks within modern representation theory and several related domains, and reviews the recent developments and new results on bricks (a.k.a Schur representations). The current survey is an…