Related papers: Course of linear algebra and multidimensional geom…
Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…
We present a systematic introduction to the geometry of linear braided spaces. These are versions of $\R^n$ in which the coordinates $x_i$ have braid-statistics described by an R-matrix. From this starting point we survey the author's…
We present a geometrical interpretation of linear regression based on vectors in n dimensions (n the number of data points). This is to be used as a didactic tool for teachers when presenting that topic.
In the Tutor Allocation Problem, the objective is to assign a set of tutors to a set of workshops in order to maximize tutors' preferences. The problem is solved every year by many universities, each having its own specific set of…
One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…
We study the transcendence of periods of abelian differentials, both at the arithmetic and functional level, from the point of view of the natural bi-algebraic structure on strata of abelian differentials. We characterise geometrically the…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
These lectures were a part of the geometry course held during the Fall 2011 Mathematics Advanced Study Semesters (MASS) Program at Penn State (\url{http://www.math.psu.edu/mass/}). The lectures are meant to be accessible to advanced…
In this paper, some real-world motivated examples are provided illustrating the power of linear algebra tools as the product of matrices, determinants, eigenvalues and eigenvectors. In this sense, some practical applications related to…
Awfully idiosyncratic lecture notes from CMI summer school in arithmetic geometry July 31-August 4, 2006. Does not include: rationality problems, techniques of the minimal model problem and much of the rest. Includes: Lecture 0: geometry…
Linear systems often involve, as a basic building block, solutions of equations of the form \begin{align*} A_Sx_S&+A_Px_P =0\\ A'_Sx_S & =0, \end{align*} where our primary interest might be in the vector variable $x_P.$ Usually, neither…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
Complex geometry represents a fundamental ingredient in the formulation of the Dirac equation by the Clifford algebra. The choice of appropriate complex geometries is strictly related to the geometric interpretation of the complex imaginary…
The nineteenth century was an important period for both Oxford mathematics and algebra in general. While there is extensive documentation of mathematical research in Oxford at this time, the same cannot be said of the teaching. The content…
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…
In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.
This text is an introduction to algebraic enumerative geometry and to applications of tropical geometry to classical geometry, based on a course given during the X-UPS mathematical days, 2008 May 14th and 15th. The aim of this text is to be…