Related papers: Real Algebraic Geometry, Positivity and Convexity
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…
This will is an expository description of quadratic rational maps. Sections 2 through 6 are concerned with the geometry and topology of such maps. Sections 7--10 survey of some topics from the dynamics of quadratic rational maps. There are…
These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.
The selection of topics in this text has formed the core of a one semester course in applied mathematics at the Arctic University of Norway that has been running continuously since the 1970s. The class has, during its existence, drawn…
Emphasis is on 2d target space (c=1 coupled to gravity). Contents: 0. Introduction, Overview, and Purpose 1. Loops and States in Conformal Field Theory 2. 2D Euclidean Quantum Gravity I: Path Integral Approach 3. Brief Review of the…
These notes are based on lectures given at the Erwin-Schrodinger Insitut in Vienna in 2006/07 and at the 2007 School on Attractor Mechanism in Frascati. Lecture I: special geometry from the superconformal point of view. Lecture II: black…
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…
Formulated problems concern the following topics: (1) Birationally nonequivalent linear actions; (2) Cayley degrees of simple algebraic groups; (3) Singularities of two-dimensional quotients.
In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
Special Relativity is taught to physics sophomores at Johns Hopkins University in a series of eight lectures. Lecture 1 covers the principle of relativity and the derivation of the Lorentz transform. Lecture 2 covers length contraction and…
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.
This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
Technology has helped to innovate in the teaching-learning process. Today's students are more demanding actors when it comes to the environment, they have at their disposal to learn, experiment and develop critical thinking. The area of…
The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…