Related papers: Scale Calculus and M-Polyfolds -- An Introduction
The $M$-polynomial was introduced by Deutsch and Klav\v{z}ar in 2015 as a graph polynomial to provide an easy way to find closed formulas of degree-based topological indices, which are used to predict physical, chemical, and pharmacological…
The M-polynomial provides a unifying framework for a wide class of degree-based topological indices. Despite its structural importance, general methods for computing the M-polynomial under graph constructions remain limited. In this paper,…
These are the notes from my courses on the arithmetic of quadratic forms.
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a paper together, and I refereed an…
The plenary lectures, parallel talks, oral presentations and panel contributions on Cosmology and Gravitation presented during the XXII Brazilian National Meeting on Particles and Fields are briefly reviewed. Some remarks on the area are…
We give a preliminary discussion of how the addition of extra coordinates in M-theory, which together with the original ones parametrise a U-fold, can serve as a tool for formulating brane dynamics with manifest U-duality. The redundant…
These lecture notes where presented as a course of the CIMPA summer school in Manila, July 20-30, 2009, Semidefinite programming in algebraic combinatorics. This version is an update June 2010.
In this paper the authors discuss their experiences with ungrading at a small public university in the U.S. as well as a large public university in Germany. The courses described are Calculus 1, Mathematics for Liberal Arts, and courses for…
These lecture notes introduce conifold transitions between complex threefolds with trivial canonical bundle from the differential geometric point of view, and with a particular view towards aspects of mathematical physics and string theory.…
These are lecture notes from a mini-course taught at Winterbraids XIII (Montpellier, 2024). The main character of these notes are curves in the complex projective plane, viewed from a topological perspective.
This evocative essay focuses on mathematical activities witnessed by the author along 1962-64 at IMPA. The list of research problems proposed in September 1962 by Mauricio Peixoto at the Seminar on the Qualitative Theory of Differential…
A degree of a module $M$ is a numerical measure of information carried by $M$. We highlight some of Vasconcelos' outstanding contributions to the theory of degrees, bridging commutative algebra and computational algebra. We present several…
We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.
These lectures on the combinatorics and geometry of 0/1-polytopes are meant as an \emph{introduction} and \emph{invitation}. Rather than heading for an extensive survey on 0/1-polytopes I present some interesting aspects of these objects;…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
These notes have been written to complete a mini-course "Introduction to (generalized) Gibbs measures" given at the universities UFMG (Universidade Federal de Minas Gerais, Belo Horizonte, Brasil) and UFRGS (Universidade Federal do Rio…
$\lambda$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as…
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…