Let $\Sigma$ be a finite type surface, and $G$ complex algebraic simple Lie group with algebra $\mathfrak{g}$. The quantum moduli of $(\Sigma,G)$ is quantization the ring functions $X_G(\Sigma)$, variety $G$-characters $\pi_1(\Sigma)$, introduced by Alekseev-Grosse-Schomerus Buffenoir-Roche in mid '90s. It can realized as invariant subalgebra so-called graph algebras, which are $U_q(\mathfrak{g...

Elimination is a basic algebraic operation which geometrically corresponds to projections. This article describes using the numerical algebraic geometric concept of witness sets to compute the projection of an algebraic set. The ideas described in this article apply to computing the image of an algebraic set under any linear map.

The primary intent of the present paper is to adapt familiar notions of algebraic topology, such as the fundamental group, homology, and cohomology to the context of algebraic maps and their (ramified) covering projections. The notion of a principal derived map is already fairly well understood in terms of the defining voltages; however, once it is recognized that voltages are essentially cohom...

This paper outlines the formal representation of the environment in which it is assumed that a wayfinding process has been occurred through a street network. Wayfinding is a process in which people navigate themselves from an origin to a destination by their common sense geospatial knowledge. Naı̈ve Geography is a field of study that investigates the body of knowledge that people have about the ...

The present paper discusses the results of a research project going on at Politecnico di Milano, aiming at analysing the idiosyncrasies of Six Sigma implementations in Italian companies. In particular, the project addresses the following research questions, regarding the approach of Italian companies towards Six Sigma: are Italian companies implementing Six Sigma exactly as it was originally co...

Let $\bigwedge_\sigma V=\bigoplus_{k\geq 0}\bigwedge_\sigma^kV$ be the quantum exterior algebra associated to a finite-dimensional braided vector space $(V,\sigma)$. For an $\mathfrak{A}$, we consider convolution product on graded $\bigoplus_{k\geq 0}\mathrm{Hom}\big(\bigwedge_\sigma^kV,\bigwedge_\sigma^kV\otimes \mathfrak{A}\big)$. Using this product, define notion of minor determinant map fro...

We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let Z be a real algebraic variety. We say that Z is generic if there exist a finite family {Di}i=1 of irreducible real algebraic curves with genus ≥ 2 and a biregular embedding of Z into the product variety Qn i=1 Di. A bijective map φ : e Z −→ Z from a real algebraic variety e Z to...