Algebraic curves and polynomial systems form a cornerstone of modern computational and theoretical mathematics. These structures are defined by polynomial equations and exhibit rich geometric and ...

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of the recent work by ...

Let K[x,y] be the polynomial algebra in two variables over a field K of characteristic 0. A subalgebra Rof K[x,y] is called a retract if there is an idempotent homomorphism (a retraction, or ...