Applications of Algebraic Combinatorics to Algebraic Geometry

Applications and Combinatorics in Algebraic Geometry

Algebraic Geometry is a deep and well-established field within pure mathematics that is increasingly finding applications outside of mathematics. These applications in turn are the source of new questions and challenges for the subject. Many applications flow from and contribute to the more combinatorial and computational parts of algebraic geometry, and this often involves real-number or posit...

Applicable Algebraic Geometry: Real Solutions, Applications, and Combinatorics

While algebraic geometry is concerned with basic questions about solutions to equations, its value to other disciplines is through concrete objects and computational tools, as applications require knowledge of specific geometric objects and explicit, often realnumber, solutions. Modern tools from computational algebraic geometry have great potential in applications, but their use requires a con...

Algebraic combinatorics

Algebraic algorithms and applications to geometry

Real algebraic numbers are the real numbers that are real roots of univariate polynomials with integer coefficients. We study exact algorithms, from a theoretical and an implementation point of view, that are based on integer arithmetic of arbitrary precision, for computations with real algebraic numbers and applications of these algorithms on problems and algorithms in non linear computational...

Categorically-algebraic topology and its applications

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...