Algebraic curves defined over finite fields have long been a rich source of enquiry, bridging abstract algebra, geometry and number theory. Their automorphism groups, which consist of self-symmetries ...
The study of curve arrangements in the framework of algebraic geometry examines configurations of algebraic curves—ranging from lines to higher degree entities—in projective spaces, where intricate ...
Algebraic geometry is a field that investigates the solutions of systems of polynomial equations and the geometric structures they define. At its core lies the study of algebraic varieties, whose ...
The study of algebraic structures and differential geometry has evolved into a dynamic interdisciplinary field that synthesises abstract algebraic concepts with the smooth variability of geometric ...
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 ...
Algebraic and differential geometry stand as two intertwined pillars of modern mathematics. Whereas algebraic geometry investigates the solution sets of polynomial equations using the refined language ...
K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to algebraic and geometric topology to operator algebras. The idea is to associate ...
The study of differential algebraic geometry and model theory occupies a pivotal position at the interface of algebra, geometry, and logic. Differential algebraic geometry investigates solution sets ...
Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.
Current Projects EXC 2044 - T01: K-Groups and cohomology K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to geometric topology to ...