Vol. 1, Issue 7, Part N (2015)

Abstract
Algebraic Geometry is the study of sets of common zeros of a family of polynomials. Such a set is called an algebraic variety. Some geometers at LSU work mostly over the complex numbers. Some work mostly over the real numbers, where one studies semi-algebraic sets whose points satisfy polynomial inequalities. Some work over finite fields, where there are connections with algebraic number theory and applications to areas such as error-correcting codes. Arithmetic algebraic geometry, the study of algebraic varieties over number fields, is also represented at LSU. The tools in this specialty include techniques from analysis and computational number theory. In all these facets of algebraic geometry, the main focus is the interplay between the geometry and the algebra. For example, to each point of an algebraic variety one can associate a ring and the question of whether this point is a smooth point or a singular point on this variety can be answered by understanding the algebraic structure of this ring.