The Algebra and Geometry group at OSU studies purely algebraic questions as well as problems from geometry and other areas of mathematics using algebraic techniques. The foundation of the intersection between algebra and geometry is finding solutions to polynomial equations and understanding the geometry associated to those solutions. This intersection has evolved to give applications in many fields, including physics, biology, and statistics, and researchers in algebra and geometry use techniques from a wide range of areas of mathematics. Methods vary from powerful abstract approaches using category theory to more concrete and computational tools, including doing experiments with computer algebra systems. In the current research of faculty in the Algebra and Geometry group at OSU, the breadth of algebra and geometry is apparent.