Algebraic Geometry is the study of the geometry of the zero set of polynomial equations. In the modern language, such zero sets are known as affine or projective varieties or more generally schemes. The general principles of algebraic geometry have deep connections to other branches of mathematics like number theory or even in physics. The algebraic geometers at OSU have broad research interests, which include projective techniques in algebraic geometry, syzygies of algebraic varieties, enumerative geometry, moduli spaces, birational geometry, Schubert varieties and arithmetic geometry.

The commutative algebra group at OSU studies ideals in polynomial rings over a field. We are especially interested in combinatorial commutative algebra, a relatively new area in which researchers use tools from combinatorics to answer questions in algebra and vice versa. Our work often focuses on monomial ideals, articularly understanding their free resolutions.

Lie theory originated from an attempt to use continuous groups of symmetries to study differential equations. The subject now plays an important role in many areas of mathematics, such as mathematical physics, number theory and geometry. Members of OSU math department study Lie theory as it relates to invariant theory, symmetries in systems of differential equations and automorphic forms. Several OSU researchers investigate the structure and invariants of representations of semisimple Lie groups through computational and geometric methods.