# Algebra and Algebraic Geometry

Algebra studies structures such as groups or rings that are ubiquitous in all branches of mathematics ranging from complex analysis to topology, number theory to algebraic statistics, and representation theory to string theory. Algebraic geometry, which studies solutions of polynomial systems, and commutative algebra, which studies rings that are the building blocks of algebraic and arithmetic geometry, are two prominent subspecialties of algebra. Research in these areas has underpinned most of the major developments in mathematics since the 19th century and continues to drive cutting edge advances. The research group in MSCS represents a wide-array of specialties in algebraic geometry and commutative algebra and has particular interests in Hodge theory, moduli spaces, birational geometry, syzygies, characteristic p techniques and perfectoid geometry.