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Algebraic Geometry      The algebraic side of algebraic geometry
addresses the study of varieties and schemes, both over the
field of complex numbers and other fields. Schemes also provide
a link with algebraic number theory. Members of this group are
interested in connections with representation theory, with
arithmetic algebraic geometry, and with complex algebraic
geometry.      Commutative Algebra      One important role of
commutative algebra is in the foundations of algebraic geometry,
through rings of functions on a variety, and generalizations,
incorporating nilpotent elements, and also sheaves of rings
lying over such a variety (or scheme). Other issues in
commutative algebra, such as factorization, also directly relate
to number theory. Members of this group study these issues and
others, such as the structure of commutative rings.
Representation Theory      Groups arise as sets of symmetries of
various structures, perhaps geometric, or