The combined Barnard-Columbia Mathematics Department has 41 faculty (23 senior and 18 junior), 3 Post-Doctoral Fellows, and 55 PhD students. In addition, each year we have many short-term and long-term visitors.
The research activity in the department is centered around groups of faculty with common interests in a subfield of mathematics. The main subfields of activity are number theory, algebraic geometry, topology, geometric analysis, probability, and mathematical physics. Each of these subfields has at least one a weekly seminar for the faculty and PhD students in the area. The seminars form one of the main training grounds for the PhD students, and almost without exception, by the beginning of the third year of the PhD program students have chosen a group and are regularly attending the seminars of that group. The groups are fluid and faculty often are regular attentees in more than one of the seminars. There is much communication between members of different groups and as mathematical subfields and individual interests evolve there is a natural flow of faculty between the various groups.
The number theory group contains both algebraic and analytic number theory as well as arithmetic geometry. It naturally overlaps with the algebraic geometry group which contains both complex algebraic geometry and algebraic geometry over fields of positive characteristics. The topology group consists mainly of low dimensional topology, including hyperbolic geometry, and the study of the topology of complex algebraic varieties. The latter has an overlap with the algebraic geometry group. The geometric analysis group focuses on partial differential equations arising in geometry and physics, with a special concentration on evolution equations. The probability group has a strong representation in stochastic processes and theoretic Mathematical Finance. It overlaps with the geometric analysis groupLastly, the mathematical physics group is concerned with the interaction between mathematics and recent developments in high energy mathematical physics. This group overlaps with the topology group, the geometric analysis group, and the algebraic geometry group.
In addition to the regular seminars, the department has a host of special research activities each year. There is an Eilenberg Visiting Professor. This is a distinguished senior mathematician in residence for a semester giving a series of talks on a subject of interest to a wide variety of people in the department. Some years we have two such, each in residence for a semester. There are also the Ritt Lectures. This is a series of two lectures each semester given by a mathematician from outside the department and aimed at the general New York mathematical audience. There is also the Kolchin lecture which is one lecture of a similar nature.
