Research groups

Research Related links: Department people, UR Math Physics Page

Algebra and Number Theory

The department has groups in algebraic geometry and number theory. Within number theory, Rochester has specialists in both analytic and algebraic number theory. These areas are among the oldest in mathematics, but are still a source of vital ideas.

Analysis

Analysis is one of the oldest and broadest areas of mathematics. The department has groups in differential equations and Fourier analysis.

Geometry

Geometry has been one of the most popular fields of mathematics in recent decades. The department has a group in differential geometry.

Mathematical Physics and Probability

Mathematics has always had a fruitful interaction with physics, from classical mechanics to quantum field theory. Newton created calculus to be the foundation for his physical theories. In recent years, string theory has stimulated a huge amount of mathematical work, and led to new mathematical ideas. Probability has strong ties to statistical physics, as well as other areas such as biology, economics, and engineering. Ideas from such applications have led to an enormous growth in probability. Both probability and mathematical physics are among the most active fields of mathematics.

Topology

The 20th century has been called the century of topology. General topology now forms one of the foundations of modern analysis and geometry. The development of algebraic topology led to the development of many of the key concepts of algebra: homological algebra, category theory, Lie groups/algebras and K-theory among them. The use of cobordism invariants and intersection theory developed in differential topology form the foundations for invariants such as the Seiberg-Witten invariants and Gromov-Witten invariants so important in current day geometry. Today topology continues to flourish as a pure endeavor. Symplectic topology and Voevodsky's recent introduction of the techniques of homotopy theory into algebraic geometry are among some examples. In addition, there are growing connections with theoretical physics, dynamical systems, computer science and DNA biology. The Rochester topology group specializes in algebraic topology, primarily homotopy theory and does significant active research in this area.