Algebraic Geometry

The UC Berkeley Department of Mathematics has a deep tradition in algebraic geometry and commutative algebra, spanning computational algebraic geometry, arithmetic algebraic geometry, and algebraic stacks, making it a core center for algebraic geometry research.

The University of Cambridge Faculty of Mathematics maintains an active research tradition in algebraic geometry, spanning complex algebraic geometry, Calabi–Yau manifolds, mirror symmetry, and enumerative geometry, making it a leading center at the intersection of algebraic geometry and mathematical physics.

The Columbia University Department of Mathematics has a deep tradition in algebraic geometry and moduli space theory, spanning algebraic stacks, hyperkähler manifolds, and Brill–Noether-type problems, making it a leading center for algebraic geometry research.

The Harvard University Department of Mathematics maintains an active research tradition in algebraic geometry, spanning derived categories, vanishing theorems, complex algebraic geometry, and mirror symmetry, making it a leading center at the intersection of algebraic geometry and geometric analysis.

The MIT Department of Mathematics maintains an active research tradition in algebraic geometry and geometric representation theory, spanning D-modules, character sheaves, symplectic geometry, and their interplay with algebraic varieties, making it a leading center for geometric representation theory.

The Oxford Mathematical Institute maintains an active research tradition in algebraic geometry, spanning geometric invariant theory, moduli spaces, Donaldson–Thomas invariants, and calibrated submanifolds, making it a leading center at the intersection of algebraic geometry and differential geometry.

The Princeton University Department of Mathematics has a deep tradition in algebraic geometry, holding a world-leading position in birational geometry and the higher-dimensional Minimal Model Program, making it a core center for the classification of algebraic varieties.

The Stanford University Department of Mathematics maintains an active research tradition in algebraic geometry, spanning the Minimal Model Program, moduli spaces, Gromov–Witten theory, and Brill–Noether theory, making it a leading center at the intersection of algebraic geometry and enumerative geometry.

The UCLA Department of Mathematics maintains an active research tradition in algebraic geometry, spanning birational geometry, the Minimal Model Program, rationality of algebraic varieties, and the period-index problem, making it a leading center for algebraic geometry research.

The Yale University Department of Mathematics maintains an active research tradition in algebraic geometry and geometric representation theory, spanning the geometric Langlands program, D-modules, motivic cohomology, and cluster algebras, making it a leading center at the intersection of algebraic geometry and representation theory.