Algebraic and differential geometry stand as two intertwined pillars of modern mathematics. Whereas algebraic geometry investigates the solution sets of polynomial equations using the refined language ...

Syllabus: We will plan to cover approximately Chapter 2 and (time permitting) part of Chapter 3 of Hartshorne. For certain parts of the material, we will follow Vakil. Homework will consist of ...

The study of algebraic geometry encompasses the investigation of geometric structures defined by polynomial equations, with particular attention given to their intrinsic and extrinsic properties. A ...

In algebraic geometry one is often interested in having moduli spaces of objects in the sense that the objects are parameterized by the points in the moduli space. In many important cases these moduli ...

K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to algebraic and geometric topology to operator algebras. The idea is to associate ...

The drive to get every student to take so-called college gateway courses has succeeded, a new federal study finds, but students taking Algebra 1 and Geometry classes are getting considerably less ...