### MATH 5020: Topics in Algebra

**Description:** Advanced topics chosen from group theory, ring theory, number theory, Lie theory, combinatorics, commutative algebra, algebraic geometry, homological algebra, and representation theory. With change of content, this course may be repeated to a maximum of twelve credits.

**Prerequisites:** MATH 5211.

**Credits:** 3

### MATH 5020 - Section 1: Class Field Theory

**Description:** Class field theory is the study of the abelian extensions of arbitrary global or local fields. It is prerequisite for most any kind of research in algebraic number theory. In the course, facility with Galois theory will be assumed.

**Offered:** Fall

**Credits:** 3

### MATH 5020 - Section 2: Introduction to Algebraic Geometry

**Description:** Algebraic geometry is an area of mathematics with deep connections to other areas: number theory, commutative algebra, complex and differential geometry, combinatorics, physics, statistics and engineering. Hence some working knowledge of algebraic geometry is useful in many different contexts.
We will introduce basic concepts in algebraic geometry, such as affine and projective varieties, the Zariski tangent space, the Hilbert polynomial, rational maps, divisors, line bundles and maps to projective spaces. We will finish with the Riemann-Roch theorem for curves. Concepts will be illustrated with many examples, such as projective spaces, Grassmannians, the Segre and Veronese embeddings, and blow-ups.

**Offered:** Fall

**Credits:** 3

**Sections: **Fall 2009 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

08023 | 5020 | 001 | Lecture | MWF 1:00-1:50 | MSB307 | Lee, Kyu-Hwan |

14013 | 5020 | 002 | Lecture | TuTh 12:30-1:45 | MSB117 | Milena Hering |