### 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: Tate's Thesis

**Description:** In number theory, the Riemann zeta-function and its various generalizations (e.g., Dirichlet L-functions) occupy a central role. These functions are at first defined only for complex numbers with real part greater than 1, but techniques from Fourier analysis can be used to establish an analytic continuation of many of these functions to the whole complex plane. John Tate, in his Ph.D. thesis, showed how to rederive the analytic continuation (and other properties) by methods of abstract harmonic analysis using integration on real and p-adic groups. The methods introduced in Tate's thesis have become an important paradigm in number theory and will be the subject of this course.

**Prerequisites:** MATH 5210 as well as the material taught in Fall 2011 in Math 5020 (number theory) and 5141 (harmonic analysis).

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2012 on Storrs Campus

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

20590 | 5020 | 001 | Lecture | MW 3:00:00 PM-4:15:00 PM | MSB219 | Conrad, Keith |