**Iwasawa Theory**

Dr. R. Taleb

Course Description: Iwasawa theory concerns the growth of the arithmetic objects, e.g. class groups, elliptic curves, abelian variety, motives, etc., over infinite towers of number fields. The aim of this course is an introduction to the basic concepts and ideas of this theory, mainly in the class group case and – if time permits – in the elliptic curve case. More precisely, we intend to describe some algebraic concepts, e.g. Iwasawa modules and some Galois groups as their examples, and also some important theorems and conjectures, e.g. Iwasawa theorem on the growth of class numbers, Leopoldt’s conjecture, µ- invariant conjecture, Greenberg conjecture, in this theory. Then, after explaining the fundamental analytic objects of this theory, i.e. p-adic L-functions attached to number fields, we can formulate the main conjecture of Iwasawa theory and discuss about it. Having some background on algebraic number theory would be helpful for this course. However, we try to make a short review of necessary tools in the first one or two sessions.

**Modular Forms**

Dr. K. Monsef

**Elliptic Curves**

**R**

**epresentation Theory Of Algebraic**

**Groups**

Dr. A. Jafari

Place: IPM, Niavaran Building

Date and Time: Thursdays, 09:00-10:30 and 12:30-14:00