##### Introduction to Algebraic Number Theory and Arithmetic Geometry

** Speaker: Caleb McWhorter (Syracuse University) **

** Friday April 20, 2018, 1:00, Carnegie 109 **

Abstract: Algebraic Number Theory (ANT) brings together the tools of Group Theory, Field Theory (especially Galois Theory), Commutative Algebra, Analysis, and Representation Theory to answer questions in Number Theory. This talk will serve to introduce the audience to the major ideas of ANT leading into the development of Arithmetic Geometry. The talk will primarily focus on the ring of integers in a number field and its properties. The talk will be concrete, using explicit examples to motivate the big theorems. Depending on interest and time, topics may include: finiteness of class ideal groups, Dirichlet's Theorem, Chebotarev Density Theorem, Quadratic Reciprocity, elliptic curves, the Class Number Formula, or introductory notions of Class Field Theory. The talk will be generally accessible to anyone who has taken (or is in) MAT 632.