Next Talk:

28.09.10, What is... Arithmetic Geometry?, Thomas Preu, Universität Zürich (Zürich)

KO2F150, 17.15-18.30

Arithmetic geometry is the study of problems from number theory (with an algebraic flavour) by means of (algebraic) geometry. In the talk I will introduce the basic problem of this subject, then give some background on the fruitful interaction between geometry, algebra and number theory, before explaining one of the mile stone theorems of the field, the classification of arithmetic behavior (wrt. the rationals) of curves. I will only assume familiarity with basic algebra, projective space and the definition of complex analytic manifolds. Finally I will dwell a little bit on algorithmic aspects in the last quarter of my talk, where I will use p-adic numbers casually. Knowledge of "schemes" is not required, although I will mention them for the experts. Here are some hand written notes which also include some remarks on Brauer-Manin obstruction.

List of talks HS 10

Date	Title	Speaker
28.09.10	What is... Arithmetic Geometry?	Thomas Preu Universität Zürich (Zürich)
05.10.10	What is...a Modular Form?	Jonas Jermann ETHZ (Zürich)
19.10.10	What is...Applied Mathematics?	( )
02.11.10	What is...Causality?	Alain Hauser ETHZ (Zürich)
16.11.10	What is...Causality?	Alain Hauser ETHZ (Zürich)
30.11.10	What is... Tropical Geometry?	Cesar Ceballos Technische Universität Berlin (Berlin)
14.12.10	What is... a Random Polymer Model?	Alessandra Cipriani Universität Zürich (Zürich)
21.12.10	What is... Categorification?	Maria Hempel Universität Zürich (Zürich)