Proseminar/Seminar on Number Theory: Geometry of Numbers
Niels Lindner
Additional information / Pre-requisites
Nötige Vorkenntnisse: Lineare Algebra und eine gewisse Vertrautheit mit den Grundbegriffen der Algebra, etwa "Gruppe", "Ring", "Körper", "Ideal", "Normalteiler", etc.
closeComments
This proseminar/seminar deals with Minkowski's "geometry of numbers", which does not only open up a geometric perspective on algebraic number theory, but also enables interesting applications in discrete geometry and combinatorial optimization. More precisely, we will dive into the following topics:
* Minkowski's classical convex body theorems
* Gaussian integers, Fermat's two-squares theorem, Legendre's four-squares theorem
* Algebraic number fields, finiteness of the class number, Dirichlet's unit theorem
* Linear equations over the integers: Hermite and Smith normal forms
* Basics of lattice theory
* Lattice basis reduction and the LLL algorithm
* The shortest vector problem
* Dense sphere packings
* Khinchine's flatness theorem
* Integer linear programming in fixed dimension
The purpose of this list is to offer a coarse thematic overview. The precise seminar topics will be fixed later, together with the participants.
Further information will be provided on the Whiteboard homepage of the seminar at the beginning of the lecture period.
close13 Class schedule
Regular appointments
More search results for 'Biochemie I - Grundlagen der Biochemie'