Caput Algebra and Geometry (21/22)

Faculteit Science and Engineering
Jaar 2021/22
Vakcode WMMA028-05
Vaknaam Caput Algebra and Geometry (21/22)
Niveau(s) master
Voertaal Engels
Periode semester I b
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Caput Algebra & Geometry (21/22)
Leerdoelen The student is able to
1. apply the bachelor's topics treated in abstract algebra in more advanced examples relevant to the course in question.
2. apply the theory presented in the course in concrete examples.
Omschrijving The subject of the course varies with the national Mastermath program.
This course intends to bridge the gap between the algebra taught in our bachelor program (Group Theory, Rings, (Finite) Fields, Modules), and various courses in Algebra and Geometry offered regularly in the national Mastermath program.

21/2022: Algebraic Curves.
We will study the (algebraic) geometry of algebraic curves, i.e., one dimensional algebraic varieties. In particular, we will give a brief introduction to affine and projective varieties, rational maps and function fields. We will also cover local properties of algebraic curves, smoothness, intersection theory, divisors and their linear spaces (Riemann-Roch theorem).

In previous years, the following topics were discussed:
20/21: Representation theory of finite groups
19/20: Theory of Complex Multiplication
18/19: Computational algebraic number theory
17/18: The arithmetic of hyperelliptic curves
16/17: Galois Theory and applications
15/16: J-P. Serre's book "A Course in Arithmetic".
2014/15 Representation Theory of Finite Groups
2013/14 Galois and Differential Galois Theory
2012/13 Algebraic structures of differential calculus in (non)commutative geometry.
2011/12 Group methods in the geometry of differential equations
2010/11 Galois correspondence
2009/10 Commutative Algebra
2008/09 Arithmetic of elliptic curves
2007/08 Algebraic geometry: cubic surfaces
2006/07 Representation Theory of Finite Groups
2005/06 Galois and Differential Galois Theory
Uren per week
Onderwijsvorm Hoorcollege (LC)
(Depending on the number of participants, the course is given as a series of lectures or as a seminar in which the participants each prepare and present a chapter from a chosen textbook.)
Toetsvorm Mondeling tentamen (OR)
(Final grade is based on the answers of a homework set and the ability to discuss these during the oral examination.)
Vaksoort master
Coördinator prof. dr. C. Salgado Guimarães da Silva
Docent(en) O. Lorscheid, PhD. ,prof. dr. C. Salgado Guimarães da Silva ,prof. dr. J. Top
Verplichte literatuur
Titel Auteur ISBN Prijs
Lecture Notes on plane algebraic curves (available online) Andreas Gathmann
Algebraic curves (available online) William Fulton
Entreevoorwaarden Linear Algebra, Group Theory, and Algebraic Structures are required.
Opmerkingen The course unit prepares students for various mastermath courses in which the learning objectives attained are required as prior knowledge.

Students are encouraged to attend and participate in the lectures.
If you need to miss some classes, please inform the course coordinator.
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