Caput Algebra and Geometry (21/22)

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.
Opgenomen in	Opleiding Jaar Periode Type MSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I b MSc Mathematics and Physics (double degree)  (Mathematics and Complex Dynamical Systems (50 ects)) - semester I b keuzegroep MSc Mathematics: Mathematics and Complex Dynamical Systems - semester I b keuzegroep MSc Mathematics: Science, Business and Policy  (Science, Business and Policy: Mathematics and Complex Dynamical Systems) - semester I b keuzegroep Tweejaarlijkse vakken  (Oneven jaren) - semester I b -