Sommersemester 2003
Vorlesungsankündigung
Franz Winkler
Kommutative Algebra und Algebraische Geometrie (326.212)
VL Zeit und Ort: Di 13:45-15:15 in P004, Fr 12:00-13:30 in T711
UE Zeit und Ort: Di 15:30-16:15 in KG416
erste VL: 11.3.2003
  Algebraic geometry is an old and intensively studied area of mathematics. It is concerned with geometric objects which can be described as the zero locus of polynomial equations, i.e. algebraic curves, surfaces, and varieties in higher dimension. Nowadays such algebraic curves and surfaces are of high importance in computer aided geometric design, computer vision, cryptography, and other application areas.   The algebraic theory which allows us to compute with such algebraic varieties is the theory of polynomials or commutative algebra. Polynomial ideals, radicals, polynomial and rational functions and mappings and the like lend themselves to computational methods from computer algebra.   In this course we will examine the relation between the algebraic theory of polynomial ideals and the geometry of curves, surfaces, and algebraic varieties.   Participants are expected to be acquainted with basics in (computer) algebra.   In the exercise session (Übungen) the students will have to solve both theoretical and practical problems with the help of some computer algebra system.  
   
Projektseminar (SS): Computeralgebra (326.812)
  Zeit: Do 14.30 - 16.00, Ort: Hagenberg
Erste Veranstaltung: 6.3.2002
    In diesem Seminar tragen Diplomanden und Dissertanten über ihre Ergebnisse vor, und wir lesen und diskutieren neue Literatur zum Thema Computer-Algebra und konstruktive algebraische Geometrie. Künftige Diplomanden sollten am Seminar teilnehmen.    
  Literaturseminar Computer-Algebra II (326.756)
 
  Time and place according to agreement
    Short description: We read and discuss recent publications in computer algebra.  
  Programmierprojekt Computer-Algebra II (326.762)
  Time and place according to agreement
    Short description: Implementation of algorithms in computer algebra and constructive algebraic geometry.
  Projektpraktikum Computermathematik (326.792)
  Time and place according to agreement
    Short description: Implementation of algorithms in computer algebra and constructive algebraic geometry for students of Informatik.  
  Diplomanden- und Dissertantenseminar II (326.722)
  Time and place according to agreement
    Short description: I discuss ongoing work with my doctoral and diploma students.
  Diplomarbeiten und Dissertationen
 

Es besteht die Möglichkeit, in meiner Arbeitsgruppe eine Diplomarbeit oder Dissertation anzufertigen zu Themen aus Computer-Algebra, algebraischer Geometrie, Computer-Aided-Geometric-Design, Kodierungstheorie, Kryptographie, differentieller Algebra, sowie verwandten Gebieten.