MAGIC004: Applications of model theory to algebra and geometry

Course details

Semester

Spring 2010
Monday, January 11th to Friday, March 19th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
0

Timetable

Tuesdays
12:05 - 12:55
Thursdays
10:05 - 10:55

Description

The course will discuss and survey some classical and recent applications of model theoretic techniques to various other areas of mathematics. In addition to introducing basic notions of model theory, the course will also introduce in a soft manner notions from algebraic geometry as well as valued fields. As such the course is aimed at the general postgraduate audience. But it would also be essential for students aiming to work in model theory and related subjects. The applications will go from elementary things (Ax's theorem) to more sophisticated ones (p-adic and motivic integration).

Prerequisites

Familiarity with first order logic, elements of group theory, general topology, and commutative algebra, will be helpful but not essential.

Syllabus

  • Lectures 1 to 8: BASICS OF MODEL THEORY WITH EXAMPLES. (First order structures and theories, definable sets, compactness, nonstandard models, saturation, quantifier elimination, model companions)
  • Lecture 9 to 14: ALGEBRAICALLY CLOSED FIELDS. (Quantifier elimination, Ax's Theorem and Nullstellensatz, Zariski topology,categoricity, affine varieties, abstract varieties, algebraic groups, Grothendieck rings.)
  • Lectures 15 to 20: VALUED FIELDS. (Henselian valued fields, Ax-Kochen theorem and Artin's conjecture, Macintyre's quantifier elimination theorem, p-adic measure, Denef's rationality theorem, introduction to motivic integration.)

Lecturer

  • AP

    Anand Pillay

    University
    University of Leeds

Bibliography

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Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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