MAGIC004: Applications of model theory to algebra and geometry

Course details

Semester

Spring 2022
Monday, January 31st to Friday, March 25th; Monday, April 25th to Friday, May 6th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Wednesdays
14:05 - 14:55

Course forum

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Description

This course is aimed at PhD students, not necessarily working in model theory, but working in areas potentially linked to model theory (e.g. other parts of logic, or parts of algebra, algebraic geometry, number theory, combinatorics). The first 5 lectures will introduce fundamental model-theoretic concepts. The second part of the course will explore various `tameness’ conditions on first order theories (e.g. concepts associated with model-theoretic stability theory and its extensions), with a focus on examples from algebra, especially fields (e.g. algebraically closed, real closed and p-adically closed fields, and pseudofinite fields). A goal will be to exhibit potentially applicable methods.

Prerequisites

Some familiarity with first order logic would be helpful but not essential.

Syllabus

Lectures 1—5: BASICS OF MODEL THEORY AND STABILITY THEORY: First order languages, structures and theories, compactness, types, saturation and homogeneity, quantifier elimination.
Lectures 6—10: TAME THEORIES, EXAMPLES, APPLICATIONS: uncountable categorical and strongly minimal theories; stable, o-minimal, simple, and NIP theories; model-theoretic notions of independence and dimension, and their interpretation in algebraically important structures (e.g. algebraically closed and real closed fields).

Lecturer

  • Dr Vincenzo Mantova

    Dr Vincenzo Mantova

    University
    University of Leeds

Bibliography

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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