MAGIC004: Applications of model theory to algebra and geometry

Course details

A specialist MAGIC course

Semester

Spring 2025
Monday, January 27th to Friday, April 4th

Hours

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

Timetable

Tuesdays
10:05 - 10:55 (UK)

Course forum

Visit the https://maths-magic.ac.uk/forums/magic004-applications-of-model-theory-to-algebra-and-geometry

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

The assessment for this course will be released on Tuesday 22nd April 2025 at 00:00 and is due in before Friday 2nd May 2025 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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