Lecture Series 1. Differential Fields 1
Anand Pillay
Chapter 1. Differential Fields 3
1.1 Basics 3
Dimension theory 8
1.2 Varieties, differential varieties and tangent bundles 18
Varieties 18
Differential varieties 19
Tangent spaces and abstract varieties 20
Differential forms 23
1.3 Strongly minimal sets of d-degree 1 27
1.4 Kolchin's logarithmic derivative 31
1.5 Prologations, torsors and the Buium-Manin homomorphism 35
Algebraic groups: Geometry 37
1.6 Manin's construction 40
Bibliography 45
Lecture Series 2. Lectures on o-Minimality 47
Patrick Speissegger
Chapter 1. Lectures on o-Minimality 49
1.1 Adding exponentiation 49
1.2 T-convexity and tame extensions 52
1.3 Piecewise linearity 56
1.4 The Wilkie inequality 58
1.5 The valuation property 61
Bibliography 65
Lecture Series 3. Tame Congrugence Theory 67
Matthias Clasen and Matthew Valeriote
Chapter 1. The Structure of Finite Algebra 69
1.1 Palfy's theorem 69
1.2 Localization and relativization 72
1.3 Centrality 79
1.4 Labelled congruence lattices 87
Chapter 2. Varieties 89



2.1 Subdirectly irreducibles 89
2.2 Facts about the abelian condition 92
2.3 The case typ(0, p) = 2 94
2.4 The case typ{S} = {1} 95
2.5 The residually large configuration 97
2.6 The case type{S} = {1, 2} 102
2.7 Multitraces 104
2.8 Parallelism 107
Bibliography 113