Por Boris Zilber, University of Oxford
I. Principles of geometric stability theory and classication of formal theories
1. dimensions and ranks
2. saturation and homogeneity
3. types: syntactic and Galois
4. beyond first-order languages
5. the landscape of mathematics and the classication grid
II. Algebra/geometry and syntax/semantics dualities
1. the idea of co-ordinatisation in geometry and model theory
2. the trichotomy principle and the special role of fields (ACF, RCF, DCF,...)
3. manifold, varieties, charts and ringed spaces
4. affine algebras and ane varieties: algebraic syntax and geometric semantics
5. principles of non-commutative geometry: quantum algebras and quantum Zariski geometries
6. schemes and varieties in algebraic geometry via syntax and semantics
III. Positive model theory
1. languages and formulas in PMT
2. the generalised Zariski topology
3. morphisms in PMT
4. model completeness
The course will take place on Mondays, from 3:30pm to 5pm in room C6.2.33 of Faculdade de Ciências da Universidade de Lisboa (aprox. 10 hour course). The first session is in October 14. [Please notice that some Mondays may be skipped and other special arrangements can be made. Please get in touch with Mário Edmundo at for extra information.]
