The Homepage of Boris Zilber

Personal Information

Full name:	Boris Zilber	Affiliation:	Mathematical Institute
			University of Oxford, and
			Merton College, Oxford

Address:	24-29 St Giles	Phone:	(+44)(0) 1865 273537
	Oxford, OX1 3LB	Fax:	(+44)(0) 1865 273583
	United Kingdom	email:	zilber@maths.ox.ac.uk

Teaching

c/Msc Course

Axiomatic Set Theory

Class Tutor: Ben Chad (chad@maths.ox.ac.uk)

Teaching assistants: Julia Erhard (julia.erhard@merton.ox.ac.uk) and Gareth Davies (gareth.davies@lmh.ox.ac.uk)

Lecture Notes (pdf) chapters 0-12

Problem sheets (pdf) week 1 week 2 week 3 week 4 week 5 week 6 week 7

Graduate Courses

Elements of Geometric Stability Theory (pdf)

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Zariski Geometries (pdf)

Forthcoming Book

Zariski Geometries are abstract structures in which a suitable generalisation of Zariski topology makes sense. Algebraic varieties over an algebraically closed field and compact complex spaces in a natural language are examples of Zariski geometries. The main theorem by Hrushovski and the lecturer states that under certain non-degeneracy conditions a 1-dimensional Zariski geometry can be identified as an algebraic curve over an algebraically closed field. The proof of the theorem exhibits, as a matter of fact, a way to develop algebraic geometry from purely geometric abstract assumptions not involving any algebra at all. Recent works in model theory of complex manifolds, differential fields and non-commutative geometry point to exciting perspectives for the theory.