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_at_maths.ox.ac.uk

Teaching

c/Msc Course

Axiomatic Set Theory

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

Teaching assistant: Bernhard Elsner (elsner@maths.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
  • Cambridge University Press, 2010
  • 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.

    B.Poizat for Russian readers: Cours de théorie des modèles

    Research

    Survey papers and some talks

    Publications and preprints


    Links:

  • Oxford Logic Group
  • Paris Logic Group
  • Lyon Logic Group
  • Urbana-Champain Logic Group
  • Leeds Logic Group
  • Ehud Hrushovski,
  • Anand Pillay,
  • John Baldwin,
  • Dave Marker,
  • Greg Cherlin
  • Thomas Scanlon