Boris Zilber

Boris Zilber
Zilber in Oberwolfach 2010
Born	1949 (age 75–76) Tashkent, Uzbekistan
Alma mater	Novosibirsk State University Saint Petersburg State University
Awards	Tarski Lectures (2002) Gödel Lecture (2003) Senior Berwick Prize (2004) Pólya Prize (2015)
Scientific career
Fields	Mathematics, Logic, Model theory
Institutions	University of Oxford
Thesis	Groups and Rings with Categorical Theories  (1975)
Doctoral advisor	Mikhail Taitslin

Boris Zilber (Russian: Борис Иосифович Зильбер, born 1949) is a Soviet-British mathematician who works in mathematical logic, specifically model theory. He is a emeritus professor of mathematical logic at the University of Oxford.

He obtained his doctorate (Candidate of Sciences) from the Novosibirsk State University in 1975 under the supervision of Mikhail Taitslin^[1] and his habilitation (Doctor of Sciences) from the Saint Petersburg State University in 1986.^[2]

Zilber received the Senior Berwick Prize (2004) and the Pólya Prize (2015) from the London Mathematical Society.^[3] He also gave the Tarski Lectures in 2002.^[4]

Research

Zilber is well known for his seminal work around several fundamental problems in mathematics, mostly in the broad area of geometric model theory.^[5] In particular, his trichotomy conjecture on the nature of strongly minimal sets has been extremely influential in geometric stability theory.^[6] Although it is false in full generality (refuted by Ehud Hrushovski), it holds in many important settings, e.g. Zariski geometries, and has been successfully applied to several problems including the Mordell-Lang conjecture for function fields.^[7] Zilber's work on model theory of complex exponentiation led him to propose several influential conjectures including the Quasiminimality conjecture,^[8] the Existential Closedness conjecture,^[9] and the Conjecture on Intersections with Tori.^[9]

See also

• Zilber-Pink conjecture
• Existential Closedness conjecture
• Schanuel's conjecture

References

1. Boris Zil'ber at Mathematics Genealogy Project
2. Prof. Zilber's page at the University of Oxford
3. List of LMS prize winners
4. "Group in Logic and the Methodology of Science - Past Tarski Lectures". logic.berkeley.edu. Retrieved 2 November 2021.
5. Kennedy, Juliette (2024), "Boris Zilber and the model-theoretic sublime", Model Theory, 3 (2): 305–315, arXiv:2306.14562, doi:10.2140/mt.2024.3.701.
6. Pillay, Anand (1996). Geometric Stability Theory. Clarendon Press. ISBN 978-0-19-853437-2.
7. Bouscaren, Elisabeth, ed. (14 March 2009). Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture. Lecture Notes in Mathematics. Springer Berlin, Heidelberg. p. 216. ISBN 978-3-540-68521-0.
8. Wilkie, Alex (2024), "Analytic continuation and Zilber's quasiminimality conjecture", Model Theory, 3 (2): 701–719, arXiv:2306.14562, doi:10.2140/mt.2024.3.701.
9. Aslanyan, Vahagn (2024), "The Existential Closedness and Zilber–Pink conjectures", Model Theory, 3 (2): 599–624, arXiv:2403.09304, doi:10.2140/mt.2024.3.599.

External links

• Prof. Zilber's homepage