Topics in pseudofinite Model Theory (SoSe 2016)
In recent years, surprising connections have emerged between model theory and
combinatorics. Bridges have been built from one subject to the other
resulting in a mutual enrichment.
For example, ground breaking work of Hrushovski on stable groups and
approximate groups lead to breakthroughs in additive combinatorics, and new
relatively simple proofs of the Szemeredi regularity lemma have lead
model theorists to greatly generalize its validity. The seminar will
explore some of these connections, focusing in particular on connections
with additive combinatorics and incidence geometry, taking the survey paper of
Hrushovski 'On pseudofinite dimensions' as guide.
The pre-seminar meeting took place on Wednesday,
the 10th of February, at 14:00h
in the Lichthof on the 8th floor. During the Münster Model Theory
Month (i.e. until the 18.5.), the seminar will take place on Wednesdays, 10:30-12:00 in M6. Afterwards, the seminar will take place on Wednesdays, 10:30-12:00h, in N2.
Breuillard-Green-Tao: Approximate subgroups of linear groups. Geom.
Funct. Anal. 21 (2011), no. 4, 774-819, arXiv:1005.1881
Cherlin, Gregory; Hrushovski, Ehud: Finite structures with few types.
Annals of Mathematics Studies, 152.
Princeton University Press, Princeton, NJ, 2003. vi+193.
Artem Chernikov; Sergej Starchenko: Regularity lemma for distal structures,
Ehud Hrushovski: Stable groups and Approximate subgroups, J. Amer. Math. Soc.
25 (2012), no. 1, 189-243.
Ehud Hrushovski: On pseudofinite dimensions, Notre Dame J. Form. Log. 54
(2013), no. 3-4, 463-495.
Ehud Hrushovski; Frank Wagner:
Counting and dimensions, in Model theory with
applications to algebra and analysis. Vol. 2, 161-176,
London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press,
Larsen-Pink: Finite subgroups of algebraic groups, J. Amer. Math. Soc.
24 (2011), no. 4, 1105-1158.
T. Tao, Expanding polynomials over finite fields of large characteristic,
and a regularity lemma for definable sets, arXiv:1211.2894.
Katrin Tent; Martin Ziegler:
A course in Model Theory, Lecture Notes in Logic, 40.
Association for Symbolic Logic, La Jolla, CA; Cambridge University
Press, Cambridge, 2012.