Research Seminar in Mathematics (MTH G450 - 30757)
Organized by Professor Jonathan Weitsman
Guest Speaker: Liat Kessler
Massachusetts Institute of Technology
Date: Tuesday, September 23, 2008
Time: 1:00 p.m.
Location: 509 Lake Hall
List of talks:
Pretalk: 1 p.m. by Liat Kessler, Introduction to Model Theory
Break 2:00 p.m. - 2:30 p.m.
Pretalk 2:30 p.m. - 3:30 p.m. by Liat Kessler, Zariski-type structures
Department tea, 3:30 p.m. - 4:00 p.m.
Talk by Liat Kessler, 4:00 p.m. - 5:00 pm.m, Holomorphic shadows in the eyes of model theory
Discussion at 5:00 p.m. followed by dinner with the speaker.
Abstract:
An almost complex manifold (M,J) is a manifold M with a complex structure J on the fibers of the tangent bundle TM. We are looking for a good definition for an almost complex subvariety. To interpret 'good', we borrow the concept of a Zariski-type structure from model theory. Zariski-type structures were introduced by Hrushovski and Zilber in their study of strongly minimal sets. A motivating example is given by the structure of complex subvarieties in the Cartesian products of a compact complex manifold. We define a subset of an almost complex manifold to be a holomorphic shadow if it is the image of a J- holomorphic map from a compact complex manifold. We show that under some conditions on J, holomorphic shadows in a compact almost complex manifold (M,J) form a Zariski type structure. Checking this leads to non-trivial geometric results.
Previous Talks:
Fall 2008:9/16,
Started: 23 September 2008 Last modified: 23 September 2008
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