Explore a comprehensive lecture on the mathematical contributions of Udi Hrushovski, delivered by David Marker from the University of Illinois at Chicago. Delve into Hrushovski's work on strongly minimal expansions of algebraically closed fields, differentially closed fields, and other significant areas of model theory. Examine key concepts such as Manin kernels, Vaught's Conjecture for DCF, and applications of Jouanolou's Theorem. Gain insights into the connections between model theory and diophantine geometry, including approaches to the function field Mordell-Lang conjecture. Discover the impact of Hrushovski's research on various aspects of mathematical logic and algebra throughout this 49-minute presentation from the Fields Institute workshop "From Geometric Stability Theory to Tame Geometry."
Some Reflections on the Work of Udi Hrushovski
Overview
Syllabus
Intro
Udi Hrushovski 1959-...
Part 1: Strongly Minimal Expansions of C
1 Let X be the intersection of C with the graph of f. Suppose for contradiction that X is infinite. Since fis non constructible C\X must also be infinite
Semialgebraic Expansions of C
Strongly minimal expansions of algebraically closed fields
Part II: Hrushovski's work on differentially closed fields
Manin kernels What about non-trial locally moduar sets?
Classification of non-trivial strongly minimal sets
Vaught's Conjecture for DCF
Diophantine applications A warm up to the function field Mardell-Lang conjecture in characteristic
Applications of Jouanolou's Theorem
Other w-stable differential fields
Further work on differential fields
Part III: Other favorites
Taught by
Fields Institute
