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Some Reflections on the Work of Udi Hrushovski

Fields Institute via YouTube

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Overview

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This course aims to explore and reflect on the work of Udi Hrushovski. The learning outcomes include understanding Strongly Minimal Expansions, Semialgebraic Expansions, and Hrushovski's work on differentially closed fields. The course covers skills such as analyzing Manin kernels, classifying strongly minimal sets, and applying Diophantine equations. The teaching method involves lectures and discussions. This course is intended for individuals interested in model theory, tame geometry, and advanced mathematical concepts.

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

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