Explore the mathematical legacies of Galois, Grothendieck, and Voevodsky in this 58-minute conference talk by George Shabat from the Russian State University for the Humanities. Delve into the common features, tensions, and lasting impacts of these three influential mathematicians. Examine key concepts such as dessins d'enfants, cartographie sets, and Belyi pairs through topological, group-theoretical, and algebro-geometric lenses. Investigate category equivalences, arithmetic geometry, and the Grothendieck program's realization. Analyze the action of the absolute Galois group on dessins, bad reductions, and generalizations. Gain insights into the connections between dessins and moduli spaces in this comprehensive exploration of advanced mathematical concepts.
Overview
Syllabus
Introduction
Three mathematicians: education, recognition
1. Three mathematicians: some common features
1. Three mathematicians: tensions with the world
Three mathematicians: common legacy?
2. Three categories
2.0. Topological language: dessins d'enfants
2.1. Group-theoretical language: cartographie sets
2.2. Algebro-geometric language: Belyi pairs (III)
2.3. Category equivalences
2.4. Arithmetic geometry and Belyi height (1)
2.5. Grothendieck's fascination
On the realization of Grothendieck's programme
3.0. Counting dessins (II)
3.1. Absolute Galois group acting on dessins
3.2. Bad reductions
3.3. Example(1)
3.4. Generalizations
Dessins and moduli spaces
Conclusion
Taught by
Institute for Advanced Study
