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Solvability and unsolvability of equations in finite terms

Speaker: 
Askold Khovanskii
Institution: 
University of Toronto
Schedule: 
Wednesday, June 12, 2019 - 16:00
Location: 
A-136
Abstract: 

Numerous unsuccessful attempts to solve certain algebraic and differential equations “in finite terms” (i.e., “explicitly”) led mathematicians to the belief that explicit solutions of such equations simply do not exist. A lot of beautiful results on unsolvabilily of equations in finite terms were obtained by Abel, Galois, Liouville, Picard and by other mathematicians.

Recently some topological obstructions to solvability in finite terms were found. I will talk about topological Galois theory which studies these obstruction. I also will shortly discuss Liouville's theory and Picard-Vessio theory. I do not expect any special knowledge.

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