The Floer Jungle: 35 years of Floer Theory

An exceptionally gifted mathematician and an extremely complex person, Floer exhibited, as one friend put it, a "radical individuality." He viewed the world around him with a singularly critical way of thinking and a quintessential disregard for convention. Indeed, his revolutionary mathematical ideas, contradicting conventional wisdom, could only be inspired by such impetus, and can only be understood in this context.

 

Poincaré's research on the Three Body Problem laid the foundations for the fields of dynamical systems and symplectic geometry. From whence the ancestral trail follows Marston Morse and Morse theory, Vladimir Arnold and the Arnold conjectures, through to breakthroughs by Yasha Eliashberg. Likewise, Charles Conley and Eduard Zehnder on the Arnold conjectures, Mikhail Gromov's theory of pseudoholomorphic curves, providing a new and powerful tool to study symplectic geometry, and Edward Witten's fresh perspective on Morse theory. And finally, Andreas Floer, who counter-intuitively combined all of this, hitting the "jackpot" with what is now called Floer theory.

 

This talk was organized jointly with Berlin Mathematical School (https://www.math-berlin.de/academics/bms-friday)

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