This is a very important development for the field, both in terms of the theorem that it proves and the techniques it introduces. Via QuantaMagazine
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Arnold predicted that every phase space of a certain type contains a minimum number of configurations in which the system it describes returns to where it started. This would be like billiard balls coming to occupy the same positions and velocities they held earlier. He anticipated that this minimum number is at least equal to the number of holes in the overall phase space, which can take the form of objects like a sphere or a doughnut .
“Typically, symplectic things are harder than purely topological things. So being able to tell something symplectically from topological information is the main interest,” saidThe first major advance on the Arnold conjecture took place decades later, in the 1980s, when a young mathematician named Andreas Floer developed a radical new way of counting holes. Floer’s theory quickly became one of the central tools in symplectic geometry.
“It’s a very important development for the field, both in terms of the theorem that it proves and the techniques it introduces,” saidTo get a sense for how configurations of a physical system can be used to build a geometric object, imagine a planet moving through space.
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