Research report 2018 - Max Planck Institute for Mathematics

Counting surfaces

Borot, Gaëtan
Max-Planck-Institut für Mathematik, Bonn
Imagining physical theories taking place in a space M allow mathematicians to extract fine geometric information on M. In particular, quantum field theories and string theories have led to the definition of new and hard-to-compute geometric invariants. The algebraic structures that govern them have in fact a wider range of applications for the enumerative geometry of surfaces, for reasons that are not completely understood yet. This report describes the principle of one these structures, called topological recursion and based on the strategy of cutting surfaces into pairs of pants.

For the full text, see the German version.

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