14/08/17 18:19:16.39
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The Work of Maryam Mirzakhani - International Mathematical Union
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This point of view led Mirzakhani to new insights into other questions about moduli space. One consequence was a new and unexpected proof of a conjecture of Edward Witten (a 1990 Fields Medalist), one of the leadingfigures in string theory.
Moduli space has many special loci inside it that correspond to Riemann surfaces with particular properties, and these loci can intersect.
For suitably chosen loci, these intersections have physical interpretations.
Based on physical intuition and calculations that were not entirely rigorous, Witten made a conjecture about these intersections that grabbed the attention of mathematicians.
Maxim Kontsevich (a 1998 Fields Medalist) proved Witten's conjecture through a direct verication in 1992.
Fifteen years later, Mirzakhani's work linked Witten's deep conjecture about moduli space to elementary counting problems of geodesics on individual surfaces.