The moduli space of metric graphs MGg is a key object in geometric group theory, algebraic geometry and quantum field theory. In particular, the cohomology of various graph complexes may be understood geometrically as sheaf cohomology on MGg. Recent advances have furthermore uncovered deep connections between MGg and objects of central interest in neighboring areas of mathematics, in particular the moduli space of Riemann surfaces Mg. Harer and Zagier’s Euler characteristic computations from 1986 showed that Mg has a huge amount of nontrivial cohomology, but few classes were explicitly known. The connection with MGg allowed Chan, Galatius and Payne to find exponentially many new cohomology classes through graph cohomology, though they still only account for a small part of the total cohomology.
Speakers:
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Anton Alekseev
- Paul Balduf
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Alexander Berglund
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Benjamin Bruck
- Ricardo Campos
- Simone Hu
- Najib Idrissi
- Siddarth Kannan
- Florian Naef
- Geoffrey Powell
- Brent Pym
- Rohini Ramadas
- Alex Takeda
- Benjamin Ward
- Nathalie Wahl
- Konstantin Wernli
