Type: Seminar

Distribution: World

Expiry: 1 Jun 2023

CalTitle1: The local motivic monodromy conjecture holds generically

Auth: laurent@p721m2.pc (assumed)

This is a combinatorics talk hiding in geometric clothing. The clothing consists of the local motivic monodromy conjecture, an analogue of the Weil conjectures. Given a polynomial f with integer coefficients, it predicts a remarkable relationship between arithmetic properties (number of solutions to f = 0 modulo an integer) and topological properties (eigenvalues of monodromy of the Milnor fibre of the complex hypersurface defined by f). The conjecture remains wide open in general. Surprisingly, it remains open for "generic" choices of f, even though there are well known and relatively simple combinatorial formulas for all the relevant quantities. This brings us to the heart of the talk: for "generic" f, we relate the local motivic monodromy conjecture to a long-standing open question of Stanley on triangulations of simplices. Progress towards the latter question then helps resolve the local motivic monodromy conjecture. This is joint work with Matt Larson and Sam Payne.

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