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Logic Online Seminar (www.mathnet.ru/conf876), Monday 16:00 MSK, Room 313 + Kontur Talk

01.12.2025, Incidences, tilings, and fields

M. Skopenkov (HSE University and KAUST, https://arxiv.org/search/?searchtype=author&query=Skopenkov%2C+M), online talk

The master theorem, introduced independently by Richter-Gebert and by Fomin and the first author, provides a method for proving incidence theorems of projective geometry (more precisely, quasi-identities) using triangular tilings of surfaces. We investigate which incidence theorems over C and R can or cannot be proved via the master theorem. For this, we formalize the notion of a tiling proof. We introduce a hierarchy of classes of theorems based on the underlying topological spaces. A key tool is considering the same theorems over finite fields.
This is a joint work with P. Pylyavskyy.

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