Aug 28 – 30, 2023
Europe/Oslo timezone

Cohomologically tropical varieties

Aug 28, 2023, 1:00 PM
55m
KE D-302

KE D-302

Mo Aug 28, 08:00 - 18:00, KE D-302, http://s.mazemap.com/2oEBdET Tu Aug 29, 08:00 - 13:00, AR Ø-110: "When you enter the main entrance in the AR building, walking straight ahead with the student expedition on the left, there are three auditoriums in a row, to the left of the stairs leading down to the cantine." Link is only an approximation: https://link.mazemap.com/EPjDAyql We, Aug 30, 08:00 - 12:00, KE E-101, http://s.mazemap.com/2F90QaY We, Aug 30, 12:00 - 17:00, AR G-001, http://s.mazemap.com/2oCQkP4

Speaker

Kris Shaw

Description

The cohomology of the complement of a hyperplane arrangement can be recovered from its tropicalisation. This talk asks what which other subvarieties of the torus does this hold. We show that the tropicalisation knows the cohomology of the variety in a strong sense if and only if it satisfies local tropical Poincaré duality and the original variety is what we call wunderschön. Following the work of Itenberg, Katzarkov, Mikhalkin, and Zharkov, we have that tropicalisations of families of varieties which locally satisfy these two conditions recover information about the mixed Hodge structures of the family.
This is joint work with Edvard Aksnes, Omid Amini, and Matthieu Piquerez

Presentation materials

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