Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, March 15, 2022, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Istvan Tomon

Hyperplane covers of finite spaces

I will talk about three long-standing conjectures from the intersection of linear algebra and combinatorics that turn out to be closely related: the Alon-Jaeger-Tarsi conjecture (1988) on non-vanishing linear maps, the Additive basis conjecture of Alon-Linial-Meshulem (1991), and a conjecture of Pyber (1996) on coset covers of abelian groups. Recently, we solved the first one in a strong form, the second one in a weak form, and the third one in just the right form. Based on joint works with Janos Nagy and Peter Pal Pach.

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