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Jialing Yu: A Journey From The Borsuk–Ulam Theorem

Master Thesis

Time: Mon 2023-04-17 09.00 - 10.00

Location: Cramér Room, Albano

Respondent: Jialing Yu

Supervisor: Gregory Arone

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This article is a journey which starts from the Borsuk–Ulam theorem and ends in the topological Tverberg conjecture. These two topics are the main concerns of this article. We first discuss the Borsuk–Ulam theorem and give some of its applications within and outside of mathematics. Later we present two generalizations of the Borsuk–Ulam theorem and show how they can be used to prove the topological Tverberg conjecture for the prime and prime power situations. In the end, we state the idea about how to disprove the topological Tverberg conjecture for the non prime power situation.