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Yoshiharu Kohayakawa, IME-USP Ramsey theory studies, broadly speaking, phenomena of persistence of structures of interest under adversarial partitions. In this talk, we will discuss concrete examples that illustrate such phenomena, with emphasis on more elementary examples of finite combinatorics. We will also discuss related structural and numerical problems. Participate and help spread the word! More information about the IME Colloquium at https://www.ime.usp.br/coloquio/.