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Explore a diverse range of unsolved problems and recent advancements in geometry, dynamics, partial differential equations, and related fields in this engaging conference talk. Delve into intriguing mathematical challenges that deserve more attention, examining partial solutions and discussing their implications. Follow the speaker's journey through various topics, potentially covering collaborations with renowned mathematicians such as D. Chen, S. Ivanov, B. Kleiner, Ya. Kurylev, M. Lassas, J. Lu, A. Novikov, and L. Polterovich. Adapt to the dynamic nature of the presentation, which may focus on two or three in-depth topics or cover multiple shorter stories, depending on audience interest and engagement.
