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2:00pm to 3:00pm - 340P Rowland Hall - Combinatorics and Probability Antoine Song - (Caltech) How large are sums of large sets? I will discuss a circle of questions about the geometry of sums of large sets in R^n endowed with the Gaussian measure, related to the convexity problem of Talagrand: if a subset A of R^n has Gaussian measure at least 2/3 say, for which integer q does A+...+A (q times) contain a large convex body? I will explain why it is closely connected to the problem of understanding sums of non-independent Gaussian random vectors. I will discuss some sharp results and partial answers. |
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3:00pm to 4:00pm - 440R - Logic Set Theory Julian Eshkol - (UC Irvine) Threading Ideals Welch games are a genre of challenge-and-response games that can be used to stratify large cardinal strength between weak compactness and measurability [Foreman, Magidor, Zeman 2020]. The known variants of this game make sense only in the context of large cardinals. In this talk, we define and explore threading ideals, a combinatorial principle necessary for importing the Welch-game idea to successor cardinals. |
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3:00pm - PSCB 210 - Graduate Seminar Paata Ivanisvili - (UCIrvine ) Experiments with AI in Mathematics In this talk, I will discuss some ways in which AI can be used in mathematical research. Through a series of examples, I will illustrate how AI can help explore problems, suggest ideas, test conjectures, and sometimes obtain partial results. I will also describe several instances where these methods contributed to ongoing work, including partial progress that eventually appeared in a paper. Part of the talk will be conducted in a live, experimental format. I will demonstrate how one can use AI in real tim by selecting a mathematical paper and attempting to engage with it on the spot. By this, I mean using AI to investigate the paper, explore related questions, and try to prove partial results inspired by it. The goal is not to present AI as a replacement for mathematical thinking, but rather as a new kind of experimental tool that may assist with exploration and discovery.
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