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moshchevitin [2020/07/15 13:59] Уланский Евгений Алесандрович [Lectures, new and old] |
moshchevitin [2020/09/18 00:03] Уланский Евгений Алесандрович [Lectures, new and old] |
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| ===== Lectures, new and old ===== | ===== Lectures, new and old ===== | ||
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| + | **13**. Tuesday, September 22, 2020, at 14:00 Moscow time (GMT+3). | ||
| + | \\ **Speaker:** Yitwah Cheung | ||
| + | \\ **Title:** Mixing properties of the BCZ map | ||
| + | \\ **Abstract:** The BCZ map was introduced by F. Boca, C. Cobeli and A. Zaharescu in their investigations of the statistical properties of the Farey sequences. This is a piecewise linear map of a certain right triangle whose connection to the horocycle flow on the modular surface was discovered by Athreya and myself, using which a newfound understanding of known results about Farey sequences was obtained, e.g. the distribution of gaps found by Hall in 1970 can be derived as the push-forward of Haar measure under the roof function of the BCZ map. In this talk I will report on joint work with Anthony Quas and Yiwei Zhang in our understanding of the mixing properties of the BCZ map. Specifically, I will explain how a miraculous property of the BCZ map, which we call infinitesimal self-similarity, allows us to prove that the BCZ map is weakly mixing. | ||
| + | The question of strong mixing remains open, correcting a claim I made earlier this year. | ||
| + | I will also describe a reformulation of the Riemann Hypothesis in terms of a BCZ cocycle. | ||
| **12**. Thursday, July 09, 2020, at 15:00 Moscow time (GMT+3). | **12**. Thursday, July 09, 2020, at 15:00 Moscow time (GMT+3). | ||