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moshchevitin [2020/07/04 10:00] Уланский Евгений Алесандрович [Lectures, new and old] |
moshchevitin [2020/09/21 07:42] Уланский Евгений Алесандрович [Lectures, new and old] |
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===== Lectures, new and old ===== | ===== Lectures, new and old ===== | ||
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+ | **14**. Tuesday, September 29, at 14:00 Moscow time (GMT+3).. | ||
+ | \\ **Speaker:** Florin Boca | ||
+ | \\ **Title:** Distribution of reduced quadratic irrationals (QIs) of even and of backward type | ||
+ | \\ **Abstract:** Reduced QIs arising from the regular CF are closely related with the Pell | ||
+ | equation and with closed geodesics on the modular surface. By a classical result of | ||
+ | Pollicott, they are known to be equidistributed with respect to the Gauss probability | ||
+ | measure, when ordered by their corresponding closed primitive geodesics length. | ||
+ | This talk will consider the reduced quadratic irrationals arising from the even CF and | ||
+ | the backward CF, where similar (and effective) equidistribution results with respect to | ||
+ | the invariant (infinite!) invariant measures have been established in recent joint work | ||
+ | with M. Siskaki. | ||
+ | |||
+ | **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). | ||
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**8**. Tuesday, June 02, 2020, at 15:00 Moscow time (GMT+3). | **8**. Tuesday, June 02, 2020, at 15:00 Moscow time (GMT+3). | ||
+ | \\ **[[https://yadi.sk/i/ezES9RyctUfT2w|Recording of the lecture]]** | ||
\\ **Speaker:** Erez Nesharim. | \\ **Speaker:** Erez Nesharim. | ||
\\ **Title:** The set of weighted badly approximable vectors is hyperplane absolute winning. | \\ **Title:** The set of weighted badly approximable vectors is hyperplane absolute winning. | ||
Строка 39: | Строка 59: | ||
**7**. Thursday, May 28, 2020, at 15:00 Moscow time (GMT+3). | **7**. Thursday, May 28, 2020, at 15:00 Moscow time (GMT+3). | ||
+ | \\ **[[https://yadi.sk/i/RUoVDKVv611nUQ|Recording of the lecture]]** | ||
\\ **Speaker:** Johannes Schleischitz | \\ **Speaker:** Johannes Schleischitz | ||
\\ **Title:** Cartesian products, sumsets and Hausdorff dimension | \\ **Title:** Cartesian products, sumsets and Hausdorff dimension | ||
Строка 51: | Строка 72: | ||
**6**. Thursday, May 21, 2020, at 15:00 Moscow time (GMT+3). | **6**. Thursday, May 21, 2020, at 15:00 Moscow time (GMT+3). | ||
+ | \\ **[[https://yadi.sk/i/SaLn9LUdhcpFBA|Recording of the lecture]]** | ||
\\ **Speaker:** Dmitri Kleinbock | \\ **Speaker:** Dmitri Kleinbock | ||
\\ **Title:** Geometry and dynamics of improvements to Dirichlet's Theorem in Diophantine approximation | \\ **Title:** Geometry and dynamics of improvements to Dirichlet's Theorem in Diophantine approximation | ||
Строка 57: | Строка 79: | ||
**5**. Thursday, May 07, 2020, at 14:30 Moscow time (GMT+3). | **5**. Thursday, May 07, 2020, at 14:30 Moscow time (GMT+3). | ||
+ | \\ **[[https://yadi.sk/i/5n9EzqbPS37_yg|Recording of the lecture]]** | ||
\\ **Speaker:** Victor Bereslevich | \\ **Speaker:** Victor Bereslevich | ||
\\ **Title:** Badly approximable points on curves are winning | \\ **Title:** Badly approximable points on curves are winning | ||
Строка 67: | Строка 90: | ||
**4**. Tuesday, May 05, 2020, at 14:00 Moscow time (GMT+3) | **4**. Tuesday, May 05, 2020, at 14:00 Moscow time (GMT+3) | ||
+ | \\ **[[https://yadi.sk/i/FAqwNIW35pCHfA|Recording of the lecture]]** | ||
\\ **Speaker:** Dmitri Badziahin | \\ **Speaker:** Dmitri Badziahin | ||
\\ **Title:** An improved bound in the problem of Wirsing | \\ **Title:** An improved bound in the problem of Wirsing | ||
Строка 77: | Строка 101: | ||
**3**. Tuesday, April 21, 2020, at 15:00 Moscow time (GMT+3). | **3**. Tuesday, April 21, 2020, at 15:00 Moscow time (GMT+3). | ||
+ | \\ **[[https://yadi.sk/i/_icxOaLKNEQagw|Recording of the lecture]]** | ||
\\ **Speaker:** Simon Kristensen | \\ **Speaker:** Simon Kristensen | ||
\\ **Title:** Arithmetic properties of series of reciprocals of algebraic integers. | \\ **Title:** Arithmetic properties of series of reciprocals of algebraic integers. |