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shared:seminars_graphs [03.11.2019 21:23] guterman |
shared:seminars_graphs [08.09.2025 13:18] (текущий) guterman |
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====Спецсеминар " | ====Спецсеминар " | ||
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- | **Семинар проходит по средам в ауд. 14-15 Главного здания, | ||
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+ | **Семинар Георгия Борисовича Шабата регулярно работает с сентября 1991г. Обычно проходит по средам в ауд. 14-05 Главного здания. В настоящее время проводится частично он-лайн, | ||
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- | **30.10.2019** | + | Для участия в он-лайн семинаре напишите elena -dot- kreines @ gmail -dot- com |
- | 1. Г.Б. Шабат, О семействах детских рисунков и пар Белого | + | **10.09.2025** |
- | 2. Н.М. Адрианов, О симметрических квадратах функций Белого | + | 1. Г.Б. Шабат, Граф |
- | **23.10.2019** | + | 2. Разное |
- | П.И. Дунин-Барковский (НИУ ВШЭ), Топологическая | + | ---- |
+ | **[[[[: | ||
- | **16.10.2019** | + | **Архив** |
- | 1. Г.Б. Шабат, Паспортные многообразия и их размерности (продолжение) | + | [[[[: |
- | 2. Разное. | + | [[[[: |
- | **09.10.2019** | + | [[[[: |
- | Г.Б. Шабат, Паспортные многообразия и их размерности (продолжение) | + | [[[[: |
- | **02.10.2019** | + | [[[[: |
- | 1. Г.Б. Шабат, О реализуемости различных паспортов | + | [[[[: |
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- | 2. Н.Я. Амбург (ИТЭФ), Цветные триангуляции и тензорная модель (продолжение) | + | |
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- | **25.09.2019** | + | |
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- | 1. Ю.Ю. Кочетков (НИУ ВШЭ), О вещественных многочленах степени 5 и 6 | + | |
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- | 2. Разное. | + | |
- | + | ||
- | **18.09.2019** | + | |
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- | 1. Г.Б. Шабат, Критическая фильтрация и отображение Ляшко-Лойенги (продолжение) | + | |
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- | 2. Н.Я. Амбург (ИТЭФ), Цветные триангуляции и тензорная модель | + | |
- | + | ||
- | **11.09.2019** | + | |
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- | Г.Б. Шабат, Критическая фильтрация и отображение Ляшко-Лойенги | + | |
- | + | ||
- | **04.09.2019** ВНИМАНИЕ: | + | |
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- | 1. Pálfia Miklós, On the recent advances in the multivariable theory | + | |
- | of operator monotone functions and means | + | |
- | Functional Analysis Research Group, Institute of Mathematics, | + | |
- | University of Szeged, Hungary, | + | |
- | Sungkyunkwan University, Korea | + | |
- | + | ||
- | Abstract: | + | |
- | The origins of this talk go back to the fundamental theorem of Loewner | + | |
- | in 1934 on operator monotone real functions and also to | + | |
- | the hyperbolic geometry of positive matrices. Loewner' | + | |
- | characterizing one variable operator monotone functions has been | + | |
- | very influential in matrix analysis and operator theory. Among others | + | |
- | it lead to the Kubo-Ando theory of two-variable operator means | + | |
- | of positive operators in 1980. One of the nontrivial means of the | + | |
- | Kubo-Ando theory is the non-commutative generalization of the | + | |
- | geometric mean which is intimately related to the hyperbolic, | + | |
- | non-positively curved Riemannian structure of positive matrices. | + | |
- | This geometry provides a key tool to define multivariable | + | |
- | generalizations of two-variable operator means. Arguably the most | + | |
- | important | + | |
- | example of them all is the Karcher mean which is the center of mass on | + | |
- | this manifold. This formulation enables us to define this mean | + | |
- | for probability measures on the cone of positive definite matrices | + | |
- | extending further the multivariable case. Even the infinite | + | |
- | dimensional | + | |
- | case of positive operators is tractable by abandoning the Riemannian | + | |
- | structure in favor of a Banach-Finsler structure provided by | + | |
- | Thompson' | + | |
- | This metric enables us to develop a general theory of means of | + | |
- | probability measures defined as unique solutions of nonlinear operator | + | |
- | equations on the cone, with the help of contractive semigroups | + | |
- | of nonlinear operators. We also introduce the recently established | + | |
- | structure theory of multivariable operator monotone functions | + | |
- | extending the classical result | + | |
- | of Loewner into the non-commutative multivariable realm of free | + | |
- | functions, providing theoretically explicit closed formulas for our | + | |
- | multivariable | + | |
- | operator means. | + | |
- | + | ||
- | 2. F. Pakovich, COMMUTING RATIONAL FUNCTIONS REVISITED | + | |
- | Ben Gurion University, Israel | + | |
- | + | ||
- | Abstract | + | |
- | Let A and B be rational functions on the Riemann sphere. The classical | + | |
- | Ritt theorem states that if A and B commute and do not have an iterate | + | |
- | in common, then up to a conjugacy they are either powers, or Chebyshev | + | |
- | polynomials, | + | |
- | information about commuting rational functions which do have a common | + | |
- | iterate. On the other hand, non-trivial examples of such functions | + | |
- | exist and were constructed already by Ritt. In the talk we present new | + | |
- | results concerning this class of commuting rational functions. In | + | |
- | particular, we describe a method which permits to describe all | + | |
- | rational functions commuting with a given rational function. | + | |
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- | **Архив** | + | |
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