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Спецсеминар "Графы на поверхностях и кривые над числовыми полями"

Семинар проходит по средам в ауд. 14-15 Главного здания, начало в 18:30.


1. П.И. Дунин-Барковский (НИУ ВШЭ), ТВА


1. Г.Б. Шабат, Паспортные многообразия и их размерности (продолжение)

2. Разное.


Г.Б. Шабат, Паспортные многообразия и их размерности (продолжение)


1. Г.Б. Шабат, О реализуемости различных паспортов

2. Н.Я. Амбург (ИТЭФ), Цветные триангуляции и тензорная модель (продолжение)


1. Ю.Ю. Кочетков (НИУ ВШЭ), О вещественных многочленах степени 5 и 6

2. Разное.


1. Г.Б. Шабат, Критическая фильтрация и отображение Ляшко-Лойенги (продолжение)

2. Н.Я. Амбург (ИТЭФ), Цветные триангуляции и тензорная модель


Г.Б. Шабат, Критическая фильтрация и отображение Ляшко-Лойенги

04.09.2019 ВНИМАНИЕ: начало в 18:00

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's theorem 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's part metric on the cone of positive definite operators. 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, or Latt`es maps. This result however provides no 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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