### Vorträge aus allen Gebieten der Funktionalanalysis

Sofern nicht näher spezifiziert, finden alle Vorträge um 16:00 Uhr ct. in Hörsaal IV in Gebäude E2.4 statt.

### Wintersemester 2020/2021

09.11.2020

Noé Bárcenas Torres (UNAM, Mexiko)

Titel: Introduction to the Baum-Connes Conjecture

Abstract: I will give a first gentle introduction to the Baum-Cones conjecture from both the partial viewpoints of Operator algebras and topology.

I will finish by explaining ongoing work on computations of the left hand side of the Baum-Connes Conjecture for mapping class groups.

Der Vortrag wird um 16.15 Uhr als Videokonferenz sattfinden.

13.05.2020

Michael Hartz (UdS)

Titel: Multipliers and operator space structure of weak products

Abstract: The classical Hardy space H^2 on the unit disc, and more generally Hilbert spaces of holomorphic functions, play an important role in operator theory and function theory. Weak product spaces generalize the notion of H^1 and were first studied using techniques from function theory and harmonic analysis. I will talk about how weak product spaces carry the structure of an operator space and how this point of view makes it possible to characterize multipliers of weak products. This is joint work with Raphael Clouatre.

Der Vortrag wird um 16.15 Uhr als Videokonferenz sattfinden.

18.05.2020

Simon Schmidt (UdS)

Titel: Quantum automorphism groups of finite graphs

Abstract: To capture the symmetry of a graph one studies its automorphism group. We will talk about a generalization of automorphism groups of finite graphs in the framework of Woronowicz’s compact matrix quantum groups. An important task in the theory of quantum automorphism groups of finite graphs is to see whether or not a graph has quantum symmetry, i.e. whether or not its quantum automorphism group is commutative. We will see that a graph has quantum symmetry if its automorphism group contains a certain pair of automorphisms. Then, focussing on distance-transitive graphs, we will discuss tools for proving that the generators of the quantum automorphism group commute. We will deduce that several families of distance-transitive graphs have no quantum symmetry.

Der Vortrag wird um 16.15 Uhr als Videokonferenz sattfinden.

08.06.2020

James Pascoe (University of Florida)

Titel: Free convexity, plurisubharmonicity, and universal monodromy

Abstract: We consider matricial analogues of the classically important classes of convex and plurisubharmonic functions. A smooth function is convex on a region if its second derivative is positive semidefinite, and plurisubharmonic if its complex Hessian is positive semidefinite. Riesz showed that a subharmonic function in one variable in the integral of a logarithmic potential. The theory of general convex functions in one variable is not so tractable, but for their matricial analogue, the so-called matrix convex functions, where one asks for a certain kind of convexity when the function is evaluated on self-adjoint operators via the functional calculus, it is. Kraus proved that a matrix convex function has a certain integral representation. Our goal will be to give representations for free noncommutative functions of several noncommuting indeterminates, which are the natural functions of functional calculus of several noncommuting operators. Towards this aim, we establish the frankly shocking fact that the monodromy theorem holds on arbitrary connected sets for free functions. Free universal monodromy itself has many consequences-- for example, every pluriharmonic free function on a connected domain has a pluriharmonic conjugate.

Der Vortrag wird als Videokonferenz sattfinden.

15.06.2020

Karl-Mikael Perfekt (University of Reading (UK))

Titel: A mean counting function for Dirichlet series and compact composition operators

Abstract: We introduce a mean counting function for Dirichlet series, measuring a weighted density of their zeros in a half-plane. The existence of the mean is related to Jessen and Tornehave's resolution of the Lagrange mean motion problem. The mean counting function plays the same role in the function theory of Hardy spaces of Dirichlet series as the Nevanlinna counting function does in the classical theory. For example, the mean counting function yields a simple characterization of all (polydisc-)inner Dirichlet series, and the analogue of Frostman's theorem holds.

We then apply the mean counting function to resolve the problem of describing all compact composition operators with Dirichlet series symbols on the Hilbert-Hardy space of Dirichlet series, which has been a central problem of the theory since the bounded composition operators were described by J. Gordon and H. Hedenmalm. A composition operator is compact if and only if the mean counting function of its symbol satisfies a decay condition at the boundary, in analogy with Shapiro's classical characterization of compact composition operators on the usual Hardy space.

Based on joint work with Ole Fredrik Brevig.

Der Vortrag wird als Videokonferenz sattfinden.

22.06.2020

Nikolaos Chalmoukis (University of Bologna, Italy)

Titel: Onto Interpolating sequences for the Dirichlet and Sobolev $W^{1,2}(D)$ spaces.

Abstract: Abstract: We will discuss a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of capacity of some condensers. The same condition in fact characterizes all onto interpolating sequences for the Sobolev space $W^{1,2}(D)$ even if the associated measure is infinite. If time permits we will discuss also a random version of the interpolation problem.

Der Vortrag wird als Videokonferenz sattfinden.

29.06.2020

Stefan Richter (University of Tennessee)

Titel: Function theory for the Drury Arveson space

Abstract: hier

Der Vortrag wird als Videokonferenz sattfinden.

25.11.2019

Baruch Solel (Technion, Haifa)

Titel: Weighted shift algebras

Abstract

02.12.2019

Michael Skeide (University of Molise, Campobasso, Italy)

Titel: CP-Semigroups and Dilations - Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond (Part I).

Abstract

09.12.2019

Michael Skeide (University of Molise, Campobasso, Italy)

Titel: CP-Semigroups and Dilations - Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond (Part II).

Abstract

13.01.2020

Marcel Scherer

Titel: Wesentliche Sphärische Isometrien

03.02.2020

Daniel Kraemer

Titel: Toeplitz operators on Hardy spaces

29.04.2019

Evelyn Weber

Titel: Factorizations of Contractions.

13.05.2019

Moritz Kunz

Titel: Längste aufsteigende Teilfolgen und die Tracy-Widom-Verteilung.

20.05.2019

Steven Klein

Titel: Die interpolierten freien Gruppenfaktoren und das Isomorphieproblem.

8.07.2019

Ernst Albrecht

Titel: Kompakte Störungen von Diagonaloperatoren.

15.10.2018

Christian Budde

Titel: Extrapolation spaces and Desch-Schappacher perturbations of bi-continuous semigroups.

Abstract: We construct extrapolation spaces for non-densely defined (weak) Hille-Yosida operators. In particular, we discuss extrapolation of bi-continuous semigroups. As an application we present a Desch-Schappacher type perturbation result for this kind of semigroups. This talk is based on joint work with B. Farkas.

26.11.2018

Xumin Wang

Titel: Some Fourier multipliers on some discrete groups.

Abstract: hier

21.01.2019

Sebastian Baltes

Titel: Die twisted SU(2) Gruppe, ein Beispiel einer Quantenmatrixgruppe.

28.01.2019

Sebastian Toth

Titel: Factorizations induced by complete Nevanlinna-Pick factors.

04.02.2019

Sebastian Langendörfer

12.03.2018

Michael Hartz

Titel: Quotients of multipliers in complete Pick spaces.

Abstract: Every function in the Hardy space on the unit disc is a quotient of two functions in $H^\infty$. I will talk about a generalization of this result, which says that every function in a complete Pick space is a quotient of two multipliers. Moreover, I will explain applications to the Corona problem and to extremal functions.This is joint work with Alexandru Aleman, John McCarthy and Stefan Richter.

14.05.2018

Volker Runde (University of Alberta, Edmonton)

Titel: Dual Banach algebras: a survey

28.05.2018

Martin Michajlow

Titel: Hilbertsudokus

Abstract: Given a sudoku, i.e. a N^2xN^2-matrix filled with numbers 1,...,N^2, we can replace every number by the projection onto the span of the standard basis vector of C^{N^2} with the respective index. Distinct projections of the same row, column or N-block will then be orthogonal. Furthermore, the projections in each row, column or N-Block sum up to the identity. More generally, we consider Hilbert sudokus, i.e. square matrices whose entries are projections on subspaces of an arbitrary Hilbert space s.t. the above orthogonalilty-/sum conditions hold for rows and columns. One main question is: Given a partially filled Hilbert sudoku - can we always fill it up to a complete Hilbert sudoku? In our Bachelor's thesis, we looked at different types of Hilbert sudokus and discuss a similiarity relation for Hilbert sudokus.

25.06.2018

Miguel Pluma

Titel: Bi-free probability theory

Abstract: In 2013, Voiculescu introduced bi-free probability in order to study simultaneously left and right representations of algebras. This gives rise to a notion of bi-free independence and bi-free convolution. In this talk we will give an exposition of the basic concepts of the theory, and explain how can we use bi-freenes to define a bi-free convolution for complactly suported proability measures in the plane R^2.

9.07.2018

Sebastian Langendörfer

13.11.2017

Tomohiro Hayase

Titel: An inverse problem in random matrix theory and free probability theory.

Abstract: Matrix valued free probability theory makes it possible to compute analytically or numerically the eigenvalue distributions of mixtures of large random matrices and deterministic ones. This talk introduces its inverse problem: how to estimate parameters (e. g. deterministic matrices) of a random matrix model from the sampled empirical eigenvalue distributions. No knowledge on free probability or random matrices is assumed for the talk.

22.01.2018

Dominik Schillo

Titel: K-contractions

29.01.2018

Martin Alt

Titel: Der Satz von Malgrange-Ehrenpreis

15.05.2017

Simon Schmidt

Titel: Quantum automorphisms of graph C^*-algebras

In this talk we present quantum automorphism groups of graphs. Those are quantum groups that generalize classical automorphism groups and there are actually two definitions of them. Our main result is that one of the definitions gives rise to the quantum symmetry group of the graph C^*-algebra. Therefore, one can think of the quantum symmetries of the graph C^*-algebra as the quantum automorphisms of the underlying graph.

29.05.2017

Ricardo Schnur

In this talk we show that for $N \geq 4$ the von Neumann algebra associated to the free orthogonal quantum group $O_N^+$ possesses the Connes embedding property. That is to say, it can be embedded into an ultrapower of the hyperfinite type $\text{\normalfont{II}}_1$ factor by a free ultrafilter. The main tool for this will be the notion of a quantum group being topologically generated by two of its quantum subgroups as introduced by Brannan, Collins and Vergnioux.