##### Teaching

### Research seminar in functional analysis

### Talks from all areas in functional analysis

The research seminars "Oberseminar Funktionalanalysis" and "Oberseminar Free Probability" have been merged to "Oberseminar Noncommutative and Functional Analysis". A new webpage will be launched in the upcoming months.

Unless otherwise indicated, all talks take place in room lecture room 4 in building E2.4 at 4.00 pm ct.

### Summer semester 2021

**Marcel Scherer**

**Title:** Spectra of quotient modules

**Abstract:**
*A reproducing kernel Hilbert space can be seen as a module over its multiplier algebra.
This talk concerns regular reproducing kernel Hilbert spaces H over the unit ball in C^n.
Every tuple of multipliers induces an operator on H. For a closed invariant subspace M in H,
we are interested in the compression of the operator tuple to the quotient space H/M.
To be precise, the goal is to describe the Taylor spectrum of such an operator tuple in terms
of the approximate zero set of the space M.
There are already some known connections if the underlying reproducing kernel Hilbert space has the
complete Nevanlinna-Pick property, but in particular, we also consider a more general case, such as the
Hardy space or the Bergman space. I will give a lower and upper bound for the Taylor spectrum when the
kernel of H is a power of the Drury-Arveson kernel. When n=1, I will give an exact description of the
spectrum for special subspaces M.
*

The talk will take place via Zoom at 17.15

**Moritz Speicher**

**Title:** Guaranteeing that the Loewner Differential Equation Generates Slits

**Abstract:**
*The Loewner differential equation was introduced in 1923 by Charles Loewner to help analyse slit-discs.
Loewner noticed that any slit-disc could be generated by the Loewner differential equation given a corresponding driving function.
Now, we can look at the reverse of this process. What can we say about the domain generated by the Loewner differential equation
given a specific driving function. In this talk I will present the result of Joan R. Lind from 2003, in which they proved that if
the driving function is Hölder-1/2 continuous with Hölder constant less than 4, the chordal version of the Loewner differential equation
(the version looking at the upper halfplane instead of the unit disc) will generate a slit-halfplane.*

The talk will take place via Zoom at 16.15

**Octavio Arizmendi Echegaray (CIMAT Mexico)**

**Title:** Energy of graphs and vertices.

**Abstract:**
*Energy of graphs, introduced in mathematics by Gutman in the 70´s is a quite studied invariant of graphs.
In (2018) with Juarez, we introduced a refinement called Energy of a Vertex.
This allows to give better bounds and a local understanding for the energy of a graph.
In this talk I will survey on the topic of Energy of Graphs and on recent results in relation with Energy of a Vertex,
that I derived with various coauthors.*

The talk will take place via Zoom at 16.15

**Martin Alt**

**Title:** Wold-Decomposition for m-Hypercontractions

The talk will take place via Zoom at 16.15

**Alexandru Aleman (Lund University, Schweden)**

**Title:** Backward shift and nearly invariant subspaces of Fock-type spaces.

The talk will take place via Zoom at 16.15

### Winter semester 2020/2021

**Adam Dor-On ** *(University of Copenhagen and University of Illinois Urbana-Champaign)*

**Title:** Finite dimensional approximations and coactions for operator algebras

**Abstract:**
*Finite dimensional approximations for all representations of a C*-algebra are available whenever some injective representation has such an approximation.
This is a classical result of Exel and Loring from 1992. We extend this paradigm to general (possibly non-self-adjoint) operator algebras. Our work is intimately related
to the question, studied by Clouatre and Ramsey, of whether the maximal C*-cover of an operator algebra is residually-finite dimensional when the algebra itself is.
We resolve this question for semigroup operator algebras as well as various algebras of functions, providing many previously-unattainable examples.
A novel key tool in our analysis is the notion of an RFD coaction by a semigroup, whose development uses and extends ideas from the theory of semigroup C*-algebras.
*

The talk will take place via Zoom at 14.15.

**Noé Bárcenas Torres** *(UNAM, Mexiko)*

**Title:** 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.
*

The talk will take place as a video conference at 16.15

### Summer semester 2020

**Michael Hartz** *(UdS)*

**Title:** 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.
*

The talk will take place as a video conference at 16.15

**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.
*

The talk will take place as a video conference at 16.15

**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.
*

The talk will take place as a video conference.

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

**Title:** 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.
*

The talk will take place as a video conference.

**Nikolaos Chalmoukis** *(University of Bologna, Italy)*

**Title:** 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.
*

The talk will take place as a video conference.

**Stefan Richter** *(University of Tennessee)*

**Titel:** Function theory for the Drury Arveson space

** Abstract: ** here

The talk will take place as a video conference.

### Winter semester 2019/2020

**Michael Skeide** *(University of Molise, Campobasso, Italy)*

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

**Michael Skeide** *(University of Molise, Campobasso, Italy)*

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

**Marcel Scherer**

**Title:** Wesentliche Sphärische Isometrien

**Daniel Kraemer**

**Title:** Toeplitz operators on Hardy spaces

### Summer semester 2019

**Evelyn Weber**

**Title: ** Factorizations of Contractions.

**Moritz Kunz**

**Title: **
Längste aufsteigende Teilfolgen und die Tracy-Widom-Verteilung.

**Steven Klein**

**Title: ** Die interpolierten freien Gruppenfaktoren und das Isomorphieproblem.

** Ernst Albrecht **

** Title: ** Kompakte Störungen von Diagonaloperatoren.

### Winter semester 2018/19

**Christian Budde**

**Title: ** 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. *

**Sebastian Baltes**

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

**Sebastian Toth**

**Title: ** Factorizations induced by complete Nevanlinna-Pick factors.

**Sebastian Langendörfer**

### Summer semester 2018

**Michael Hartz**

*Title: 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.*

**Volker Runde (University of Alberta, Edmonton)**

*Title: Dual Banach algebras: a survey*

**Martin Michajlow**

*Title: 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. *

** Miguel Pluma **

*Title: 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. *

** Sebastian Langendörfer **

### Winter semester 2017/2018

**Tomohiro Hayase**

* Title: 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.*

**Dominik Schillo**

*Title: K-contractions*

**Martin Alt**

*Title: Der Satz von Malgrange-Ehrenpreis*

### Summer semester 2017

**Simon Schmidt**

*Title: 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.

**Ricardo Schnur**

*Title: The Connes embedding property for free orthogonal quantum groups*

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.

**Michael Hartz**

**Sebastian Toth**

*Title: Ein Satz über Randdarstellungen von Arveson*