45. Nordwestdeutsches Funktionalanalysis-Kolloquium

Das Nordwestdeutsche Funktionalanalysis-Kolloquium (NWDFAK) wurde 1985 von den Professoren K. Floret und H.G. Tillmann gegründet. Seitdem wird es im jährlichen Wechsel von mehereren Universitäten - darunter Oldenburg, Paderborn, Münster, Bielefeld, Dortmund uvm. - veranstaltet. Ziel der Tagungsreihe ist es, Forschende aus dem Bereich der Funktionalanalysis sowie aus ihren Andwendungsgebieten und angrenzenden mathematischen Disziplinen zusammenzubringen.

Samstag, 27. Juni 2026, TU Dortmund

Die 45. Sitzung des Nordwestdeutschen Funktionalanalysis-Kolloquiums findet am Samstag den 27. Juni 2026 an der TU Dortmund statt.

Registrierung zum 45. NWDFAK in Dortmund

Falls Sie teilnehmen wollen, registrieren Sie sich bitte unter:
Registrierung zum 45. NWDFAK in Dortmund

Veranstaltungsort

TU Dortmund
Campus Nord
Raum TBA

Zeitplan

09:30 - 10:00 Kaffee und Tee
10:00 - 10:50 Christian Meyer
10:50 - 11:40 Konstantin Pankrashkin
11:40 - 12:00 Kaffeepause
12:00 - 12:50 Jürgen Saal
12:50 - 15:00 Gemeinsames Mittagessen bei TBA
15:00 - 15:50 Jochen Glück
15:50 - 16:40 Sven-Ake Wegner
16:40 - 17:00 Kaffee und Tee

Vorträge

Christian Meyer (Dortmund): Optimal Control of the Poisson Equation with Wasserstein Regularization
Optimal control problems with controls in the space of regular Borel measures have gained significant interest in the recent past. The standard approach to guarantee the existence of solutions is to add a Tikhonov regularization term in form of the total variation resp. Radon norm to the objective. In contrast to this, we consider a Wasserstein distance (or more generally a transport distance) to a given prior as regularizer. Existence of optimal solutions is shown and first-order necessary optimality conditions are derived. The latter are used to deduce structural a priori information about the optimal control and its support based on properties of the associated optimal transport plan. Depending on the data of the problem, e.g., structure of the transportation costs, regularity of the prior, and smoothness of the domain, the characteristics of optimal solutions are shown to substantially differ from case to case.
Konstantin Pankrashkin (Oldenburg): MIT bag operator in non-smooth convex domains
The MIT bag operator was introduced to describe quark confinement within hadrons. Mathematically, it corresponds to the Dirac operator in bounded domains with special (local) boundary conditions, which can be seen as a relativistic analog of the Dirichlet Laplacian. We show that many results on the Dirac operator with MIT bag boundary conditions in smooth domains (in particular, the $H^1$-regularity of the operator domain) can be carried over to the case of convex domains.
Jürgen Saal (Düsseldorf): Dynamical Systems, Global Attractors, and Maximal Regularity
The theory of dynamical systems is in most instances very general. Important properties of an existing attractor for many systems can be verified in a direct manner. In this talk we raise the question, to what extend for more specific classes of PDE such kind of properties follow directly from their structure. Of particular interest in this context are quasilinear parabolic $C^1$ evolution systems. Based on maximal regularity we will be able to show that for suitable but still fairly general subclasses properties like injectivity of a corresponding semiflow, existence of a dynamical system, globality and finite dimensionality of the attractor can be deduced in an abstract manner. We also demonstrate how the obtained abstract theorem applies to concrete PDE, by considering exemplary a system describing living fluids.
Jochen Glück (Wuppertal): Maximal inequalities and order bounds
A sequence of operators $(T_n)$ on an $L^p$-space is said to satisfy a maximal inequality if there exists a number $M \ge 0$ such that $\|\sup_{n\ge 0}|T_nf |\|_p \le M \|f \|_p$ for all $f\in L^p$. Such inequalities are an important and classical tool in harmonic analysis and ergodic theory. This talk has three goals: (a) We motivate maximal inequalities by showing one of their classical applications to the long-term behaviour of dynamical systems. (b) We discuss a more abstract interpretation of maximal inequalities in terms of order bounds. (c) We outline a recent result on the relation between maximal inequalities and the spectral theory of positive operators.
Sven-Ake Wegner (Hamburg): A homological approach to (Grothendieck's) completeness problem for regular LB-spaces
It is well-known that every complete $LB$-space(=countable inductive limit of Banach spaces) is regular, i.e., for every bounded $B \subset X = ind_{n\in\mathbb{N}}X_n$ there exists $n\in \mathbb{N}$ such that $B \subset X_n$ and $B$ is bounded in $X_n$. The question of whether the converse holds traces back to Grothendieck's early work in functional analysis and has remained open since the 1950s. In the talk, we first define the categories $LB_{com}$ and $LB_{reg}$ of all complete and, respectively, all regular $LB$-spaces; then we define their bounded derived categories $D^b(\cdot)$. The latter is a standard tool in algebra, topology and geometry, but it must be carefully adapted to our situation. We outline its definition and then formulate a ‘homologification’ of Grothendieck's original question by asking whether (at least) the derived categories of $LB_{com}$ resp. $LB_{reg}$ are equivalent. Clearly, a negative answer would imply a negative answer to the original problem, while a positive answers to the derived version would suggest that the original problem may have an affirmative answer. Using a variant—the so-called ‘relative’ derived category—the same paradigm applies and here we are able to show that $D^b(LB_{com}) \simeq D^b(LB_{reg})$ indeed holds.

Das Kolloquium wird organisiert von Ivan Veselic und Marco Vogel.

Vorherige Ausgaben

Kontakt

Adresse

TU Dortmund
Fakultät für Mathematik
Lehrstuhl IX
Vogelpothsweg 87
44227 Dortmund

Sie finden uns auf dem sechsten Stock des Mathetowers.

Sekretariat

Janine Textor (Raum M 620)

Tel.: (0231) 755-3063
Fax: (0231) 755-5219
Mail: janine.textor@tu-dortmund.de
Bürozeiten:
Di. und Do. von 8 bis 12 Uhr
Home Office:
Mo. und Fr. von 8 bis 12 Uhr