Kolloquium SS 2025
Speaker: Ricardo Correa da Silva, Friedrich-Alexander-Universität Erlangen-Nürnberg – Invited by G. Lechner
Abstract: Quantum Field Theory is the most precise physical theory to date, yet its mathematical foundations are still under development. In this talk, we explore (non) locality and its connection to real subspaces of a complex Hilbert space from the perspective of Algebraic Quantum Field Theory. We will also discuss how these subspaces can be used to construct local nets of von Neumann algebras, ensuring they satisfy essential properties relative to the vacuum vector.
Speaker: Joachim Cuntz, Universität Münster – Invited by K. Li
Abstract: In algebraic topology one can distinguish topological spaces by their homology or cohomology invariants. A compact or locally compact space X is completely described by the algebra of continuous complex-valued functions on X. This algebra is a commutative C*-algebra. C*-algebras are charcterized by the fact that they can be isomorphically represented by bounded operators on Hilbert space. Now, K-theory is a very powerful cohomology theory that can be extended from commutative C*-algebras (locally compact spaces) to arbitrary C*-algebras. In fact in this setting K-theory even becomes more natural and one gains access to a whole new array of techniques and applications. In this talk we will try to explain some of the new methods and applications.
Speaker: Tomoyuki Arakawa, Kyoto University – Invited by P. Fiebig and T. Creutzig
Abstract: The 4-dimensional quantum field theory (4D QFT) in theoretical physics is conceptually rich and produces many interesting mathematical objects, although a fully rigorous mathematical definition of the theory itself is still lacking. Quite recently, it was discovered that to each 4D N=2 superconformal field theory, one can associate a representation-theoretic object called a vertex algebra, which serves as an invariant (or observable) of the theory. Although vertex algebras are purely algebraic in nature, those arising as invariants of 4D QFT exhibit intriguing connections with certain geometric objects that also appear as invariants of the same physical theory.
In this talk, I will discuss some examples of such phenomena.
Speaker: Martin Wendler, Otto-von-Guericke-Universität Magdeburg – Invited by M.-C. Düker
Abstract: For functional data time series (i.e. a series of functions observed over time), it is often recommended to use dimension reduction or regularization techniques. But with the help of probability theory in Hilbert-spaces, it is also possible to use the full functional information without dimension reduction. In the talk, I will discuss how tests for change-point detection can be generalized to observations that take values in a Hilbert-space. In order to obtain critical values, one can use different types of Bootstrap, which are based on the Monte-Carlo-Method.
Speaker: Sergiy Neshveyev, University of Oslo – Invited by G. Lechner
Abstract: Representation theory studies realizations of groups by unitary operators, more generally, realizations of algebras by bounded operators on Hilbert spaces. To a group or an algebra, one then associates two topological spaces encoding the representations – the unitary dual and the primitive dual equipped with Zariski-type topologies. These spaces have been computed in many cases as sets, but not that much is known about their topology. The talk will review the history of the problem and some recent progress on it, concentrating eventually on semidirect products and algebras arising from dynamical systems.
Speaker: Volker Schomerus, Universität Hamburg – Invited by T. Creutzig
Abstract: Hermann Weyl’s seminal 1928 book {\it The Theory of Groups and Quantum Mechanics} ({\it Gruppentheorie und Quantenmechanik}) marked the beginning of a profound and fruitful interplay between group theory and quantum physics. Over the decades, mathematical methods from group and representation theory have become essential tools in understanding quantum systems, with applications ranging from the analysis of atomic spectra to the modern conformal bootstrap program in conformal field theory. Remarkably, the connection also works in the opposite direction.
Through constructions developed by Gaudin and Hitchin, group-theoretic problems can be systematically embedded into the framework of quantum integrable models. This perspective opens up new avenues for progress in group and representation theory, inspired and informed by recent advances in the study of quantum integrable systems.
Speaker: Magdalena Elena Musat, University of Copenhagen – Invited by K. Li
Abstract: I will discuss recent developments in the analysis of quantum correlations and their deep interconnections with the multi-faceted Connes-Kirchberg Problem in operator algebras, leading also to infinite dimensional phenomena in quantum information theory.
Speaker: Willy Dörfler, Karlsruher Institut für Technologie – Invited by E. Bänsch and N. Neuß
Abstract: Die Landau–Lifshitz–Gilbert-Gleichungen (LLG) sind ein Modell zur Beschreibung Mikromagnetischer Phänomene wie sie etwa in magnetischen Sensoren oder Speichern auftreten. Dabei wird die Magnetisierung durch externe elektromagnetische Felder erzeugt, d. h., hier ist es nötig LLG mit dem Maxwell-System zu koppeln (MLLG). Die Analysis und die Numerik der LLG und MLLG Gleichungen ist sehr anspruchsvoll. Der Vortrag soll Einblicke in vergangene und aktuelle Forschung geben.
(Die Veranstaltung findet um 13.30 Uhr im Besprechungsraum 01.382 statt)
Speaker: Ulrike Meier-Robisch und Sylvia Stark (Seminarlehrerinnen), Staatliche Realschule Herzogenaurach – Invited by M. Linsner and J. Schindler
Diese Veranstaltung richtet sich an alle Studierenden, die einen Einblick in den Schulalltag einer Mathematiklehrkraft gewinnen möchten, unabhängig davon, welche Schulart Sie studieren.
Es wird aufgezeigt, wie sich der zu haltende Mathematikunterricht an der Realschule von dem an der Universität erworbenen mathematischen Fachwissen unterscheidet. Spannend wird es, wenn eine Abschlussprüfung für Realschülerinnen und Schüler betrachtet wird.
Für Studierende im Realschullehramt Mathematik, die neugierig sind, was sie im Referendariat erwartet, berichten zwei Seminarlehrerinnen über den Vorbereitungsdienst und die sich daran anschließende Tätigkeit als Mathematiklehrkraft. Es wird u.a. darauf eingegangen, wie das Referendariat zeitlich aufgebaut ist und welche Ausbildungs- und Prüfungsbestandteile enthalten sind. Weiterhin wird erklärt, wieviel Stunden zu unterrichten sind und welcher Arbeitsaufwand zu erwarten ist.
Dem Vortrag schließt sich die Möglichkeit zu Fragen und Diskussion unter allen Teilnehmenden an. Anschließend kann dies bei Kaffee und Tee fortgesetzt werden.
Studierende, die teilnehmen möchten, können sich bis zum 10.07.25 anmelden:
https://www.studon.fau.de/studon/go/crs/5706975
Studierende und alle anderen Interessenten können im Vorfeld Fragen einreichen.
Mailen Sie dazu an: ssc@math.fau.de
Speaker: Albrecht Kliem, Wirsberg-Gymnasium Würzburg – Invited by E. Wiedemann
Abstract: Mathematik lebt von der Faszination, die von interessanten Problemen ausgeht. Gerade in der Schulzeit können gehaltvolle Mathematikaufgaben die Begeisterung von Jugendlichen wecken. Im Vortrag wird dies an unterschiedlichsten Aufgaben von Mathematikwettbewerben deutlich.
Die Beispiele stammen aus 30 Jahren Erfahrung in der Arbeit mit begabten Schülerinnen und Schülern und zeigen die Wirkmächtigkeit gut gestellter Herausforderungen.
Speaker: Peter Bastian, Universität Heidelberg – Invited by E. Bänsch, C. Gräser and N. Neuß
Abstract: High mountain catchments convert glacier melt, snow melt and liquid precipitation into surface runoff. Part of the surface runoff recharges the groundwater aquifer, while the remaining part appears as surface discharge at the valley outlet. Being considered unimportant initially, it is now established that groundwater, and not just surface water, plays a critical role in mountain hydrogeology by supplying baseflow in rivers. In this contribution we will present a mathematical model to describe shallow coupled surface-subsurface flow in mountain catchments, consider its numerical solution and discuss a case study of a glacierised catchment in the cold-arid region of Ladakh, Trans-Himalaya, India.