The weekly colloquium takes place every Tuesday at 4:45 pm in Emmy-Noether-Hörsaal H13, Cauerstr. 11, 91058 Erlangen.
For the talks marked with * we provide a brief introduction for students and doctoral researchers starting already at 4pm in H13.
Speaker: Prof. Lukas Woike (Dijon) – invited by: Prof. Meusburger
Abstract: In my talk, I will first provide an overview of the algebraic and topological tools of two-dimensional conformal field theory. These include concepts such as spaces of conformal blocks, modular functors, and consistent systems of correlators. Subsequently, I will explain how these objects can be constructed and classified in the strongly rational case (the TFT construction by Fuchs, Runkel, and Schweigert). The remainder of the talk will then be devoted to solutions that go beyond the strongly rational case. These rely on a tool from algebraic topology, namely factorization homology, that allows us to integrate braided categories over surfaces. This is partly based on joint work with A. Brochier (Paris Cité) and Lukas Müller (LMU).
Speaker: Eva-Maria Hekkelman (MPI Bonn) – invited by: Prof. Schulz-Baldes
Abstract: Musical intervals which sound pleasant, consist of frequencies that are some rational multiple of one another. In recent work with Malte Leimbach and Oliver Fürst, we have shown that generically, the sound of a drum (or manifold) contains no such harmonies at all. This has implications for a recent physics-inspired research programme initiated by Connes and Van Suijlekom in noncommutative geometry. In my talk, I will try to explain how geometry and sound are connected, how this led to the development of noncommutative geometry, and what relevance these ideas have for physics.
Speaker: Frank den Hollander (Leiden) – invited by: Andreas Greven
„Abstract: In this talk I present an overview of what is known and is not known about random
processes on dynamic random graphs in co-evolution, i.e., with mutual feedback. The
literature offers plenty of heuristics, simulations and conjectures, but so far
mathematical results are extremely scarce. I describe some of these results, with a focus
on opinion dynamics. In particular, I consider random graphs in which vertices can have
one of two possible opinions. Pairs of vertices connected by an edge share their opinions
according to a rate that may depend on the size of the graph. Each edge turns on or off
according to a rate that depends on whether the vertices at its two endpoints have the
same opinion or not. I exhibit joint evolution equations and describe the occurrence of
phase transitions between consensus and polarisation.“
Speaker: Katharina Kirsten (Uni Münster) – Invited by Prof. Lindmeier.
Abstract: Die eigenständige Konstruktion von Beweisen stellt für viele Erstsemesterstudierende eine Herausforderung dar. Schwierigkeiten treten dabei unter anderem im Zusammenhang mit fehlendem konzeptuellem, methodischem oder strategischem Wissen auf. Dies wird beispielsweise dann deutlich, wenn die zu zeigende Aussage nur oberflächlich betrachtet wird, der formulierte Beweis Zirkelschlüsse enthält oder Skizzen wenig gewinnbringend genutzt werden. Der Erwerb solcher beweisrelevanter Wissenselemente verläuft im Hochschulkontext überwiegend implizit: Studierende lernen Beweise zu konstruieren, indem sie sich mit in der Vorlesung oder in Lehrbüchern präsentierten Beweisen beschäftigen. Entsprechend wird gefordert, dass Studierende die präsentierten Beweise verstehen, zentrale Merkmale eines Beweises prüfen und hieraus Erkenntnisse ableiten, die sie für zukünftige Beweiskonstruktionen nutzen können. Im Vortrag wird ein Überblick über aktuelle Forschungserkenntnisse zu diesem intendierten Lernmechanismus gegeben. Insbesondere werden dabei die Aktivitäten des Verstehens und Validierens fokussiert und potenzielle Hürden diskutiert. Hieraus lassen sich sodann konkrete Implikationen ableiten, wie die eigenständige Beweiskonstruktion unterstützt werden kann.
Speaker: Tilman Sauer (Uni Mainz) – invited by: Emil Wiedemann
Speaker: David Gontier (Ecole Nationale des Ponts et Chaussées, Paris) – invited by: Prof. Schulz-Baldes
Abstract: I will talk about the Keller inequality, which concerns the optimization of the first eigenvalue of an operator depending on an external potential, under some Lp constraints on this potential. I will provide a novel technique which allows to tackle the problem both for all kinds of operators, including Schrödinger and Dirac, and which provides interesting numerical schemes for this optimization problem.
This is joint work with Hanne Van Den Bosch, Jean Dolbeault, and Fabio Pizzichillo.
Speaker: Michael Coons (Aarhus) – invited by: Christoph Richard
Abstract: In the 1940s, Salem proved that the graph of the Minkowski ?-function is singular continuous. He did this as an example of a more complicated singular continuous function that was not related to weighted coin flips, the first objects of his paper. In this talk, we will relate Minkowski’s function to the Stern sequence and show that this example is not as far away as Salem suggested. Indeed, we give a new proof his result by using properties of a pair of small nonnegative integer matrices. In particular, this follows since the maximal Lyapunov exponent of this pair of matrices is strictly greater than log 2.
Speaker: Neil Manibo (Bielefeld) – invited by: Christoph Richard
Abstract: In this talk, I will give a brief history and walk through modern developments in the mathematical theory of aperiodic order through the lens of spectral theory. Aperiodic order studies structures that are non-periodic, yet exhibit long-range positional order, making them viable models for quasicrystalline matter. Within mathematics, this research area connects several fields including harmonic analysis, discrete geometry, ergodic theory, number theory, algebra, combinatorics, and functional analyis to name a few. I will explain how aperiodic tilings (such as the well-known Penrose tilings, the Hat tilings, and the newly-discovered 3D-monotilings based on the chair tiling) can be viewed as mathematical quasicrystals. At the end of the talk, we will discuss the state-of-the-art regarding the exclusion of absolutely continuous spectrum for some of these tiling models, which immediately distinguishes them from structures with inherent level of randomness.