Das Mathematische Kolloquium ist eine gemeinsame wissenschaftliche Veranstaltung des gesamten Mathematischen Instituts. Es steht allen Interessierten offen und richtet sich neben den Mitgliedern und Mitarbeitern des Instituts auch an die Studierenden. Das Kolloquium findet dreimal im Semester am Donnerstag um 15:00 s.t. im Hörsaal II, Albertstr. 23b statt. Danach (gegen 16:15) gibt es Kaffee und Kekse, zu dem der vortragende Gast und alle Besucher eingeladen sind.
Recent Developments in Namba Forcing
Donnerstag, 6.11.25, 15:00-16:30, Hörsaal 2
I will discuss work done in Freiburg on a technique called Namba forcing. This technique was originally used by Namba and Bukovsky to, in essence, demonstrate certain differences between the cardinals \(\aleph_0\), \(\aleph_1\), and \(\aleph_2\). I found an argument for what is called ``the weak approximation property,'' which, in the context of forcing, means that certain functions are not added in the extension. In joint work with Heike Mildenberger and with Hannes Jakob, this led to the resolution of some longstanding open questions in PCF theory, which concerns the study of singular cardinals. With a similar argument I solved an old question about the minimality of forcing extensions. The talk is not meant to be technical, but rather an overview of what is happening in the area.
How to grasp Emmy Noether’s approach to mathematics (and physics)
Donnerstag, 27.11.25, 15:00-16:30, Hörsaal 2
Fluctuations in Continuum
Donnerstag, 4.12.25, 15:00-16:30, Hörsaal 2
Fluctuations are ubiquitous in real world contexts and in key technological challenges, ranging from thermal fluctuations in physical systems to algorithmic stochasticity in machine learning and fluctuations driven by small-scale weather patterns in climate dynamics. At the same time, such complex systems are influenced by a multitude of factors, relying on a wide range of parameters and interactions. This motivates the exploration of scaling limits and continuum dynamics. A systematic understanding of such interplay of stochasticity, complex dynamical behaviour, and continuum limits seeks to reveal universal properties, irrespective of the specific details of the systems in question. In this presentation we will examine the importance of modelling fluctuations in large systems through several examples, ranging from non-equilibrium thermodynamics to stochastic fluid dynamics and machine learning. We will demonstrate how their analysis uncovers deep connections between probabilistic features, partial differential equations with irregular coefficients, and geometric structures in the form of gradient flows on infinite dimensional manifolds.
Emile Borel and the probabilistic turn of a worried Cantorian
Donnerstag, 8.1.26, 15:00-16:30, Hörsaal 2
In this talk, I shall present the singular way in which Émile Borel, from his studies on the structure of real numbers and a certain rejection of Cantor's abstract vision, found in the calculus of probabilities an adequate tool to formulate a new approach to problems. At the same time, he became aware of its usefulness for the study of phenomena of physics and society and developed a singular viewpoint on the concept of probability, merging subjectivist and objectivist aspects under an idiosyncratic formulation of the so-called Cournot principle.
Combining potential theory with general relativity: a divergence theorem-based approach to proving geometric inequalities
Donnerstag, 5.2.26, 15:00-16:30, Hörsaal 2