2024/2025🔗

Tomasz Miller🔗

Jagiellonian University

Date: 15th of October 2024

Title: Causal evolution of probability measures and continuity equation

Abstract: One of the most important concepts of relativistic physics is that of a world line, i.e., the space-time trajectory of a point particle. In Lorentzian geometry, it is modelled by the so-called causal curve, and the questions concerning which spacetime points can be connected by means of causal curves lead to a vast area of study known as causality theory. In the talk, I will present how the basic notions of causality theory can be naturally extended to probability measures on spacetimes (what is motivated by both classical and quantum physics). In particular, I will discuss the notion of a causal evolution of probability measures, its deep connection with the continuity equation (known from elementary physics) and a surprisingly nice topological properties of the space of causal curves.

Maksymilian Safarewicz🔗

Warsaw University of Technology

Date: 8th of October 2024

Title: Isoperimetric inequalities

Abstract: This presentation explores isoperimetric inequalities, which are fundamental results in mathematics linking the area of a shape to its perimeter. We will discuss the historical context and significance of these inequalities, highlighting classical results such as the isoperimetric theorem in the plane, which asserts that among all simple closed curves with a given length, the circle encloses the maximum area. Additionally, we will examine various extensions and generalizations of these inequalities. The presentation aims to provide a comprehensive overview of the principles underlying isoperimetric inequalities.