08. Februar 2023, 17:15-19:00
Uhrturmhörsaal der Physik
Zuvor findet um 16:45 Uhr die Teerunde in Raum 244 des Mathematikgebäudes (S2|15) Schlossgartenstr. 7, statt.
zu 1.) Prof. Dr. Volker Betz, TU Darmstadt
Spin systems are widely used in mathematical physics as models for materials, magnetism or solids. Mathematically, they consist of a large number of (typically rather simple) random variables (the ’spins’) that are embedded into some spatial structure and interact with their nearest neighbours. The strength of the interaction is encoded by a real number that is called the order parameter. The collective, large scale behaviour of such spin systems often exhibits a phase transition: in the limit of infinitely large systems, some key quantity (often the correlation length) changes in a non-smooth way at a certain value of the order parameter. Physically, this corresponds to spontaneous magnetization, or to the transition between water and ice. Hugo Duminil-Copin was awarded the Fields medal for, among other things, a large number of significant breakthroughs in the field of spin systems. His methods often combine geometrical, combinatoric and algorithmic ideas with probabilistic methods, and are at the same time highly original and surprisingly accessible (on the surface). In my talk, I will focus on one specific result of his and try to describe the model, the result, and the main ideas and ingredients of the proof.
zu 2.) Prof. Dr. Jan Hendrik Bruinier, TU Darmstadt
James Maynard was awarded a Fields Medal in 2022 for his contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation. In this colloquium lecture we will give an introduction to his work on the finer structure in the distribution of primes, including his breakthrough results on pairs of primes with bounded distance.