Quantum optimal transport is a flourishing research field these days with several different approaches and interpretations ranging from semi-classical to free probabilistic, and from static to dynamic, respectively.
The theory of automorphic forms is a dynamically expanding part of number theory with an increasing number of connections and applications to other branches of mathematics as well as physics. Research is driven by long standing conjectures and unexpected breakthroughs.
The semester focuses on discrete structures and their limits. This is an active area of research that connects discrete mathematics with ergodic theory, stochastic processes, spectral theory, measured group theory and various branches of analysis and topology.