Alpha-induction is a tensor functor producing a new fusion category from a modular tensor category and a Q-system. This can be formulated in terms of quantum 6j-symbols and braiding and gives alpha-i...
In a first part - after recalling some basics of proof theory, namely what is a formal proof - we will introduce the key concept of Realisability. The Brouwer-Heyting-Kolmogorov (BHK) interpretation o...
The small-world effect is a universal feature used to explain many different phenomena like percolation, diffusion, and consensus. Starting from any regular lattice of N sites, the small-world effect ...
Starting from Mordell, many conjectures have been put forward (and proved) about how geometry influences the behaviour of diophantine problems. It turns out that many of them can be put in a common fr...
Let G be a connected reductive group over an algebraically closed field. A challenging task is the computation of the (intersection) cohomology of the moduli space of G-Higgs bundles over a curve. One...
Given the moduli space of hyperplanes in projective space, V. Alexeev constructed a family of compactifications parametrizing stable hyperplane arrangements with respect to given weights. In particula...
The role of automorphic forms as intertwiners between various representations of free group factors was discovered a long time ago by Vaughan Jones, starting with a remarkable formula relating Peterso...
For many known families of algebro-geometric objects indexed by natural numbers (symmetric groups, braid groups, ...), a phenomenon known as homological stability happens: their homology H_d(X_n) beco...
Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiolog...
In this talk, we will describe how to construct a basis of Bott-Samelson bimodules, called singular light leaves. Bott-Samelson bimodules are algebraic objects that correspond geometrically to resolut...
