# Seminars

## Noa Zilberman, 2019/02/07, 14h 30m, Quantum effects near the inner horizon of a black hole

The analytically extended Kerr and Reissner-Nordström metrics, describing respectively spinning or spherical charged black holes (BHs), reveal a traversable passage through an inner horizon (IH) to another external universe. Consider a traveler intending to access this other universe. What will she encounter along the way? Is her mission doomed to fail? Does this other external universe actually exist?

## Ismar Volic, 2019/01/16, 15h, Cohomology of braids, graph complexes, and configuration space integrals

I will explain how three integration techniques for producing cohomology classes — Chen integrals for loop spaces, Bott-Taubes integrals for knots and links, and Kontsevich integrals for configuration spaces — come together in the computation of the cohomology of spaces of braids. The relationship between various integrals is encoded by certain graph complexes. I will also talk about the generalizations to other spaces of maps into configuration spaces (of which braids are an example).

## Marco Mackaay, 2019/01/10, 15h, The 2-representation theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations

I will first recall Lusztig's asymptotic Hecke algebra and its categorification, a fusion category obtained from the perverse homology of Soergel bimodules. For example, for finite dihedral Coxeter type this fusion category is a 2-colored version of the semisimplified quotient of the module category of quantum $\operatorname{sl}(2)$ at a root of unity, which Reshetikhin-Turaev and Turaev-Viro used for the construction of 3-dimensional Topological Quantum Field Theories.

## Gonçalo Oliveira, 2018/12/19, 16h, Yang-Mills flow and calibrated geometry

This is a report on joint work with Alex Waldron.

The Yang-Mills functional is the most studied functional on the space of connections on a vector bundle over an oriented Riemannian manifold. Its negative gradient flow leads to a semi-parabolic PDE known as the Yang-Mills flow.

## Daniel Gonçalves, 2018/12/17, 15h, Inﬁnite alphabet ultragraph edge shift spaces: relations to $C^\ast$-algebras and chaos

We explain the notion of ultragraphs, which generalize directed graphs, and use this combinatorial object to deﬁne a notion of (one-sided) edge shift spaces (which, in the ﬁnite case, coincides with the edge shift space of a graph). We then go on to show that these shift spaces have some nice properties, as for example metrizability and basis of compact open sets.