Vorträge in der Woche 06.01.2025 bis 12.01.2025

Donnerstag, 09.01.2025: Insights on Michel charges in the asymptotically hyperboloidal setting and their evolution

Anna Sancassani und Saradha Senthil-Velu (Universität Tübingen)

We consider asymptotically hyperboloidal initial data sets (M, g, K), with background data (H3,b,b), where (H3,b,b) is the standard hyperboloid embedded in Minkowski. We compute charges with respect to the KIDs of this background as done in Michel (B. Michel, Geometric invariance of mass-like asymptotic invariants, arxiv.org/abs/1012.3775). With appropriately chosen asymptotics and direction of evolution, we find that the behaviour of these charges is very similar to that in the null setting. This could shed some light on the physical interpretation of these charges on asymptotically hyperboloidal initial data.

Donnerstag, 09.01.2025: Exponential tail estimates for quantum lattice dynamics

Dr. Christopher Cedzich (Uni Düsseldorf)

We consider the quantum dynamics of a particle on a lattice for large times. Assuming translation invariance, and either discrete or continuous time parameter, the distribution of the ballistically scaled position $Q(t)/t$ converges weakly to a distribution that is compactly supported in velocity space, essentially the distribution of group velocity in the initial state. We show that the total probability of velocities strictly outside the support of the asymptotic measure goes to zero exponentially with $t$, and we provide a simple method to estimate the exponential rate uniformly in the initial state.

Donnerstag, 09.01.2025: Local Topological Quantum Order in the Hexagonal Lattice AKLT Model

Thomas Jackson (UC Davis)

Using the Kotecky-Preiss criterion for convergence of cluster expansions we prove the local indistiguishability of the finite-volume ground states for the AKLT model on the hexagonal (honeycomb) lattice. This proves this two-dimensional SU(2)-invariant ground state possesses local topological quantum order (LTQO), which is one of the key assumptions needed to show the stability of the spectral gap above the ground state against local perturbations. We also prove these results hold true for decorated hexagonal lattices for all decoration numbers d>0.

Freitag, 10.01.2025: Einführung in die (topologische) K-Theorie

David Seez M.Sc. (Uni Tübingen)