Schedule

Title: Index theory for solid state systems: from Jean's findings to more recent developments

Title: Ring states as a probe of topology

Abstract: Topological bands host stable mid-gap impurity states. These states carry a canonically gauge-fixed spinor whose Bloch texture provides an exact pointwise image, Φ:S2→S2, of the host band’s texture. I will discuss experiments on a silicon-based resonator network that characterize these mid-gap states and present results on the topological bounds governing their spatial footprint.

Titel: Consistent symmetry breaking and topological phases

Abstract: Operators that are invariant under a symmetry group are also invariant under any of its finite-index subgroups. The K-theory equivariant indices for these subgroups must be consistent under the process of "symmetry breaking", that is, the natural inclusion maps between the C*-algebras generated by invariant operators. This yields a diagram of C*-algebras and their K-theory groups, whose directed colimit provides a dichotomy of weak/strong K-theory elements that occur in time-reversal symmetric topological insulators. This is based on joint work with Guo Chuan Thiang (Peking University).

Titel: The Deift Conjecture and Generalized Almost Periodicity

Abstract: This talk will present joint work with Long Li and Nicolae Strungaru on a new perspective on the Deift conjecture. This conjecture states that the Korteweg-de Vries (KdV) equation with almost periodic initial data admits global solutions that are almost periodic in space and time. There has been exciting progress on this conjecture in the past couple of decades. The status quo is that it has been confirmed for suitable classes of almost periodic initial data, and it has also been realized that almost periodic initial data may develop discontinuities, which are incompatible with Bochner/Bohr almost periodicity. Our work is motivated by recent work of Daniel Lenz, Timo Spindeler, and Nicolae Strungaru on the characterization of structures with pure point diffraction  - the central property in mathematical quasicrystal theory. It had been understood for a long time that Bochner/Bohr almost periodicity is not the right notion in the diffraction context, but Lenz-Spindeler-Strungaru have only recently realized precisely which almost periodicity notions are the correct ones when studying and even characterizing key properties in diffraction theory. Armed with these realizations, we give the Deift conjecture a fresh look.

Titel: AI in Computational Condensed Matter Physics: From Materials Discovery to Machine-Learned Density Functionals

Abstract: Artificial intelligence is opening new routes to materials discovery and atomistic simulation. This talk explores its integration with density functional theory, covering high-throughput materials screening, symmetry-equivariant interatomic potentials, and Hamiltonian learning. Particular emphasis is placed on implementing the nonlocal Skala exchange-correlation functional in CP2K for molecular and periodic systems. We discuss complementary approaches based on atom-centered quadrature and native computational grids, highlighting the challenges of nonlocality, numerical convergence, and compatibility with GPW and GAPW methods. Preliminary results illustrate the potential of machine-learned density functionals while emphasizing the importance of physically consistent implementations and GPU acceleration for practical large-scale simulations.

Titel: Spectral flow distinguishes 1-d quasicrystalline topological insulators

Abstract: Aperiodic materials have a richer topological phase structure than periodic ones. These phases distinguish different classes of aperiodic materials. For 1-dimensional materials, this can be analysed by looking at a spectral flow of their edge eigenvalues. In this way we can distinguish, among quasicrystals, those which are entirely determined by their Bragg spectrum, like for instance the Fibonacci chain, from the others, like the period doubling chain, where there are phases which cannot be predicted by Bragg diffraction.