This grant application proposes the establishment of Ultrafast Low-Energy Electron Diffraction (ULEED) as a novel and versatile approach to investigate ultrafast structural dynamics at surfaces and in ultrathin films. Two-dimensional systems such as surfaces and molecular monolayers exhibit a multitude of intriguing phases and complex transitions. Studying the ultrafast dynamics of these materials elucidates correlations and microscopic couplings, but the access to structural degrees of freedom with ultrahigh time resolution remains challenging. Low-Energy Electron Diffraction (LEED) is a powerful technique in surface science to determine the atomic-scale structure and symmetry of surfaces. However, time-resolved LEED has proven exceedingly difficult to realize, owing to the problems in realizing suitable low-energy electron pulses of sufficiently short pulse duration and high beam quality. This project targets both of these present limitations by using laser-triggered nanoscopic electron sources to generate high-brightness beams of low-energy electrons. Specifically, nanotip cathodes driven by nonlinear photoemission will be integrated in compact micro- and nanofabricated electrostatic lens assemblies. This will allow for a drastic reduction of electron beam propagation distances while maintaining a high level of beam control and focusing ability. Using this electron source, we plan to develop a laser-pump/electron-diffraction-probe setup at low electron energies with a temporal resolution of few hundred femtoseconds and less. A number of strategies will be followed to improve the temporal resolution of the setup, including wavelength-tuning of the laser excitation and active spectral compression of the electron pulses using locally enhanced THz fields. We will apply ULEED in the investigation of the structural dynamics within a range surface systems, including molecular monolayers, intrinsic surface reconstructions and adsorbate-induced charge-density waves.

Chirality, describing the “handedness” of a system, is a fundamental property of physical entities such as magnets, spins, the DNA double-helix, or circularly and elliptically polarized light. This proposal aims at employing intense ultrashort laser fields to control the chirality of two physical entities: photons of extreme-UV high harmonics, and free-flying electrons in a coherent pulsed beam. Specifically, the proposal “UCHIRAL” entails two main objectives: First, we develop a bright ultrafast source of circularly polarized extreme-UV high harmonics with optically controlled helicity (left vs. right) by combining the applicant's expertise with chiral harmonics with the host's efficient source. We will then use these chiral extreme-UV pulses for imaging of nanoscale magnetic features in ferromagnetic metals, which is currently inaccessible for high harmonics. The difference between images acquired with left- vs. right-circularly polarized extreme-UV radiation can isolate magnetic effects from a non-magnetic background. In a second system, we will coherently convert the chirality of optical near-fields into orbital angular momentum of a beam of free electrons. This interaction will be mediated by designed nanostructures exhibiting surface plasmon-polariton excitations with optically-controlled chirality. The envisaged mechanism relies on optical phase control of free electron wave functions in an ultrafast transmission electron microscope, which was recently established in the host institute. Both aspects of the proposal address fundamental interactions of chiral light with matter, currently at different levels of maturity, with expected scientific and potentially industrial applications. In particular, ultrafast chiral microscopy based on photons (first objective) and electrons (second objective) may enable future technologies by tracking chiral dynamics in nanosystems with intrinsic handedness, ranging from magnetic storage materials to biomolecules.

SoundKnowledge aims to rethink, for the first time, music in terms of the procedural knowledge inherent in and specific to music-making by exploring music-making as knowledge practices in Micronesia, Western Pacific Island world. This knowledge, formed in the performance of musical practice, may prove to be key to survival in the complex postcolonial predicament of Micronesia. I will address the issues of climate change, social alienation and postcolonial trauma in specific parts of Micronesia by fleshing out the nature and dynamics of that knowledge both conceptually and ethnographically. The systematic analysis of music as knowledge will allow me to identify strategies to foster resilience in the face of these urgent crises. At the same time, it will offer a first-of-its-kind theorization of the procedural knowledge inherent in and specific to music-making. The knowledge of music is self-referential and forms multilayered connections and ruptures with pasts, presents and futures and surrounding orders of knowledge. SoundKnowledge asks what Western Pacific musical practices know and how do they know it, how music-making makes this knowledge operable and how humans mobilize upon this knowledge in coping with their life-world through music. The project, therefore, explores how music functions as a distinct epistemic form that is often referred to as the proverbial power of music. Music research has the tools to unlock this power, and SoundKnowledge intends to plough a path here. SoundKnowledge provides insights into the specific knowledge of Western Pacific music in its entanglement with pressing cultural and social issues of the early 21st century. In contributing to the theoretical debate on the knowledge of music, the project probes vital questions of knowledge resources and human futures. SoundKnowledge will also instigate change: In collaboration with local institutions, the research results will be used towards the development of community action strategies.

The last decade has seen remarkable progress in the study of growth in infinite families of groups. The main approach has its roots in additive combinatorics, but has truly given fruit in a non-commutative context. It is becoming clear that the central role is played not by groups in isolation, but by actions of groups. It is from this perspective that my plan addresses, at the same time, questions on growth in groups as such and hard problems in analytic number theory. While this line of research on growth started with the study of matrix groups, it has now given strong results on permutation groups as well. Two outstanding matters are the control of dependence on rank in matrix groups, and the removal of the need for the Classification Theorem in permutation groups. Going beyond these questions on diameter and expansion, there are at least three new directions I propose to follow: towards algorithms, towards geometric group theory, and towards number theory. Some of the main recent results in the area take the form of diameter bounds. Bounding a diameter amounts to showing that one can express any element of a group as a short product of generators. One of the main algorithmic questions consists in actually finding such an expression, and doing so rapidly. Links between geometric group theory (which studies growth in infinite groups) and the new combinatorial techniques ought to become stronger. Sofic and hyperlinear groups -- which arose in part from geometric group theory -- seem to invite a combinatorial approach. Additive combinatorics has already shown its relevance to exponential sums, a key subject in analytic number theory. Can a newer perspective based on actions of groups give more general results? Short Kloosterman sums, which are particularly hard to bound, can be framed as a test case. I also plan to pursue related interests in automorphic forms - which are a classical example of the relevance of group actions to number theory - and model theory.