Multiple future lepton colliders have been proposed, offering powerful tools for precise studies of electroweak (EW) physics. This talk will first give a brief overview and then focus on two selected topics. The first concerns the EW dipole operators of the bottom quark, often omitted in SMEFT analyses. Using the process $e^+e^- \to b \bar{b}$ at future lepton colliders, we explore the subtle interplay between linear and quadratic effects, and show that multiple-energy runs are important for resolving coefficient degeneracies. The other topic is Z/W pole physics at a future muon collider. Although muon colliders cannot run at the Z-pole, they can probe electroweak by taking advantage of the high energy and large luminosity. We study the vector boson fusion processes of WW/WZ/W$\gamma$ to fermion pairs, and examine their potential to probe the dimension-6 operators that directly modify fermion couplings to the Z/W. Using kinematic distributions, the precision is generally comparable to future $e^+e^-$ colliders. Together, these studies highlight the strong potential for EW probing in the next lepton collider era.

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More than 25 years after the discovery of the accelerated expansion of the Universe, understanding dark energy remains the biggest open problem in cosmology. The Dark Energy Spectroscopic Instrument (DESI) is the first of a new generation of “Stage-IV” cosmology survey experiments aiming to improve this understanding. By precisely mapping the positions of over 50 million galaxies and quasars, DESI is measuring the expansion history of the Universe over the last 11 billion years. I will describe the experiment and discuss the cosmological results from the first 3 years of data, from baryon acoustic oscillations (BAO) and the full shape of the clustering power spectrum. These include exciting hints of an anomaly in the cosmological constant model of dark energy, and unprecedented constraints on the neutrino mass scale. I will describe the nature of the data constraints and comment on the implications for fundamental physics models.

Recent experiments in arrays of optical waveguides have shown (fractionally) quantized topological transport of solitons [1,2]. I will present a fully quantum mechanical description of such topological pumps of bosons with attractive on-site interactions [3]. The transport of bound N-particle composite objects in a 1D lattice upon cyclic adiabatic changes of the Hamiltonian is determined by the elective band-structure of its center-of-mass (COM) motion. If the COM band is energetically separated from all other many-body states in a full cycle the transport is quantized and characterized by a many-body Chern number. Increasing the interaction energy leads to a successive merging of COM bands resulting in topological phase transitions from phases with integer quantized transport through different phases of fractional transport, characterized by a non-trivial Wilson loop, and eventually to a phase without topological transport. I will discuss an approach to numerically calculate the Chern numbers and Wilson loops for composites that are sufficiently tightly conned. Furthermore, I present a minimal model for which we can explicitly construct an elective single-particle Hamiltonian of the bound object that shows an interaction-induced transition between phases of different quantized transport. In an outlook I will discuss the extension of the composite approach to topological properties of self-bound many-particle states in 2D lattices. References [1] M. Jurgensen, S. Mukherjee, and M. C. Rechtsman, Quantized nonlinear Thouless pumping, Nature 596, 63 (2021) [2] M. Jurgensen, S. Mukherjee, C. Jorg, and M. C. Rechtsman, Quantized fractional Thouless pumping of solitons, Nature Physics 19, 420 (2023) [3] Julius Bohm, Hugo Gerlitz, Christina Jorg, and Michael Fleischhauer Quantum theory of fractional topological pumping of lattice solitons, arxiv:2506.00090