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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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