We present an update on the ongoing computation of the isospin-breaking effects in the Pion Decay Constant from the BMW Collaboration. The calculation is carried out with N$_f$=2+1+1 staggered quarks with a near-physical pion mass and QED$_{\text{L}}$. We give an update on the isosymmetric value and the current determination used to compute the gradient-flow scale $w_{0}$, then we present some preliminary results of the valence-valence contribution to the axial-pseudoscalar correlator for different volumes and lattice spacings. We also discuss the next steps and plans.

Motivated by recent experimental observations of the flavour-exotic $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, we present the first lattice QCD study of coupled-channel scattering of a charm meson with a light meson in the flavour-exotic sectors at the $SU(3)_f$ flavour symmetric point. Utilising five volumes with $m_\pi \approx 700$ MeV and employing large bases of meson-meson operators, finite-volume spectra are extracted and used to constrain infinite-volume scattering amplitudes with $J^P = \{0, 1, 2, 3, 4\}^+$ via the Lüscher formalism. In the flavour $\mathbf{6}$ sector, each $S$-wave channel considered is found to be attractive with the scattering amplitudes having an associated pole singularity on an unphysical sheet below threshold, giving six flavour-exotic poles in the energy region constrained. In $J^P = 0^+$ there is a virtual bound state and a resonance. The latter is identified with the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, appearing as one state in the $SU(3)_f$ flavour symmetric limit, and suggests the existence of an isospin-$\frac{1}{2}$ partner. In $J^P =1^+$ there are three poles, one of which is identified as a $J^P =1^+$ partner of the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, and $J^P =2^+$ contains one pole which is identified as their $J^P =2^+$ partner. Only mild interactions and no poles are seen in the $J^P = \{3, 4\}^+$ scattering amplitudes. In the flavour $\overline{\mathbf{15}}$ sector, weak interactions are observed in $J^P = \{0, 1, 2, 3, 4\}^+$ with no well-determined poles in the energy region constrained.

We present the results of continuum-extrapolated lattice simulations of quantum chromodynamics (QCD) above the crossover temperature and for unprecedentedly high baryon densities at the physical point, employing the complex Langevin equation. In particular, we determine the QCD equation of state by computing the baryon density as well as the pressure as functions of the baryon chemical potential and the temperature. Potential issues with wrong convergence of complex Langevin dynamics are under control and we indeed find agreement with previous lattice studies working at smaller chemical potentials, as well as with perturbative hard-thermal-loop calculations at high temperatures.

We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed propagators and vertices as well as graviton flow lines which describe the evolution of gravity along the Ricci flow. By calculating vacuum expectation values of a number of independent operators at the two-loop level, we derive the required counterterms of the flowed action. Our results allow us to define a Ricci-flow based renormalization scheme for Newton's constant $G_N$. Studying its renormalization group behavior, we recover a non-Gaußian fixed point in accordance with well-known non-perturbative considerations

We study at zero temperature a microscopic quantum spin-1 model on the fuzzy sphere that realizes the $O(2)$ Wilson-Fisher conformal field theory (CFT) in $(2+1)$-dimensional spacetime at a quantum critical point. Here, we use the fuzzy-sphere regularization as it preserves the full spatial $SO(3)$ rotational symmetry of the CFT, enabling the state-operator correspondence that maps energy eigenstates directly to CFT operators. Using exact diagonalization (ED) and matrix product state (MPS) techniques combined with conformal perturbation theory (CPT), we extract conformal data including scaling dimensions and operator product expansion (OPE) coefficients. We identify 32 primary operators and their descendants, organized by the conserved $O(2)$ charge $S^{z}$ and spatial angular momentum $L$. Our numerical results for the scaling dimensions of the lowest primary operators show good agreement with conformal bootstrap predictions. We verify predictions from the large charge expansion, which provides systematic predictions for operators carrying large $U(1)$ charge, connecting the Goldstone mode physics in the ordered phase to phonon primaries at the critical point.

In this work, we investigate the mass spectra, magnetic moments, and Regge trajectories of the triply heavy baryons $\Omega_{ccb}$ and $\Omega_{cbb}$ within a nonrelativistic constituent quark model based on the quark--diquark approximation, which reduces the three-body problem to an effective two-body system. For each baryon, all three possible diquark clusterings are considered, providing a qualitative indication of the sensitivity of the results to the quark--diquark decomposition. The model parameters are fixed by a fit to the measured $B_c$ meson spectrum, thereby anchoring the baryon predictions to experimentally constrained inputs and establishing a consistent link between the heavy meson and baryon sectors. We obtain ground-state masses of approximately $8.0$~GeV for $\Omega_{ccb}$ and $11.0$~GeV for $\Omega_{cbb}$, with radial and orbital excitation patterns in good agreement with the results reported in the literature. The computed magnetic moments of the spin-$\tfrac{1}{2}$ and spin-$\tfrac{3}{2}$ states are consistent with the results of various approaches. A radial Regge analysis in the $(n_r, M^2)$ plane reveals approximately linear $P$-wave trajectories and mildly curved $S$-wave trajectories, with slope and intercept parameters that scale systematically with the heavy-quark content of the baryon. These results suggest that the nonrelativistic quark--diquark framework provides a reliable description of triply heavy baryons and serves as a useful reference for future experimental searches, particularly at LHCb.