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Abstract We prove that the Tate conjecture for divisors is “generically true” for $\mathrm{mod}p$\operatorname{mod}preductions of complex projective varieties with $h^{2,0}=1$h^{2,0}=1, under a mild assumption on moduli.By refining this general result, we establish a new case of the BSD conjecture over global function fields, and the Tate conjecture for a class of general type surfaces of geometric genus 1. 

Abstract We construct singular quartic double fivefolds whose Kuznetsov component admits a crepant categorical resolution of singularities by a twisted Calabi–Yau threefold. We also construct rational specializations of these fivefolds where such a resolution exists without a twist. This confirms an instance of a higher-dimensional version of Kuznetsov’s rationality conjecture and of a noncommutative version of Reid’s fantasy on the connectedness of the moduli of Calabi–Yau threefolds. 

Hybrid photonic integration provides a platform to design and implement novel functionalities unavailable to active or passive material systems alone. We present an automated alignment and assembly process for hybrid-integrated laser systems, comprising silicon nitride (Si₃N₄) photonic integrated circuits (PICs) edge-coupled to gallium arsenide (GaAs) gain chips (GCs). We design and optimize spot size converters (SSCs) to increase the alignment tolerances between the PICs and GCs. Our automated assembly process has achieved experimental coupling losses of 2.7 dB between the PICs and GCs, closely matching the simulated values. Packaged hybrid lasers, when coupled to a lensed fiber, exhibit slope efficiencies of ∼ 97 mW/A. These results show the feasibility of scaling the production and widespread application of these hybrid laser systems by automating their assembly, which should drive down packaging costs and accelerate research. 

Abstract Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with linearly reductive automorphism groups in the bounded derived category of a K3 surface. As an application, we prove the formality conjecture for polystable objects in the Kuznetsov components of Gushel–Mukai threefolds and quartic double solids. 

Metal halide perovskites represent a promising class of gain media for next‐generation nonepitaxial laser diodes. However, fully electrically pumped perovskite laser diodes have not been achieved yet. Herein, the use of sodium fluoride (NaF) is explored as an efficient additive in halide perovskite films to improve their optical and light amplification properties. The incorporation of NaF in perovskites leads to a remarkable threefold increase in light‐emitting intensity. The threshold of amplified spontaneous emission (ASE) by optical pumping is reduced by more than 20%, from ≈13.5 to 10.4 μJ cm⁻². Furthermore, the NaF‐modified perovskites exhibit stable ASE emission, even after exposure to 1.5 billion optical pulses, highlighting substantial improvements in the material's photostability. Finally, optically pumped ASE is observed from a full perovskite light‐emitting diode stack, including lossy metal electrodes. This work demonstrates significant progress toward the development of electrically pumped perovskite lasers. 

Abstract We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from 2 are isomorphic if their Kuznetsov components are equivalent. This improves and completes our previous result joint with Nuer where the same statement is proved for generic Enriques surfaces. 

Abstract We prove a general criterion that guarantees that an admissible subcategory of the derived category of an abelian category is equivalent to the bounded derived category of the heart of a bounded t‐structure. As a consequence, we show that has a strongly unique dg enhancement, applying the recent results of Canonaco, Neeman, and Stellari. We apply this criterion to the Kuznetsov component when is a cubic fourfold, a GM variety, or a quartic double solid. In particular, we obtain that these Kuznetsov components have strongly unique dg enhancement and that exact equivalences of the form are of Fourier–Mukai type when , belong to these classes of varieties, as predicted by a conjecture of Kuznetsov.