arXiv subjects
Publications and source records attributed to João Lourenço.
We propose a uniform moduli-theoretic description of the v-sheaf local model $\mathbb{M}_{\mathcal G,μ}$ for an arbitrary parahoric group scheme $\mathcal G$ and an arbitrary dominant cocharacter $μ$. Our approach is Tannakian and builds on a new theory of parahoric induced modules. When $μ$ is minuscule, this framework explains the linear-algebraic conditions arising in the theory of local models of Shimura varieties.
We characterize Cohen--Macaulay and $φ$-rational perfect schemes in terms of their perverse étale mod $p$ sheaves. Using inversion of adjunction, we prove that sufficiently small Schubert varieties in the Witt affine flag variety are perfections of globally $+$-regular varieties, and hence they are $φ$-rational. Our methods apply uniformly to all affine Schubert varieties in equicharacteristic, as well as classical Schubert varieties, thereby answering a question of Bhatt. As a corollary, we deduce that scheme-theoretic local models always have $φ$-split special fiber.
We prove a folklore conjecture identifying two categorical enhancements of the automorphic side of the local Langlands correspondence. Concretely, we construct an equivalence for torsion coefficients between the category considered by Zhu and the one considered by Fargues-Scholze. To achieve this, we revisit Scholze's analytification functor and apply the first author's theory of kimberlites. We discuss unconditional applications to the splitting of the semi-orthogonal decomposition on BunG, and the compatibility with Eisenstein functors. Finally, we formulate a linearity conjecture for our functor with which we can show new vanishing statements for the cohomology of local Shimura varieties, and perverse exactness statements for Hecke operators.
The application of Machine Learning techniques in code generation is now a common practice for most developers. Tools such as ChatGPT from OpenAI leverage the natural language processing capabilities of Large Language Models to generate machine code from natural language descriptions. In the cybersecurity field, red teams can also take advantage of generative models to build malicious code generators, providing more automation to Pentest audits. However, the application of Large Language Models in malicious code generation remains challenging due to the lack of data to train and evaluate offensive code generators. In this work, we propose RedShell, a tool that allows ethical hackers to generate malicious PowerShell code. We also introduce a ground truth dataset, combining publicly available code samples to fine-tune models in malicious PowerShell generation. Our experiments demonstrate the strong capabilities of RedShell in generating syntactically valid PowerShell, with fewer than 10% of the generated samples resulting in parse errors. Furthermore, our specialized model was able to produce samples that were semantically consistent with reference snippets, achieving a competitive performance on standard output similarity metrics such as Edit Distance and METEOR, with their mean similarity scores exceeding 50% and 40%, respectively. This work sheds light on the state-of-the-art research in the field of Generative AI applied to Pentesting, and also serves as a steppingstone for future advancements, highlighting the potential benefits these models hold within such controlled environments.
Large Language Models (LLMs) are redefining offensive cybersecurity by allowing the generation of harmful machine code with minimal human intervention. While attackers take advantage of dark LLMs such as XXXGPT and WolfGPT to produce malicious code, ethical hackers can follow similar approaches to automate traditional pentesting workflows. In this work, we present RedShell, a privacy-preserving, hardware-efficient framework that leverages fine-tuned LLMs to assist pentesters in generating offensive PowerShell code targeting Microsoft Windows vulnerabilities. RedShell was trained on a malicious PowerShell dataset from the literature, which we further enhanced with manually curated code samples. Experiments show that our framework achieves over 90% syntactic validity in generated samples and strong semantic alignment with reference pentesting snippets, outperforming state-of-the-art counterparts in distance metrics such as edit distance (above 50% average code similarity). Additionally, functional experiments emphasize the execution reliability of the snippets produced by RedShell in a testing scenario that mirrors real-world settings. This work sheds light on the state-of-the-art research in the field of Generative AI applied to malicious code generation and automated testing, acknowledging the potential benefits that LLMs hold within controlled environments such as pentesting.
We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models for local Shimura varieties, as well as the test function conjecture of Haines--Kottwitz in this framework. To this end, we establish a specialization principle for well-behaved $p$-adic kimberlites, show that these include the v-sheaf local models, determine their special fibers using hyperbolic localization for the étale cohomology of small v-stacks, and analyze the resulting specialization morphism using convolution.
III-V semiconductor nanolight sources with deep-subwavelength dimensions ($<<$1 $μ$m) are essential for miniaturized photonic devices such as nanoLEDs and nanolasers. However, these nanoscale emitters suffer from substantial non-radiative recombination at room temperature, resulting in low efficiency and ultrashort lifetimes ($<$100 ps). Previous works have predominantly studied surface passivation of nanoLEDs under optical pumping conditions, while practical applications require electrically driven nanoLEDs. Here, we investigate the influence of surface passivation on the efficiency and high-speed modulation response of electrically pumped III-V GaAs/AlGaAs nanopillar array LEDs. Surface passivation was performed using ammonium sulphide chemical treatment followed by encapsulation with a 100 nm silicon nitride layer deposited via low-frequency plasma-enhanced chemical vapour deposition. Time-resolved electroluminescence measurements reveal differential carrier lifetimes ($τ$) of ~0.61 ns for nanoarray LEDs with pillar diameters of ~440 nm, a record-long lifetime for electrically driven GaAs-based nanopillar arrays. Under low injection conditions, the devices exhibited carrier lifetimes of ~0.41 ns, indicating successful suppression of non-radiative effects and a low surface velocity, ranging from $S$~0.7$\times$10$^4$ cm/s to 2.7$\times$10$^4$ cm/s. This reveals a potential high internal quantum efficiency $IQE$~0.45 for our nanoLEDs operating under very high injection conditions, limited only by Auger recombination and self-heating effects at high current density. These miniaturized nanoLEDs with high radiative recombination efficiency and sub-ns modulation response pave the way for optical data communications, energy efficient optical interconnects, AR/VR displays, and neuromorphic computing applications.
We show that the nearby cycles functor for the $p$-adic Hecke stack at parahoric level is perverse t-exact, by developing a theory of Wakimoto filtrations at Iwahori level, and that it lifts to the $\mathbb{E}_1$-center. We apply these tools to construct the Arkhipov-Bezrukavnikov functor for $p$-adic affine flag varieties at Iwahori level, and prove that it is an equivalence for all classical groups and also exceptional groups of type $E_6$ and $E_7$.
We show that the v-sheaf local models of moduli spaces of $p$-adic shtukas are unibranch. In particular, this proves that the scheme-theoretic local models defined in our joint work with Anschütz and Richarz are always normal with reduced special fiber, thereby establishing the remaining cases of the geometric part of the Scholze$-$Weinstein conjecture when $p \leq 3$. Our methods are general, topological, and simplify Zhu's proof of the coherence conjecture. As a technical input, we generalize a comparison theorem of nearby cycles of Huber to the v-sheaf setup.
We construct local models of Shimura varieties and investigate their singularities, with special emphasis on wildly ramified cases. More precisely, with the exception of odd unitary groups in residue characteristic $2$ we construct local models, show reducedness of their special fiber, Cohen$-$Macaulayness and in equi-characteristic also (pseudo-)rationality. In mixed characteristic we conjecture their (pseudo-)rationality. This is based on the construction of parahoric group schemes over two-dimensional bases for wildly ramified groups and an analysis of singularities of the attached Schubert varieties in positive characteristic using perfect geometry.
We extend the ramified geometric Satake equivalence due to Zhu (for tamely ramified groups) and the third named author (in full generality) from rational coefficients to include modular and integral coefficients.
We derive a Serre presentation of distribution algebras of loop groups in characteristic $p$ and apply it to give a new proof of the normality of Schubert varieties inside parahoric affine Grassmannians, for all connected reductive groups whose fundamental group is $p$-torsion free.
Application of soft and compliant joints in grasping mechanisms received an increasing attention during recent years. This article suggests the design and development of a novel bio-inspired compliant finger which is composed of a 3D printed rigid endoskeleton covered by a soft matter. The overall integrated system resembles a biological structure in which a finger presents an anthropomorphic look. The mechanical properties of such structure are enhanced through optimization of the repetitive geometrical structures that constructs a flexure bearing as a joint for the fingers. The endoskeleton is formed by additive manufacturing of such geometries with rigid materials. The geometry of the endoskeleton was studied by finite element analysis (FEA) to obtain the desired properties: high stiffness against lateral deflection and twisting, and low stiffness in the desired bending axis of the fingers. Results are validated by experimental analysis.
We prove that all $p$-adic period domains (and their non-minuscule analogues) are geometrically connected. This answers a question of Hartl [Har13] and has interesting consequences to the geometry of Shimura and local Shimura varieties.
Recent research has proposed different approaches on the automated identification of candidate microservices on monolith systems, which vary on the monolith representation, similarity criteria, and quality metrics used. On the other hand, they are generally limited in the number of codebases and decompositions evaluated, and few comparisons between approaches exist. Considering the emerging trend in software engineering in techniques based on the analysis of codebases' evolution, we compare a representation based on the monolith code structure, in particular the sequences of accesses to domain entities, with representations based on the monolith development history (file changes and changes authorship). From the analysis on a total of 468k decompositions of 28 codebases, using five quality metrics that evaluate modularity, minimization of the number of transactions per functionality, and reduction of teams and communication, we conclude that the best decompositions on each metric were made by combining data from the sequences of accesses and the development history representations. We also found that the changes authorship representation of codebases with many authors achieves comparable or better results than the sequence of accesses representation of codebases with few authors with respect to minimization of the number of transactions per functionality and the reduction of teams.
In this paper we determine the scheme-theoretic fixed points of pinned reductive group schemes acted upon by a group of pinning-preserving automorphisms. The results are used in a companion paper to establish a ramified geometric Satake equivalence with integral or modular coefficients.
We study the geometry of equicharacteristic partial affine flag varieties associated to tamely ramified groups $G$ in characteristics $p>0$ dividing the order of the fundamental group $π_1(G_{\text{der}})$. We obtain that most Schubert varieties are not normal and provide an explicit criterion for when this happens. Apart from this, we show, on the one hand, that loop groups of semisimple groups satisfying $p \mid \lvert π_1(G_{\text{der}})\rvert$ are not reduced, and on the other hand, that their integral realizations are ind-flat. Our methods allow us to classify all tamely ramified Pappas-Zhu local models of Hodge type which are normal.
We present a model of leptonic mixing based on two $A_5$ modular symmetries using the Weinberg operator. The two modular symmetries are broken to the respective diagonal $A_5$ subgroup. At the effective level, the model behaves as a model with a single $A_5$ modular flavour symmetry, but with two moduli. Using both as stabilisers, different residual symmetries are preserved, leading to golden ratio mixing that is perturbed by a rotation.