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1. Generic Types and Generic Elements in Divisible Rigid Groups

   https://doi.org/10.1007/s10469-023-09726-x  

   Myasnikov, A. G.; Romanovskii, N. S. (March 2023, Algebra and Logic)

   In this paper we describe generic elements and generic types in divisible rigid groups, in particular divisible free solvable groups. 

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2. Generic Beauville’s Conjecture

   https://doi.org/10.1017/fms.2024.21  

   Coskun, Izzet; Larson, Eric; Vogt, Isabel (January 2024, Forum of Mathematics, Sigma)

   Abstract Let$$\alpha \colon X \to Y$$be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under$$\alpha $$is semistable if the genus ofYis at least$$1$$and stable if the genus ofYis at least$$2$$. We prove this conjecture if the map$$\alpha $$is general in any component of the Hurwitz space of covers of an arbitrary smooth curveY. 

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3. Generic Refinement Types

   https://doi.org/10.1145/3704885  

   Lehmann, Nico; Kurashige, Cole; Akiti, Nikhil; Krishnakumar, Niroop; Jhala, Ranjit (January 2025, Proceedings of the ACM on Programming Languages)

   We present Generic Refinement Types: a way to write modular higher-order specifications that abstract invariants over function contracts, while preserving automatic SMT-decidable verification. We show how generic refinements let us write a variety of modular higher-order specifications, including specifications for Rust's traits which abstract over the concrete refinements that hold for different trait implementations. We formalize generic refinements in a core calculus and show how to synthesize the generic instantiations algorithmically at usage sites via a combination of syntactic unification and constraint solving. We give semantics to generic refinements via the intuition that they correspond to ghost parameters, and we formalize this intuition via a type-preserving translation into the polymorphic contract calculus to establish the soundness of generic refinements. Finally, we evaluate generic refinements by implementing them in Flux and using it for two case studies. First, we show how generic refinements let us write modular specifications for Rust's vector indexing API that lets us statically verify the bounds safety of a variety of vector-manipulating benchmarks from the literature. Second, we use generic refinements to refine Rust's Diesel ORM library to track the semantics of the database queries issued by client applications, and hence, statically enforce data-dependent access-control policies in several database-backed web applications. 

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4. Generic Quantum Metric Rigidity

   https://doi.org/10.1093/imrn/rnaa028  

   Chirvasitu, Alexandru (March 2020, International Mathematics Research Notices)

   Abstract We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric measure spaces appropriately, the subset consisting of those with trivial compact quantum automorphism group is of 2nd Baire category. The latter result can be paraphrased as saying that “most” compact metric measure spaces have no (quantum) symmetries; in particular, they also have trivial ordinary (i.e., classical) automorphism group. 

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5. Generic Action Start Detection

   https://doi.org/10.1109/MIPR54900.2022.00074  

   Zhang, Yuexi; Chen, Ming; Li, Yikang; Hsiao, Jenhao; Camps, Octavia; Ho, Chiuman (August 2022, IEEE 5th Int. Conf. on Multimedia Information Processing and Retrieval (MIRP))