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1. 𝚤Hall algebra of the projective line and 𝑞-Onsager algebra

   https://doi.org/10.1090/tran/8798  

   Lu, Ming; Ruan, Shiquan; Wang, Weiqiang (April 2023, Transactions of the American Mathematical Society)

   The ı \imath Hall algebra of the projective line is by definition the twisted semi-derived Ringel-Hall algebra of the category of 1 1 -periodic complexes of coherent sheaves on the projective line. This ı \imath Hall algebra is shown to realize the universal q q -Onsager algebra (i.e., ı \imath quantum group of split affine A 1 A_1 type) in its Drinfeld type presentation. The ı \imath Hall algebra of the Kronecker quiver was known earlier to realize the same algebra in its Serre type presentation. We then establish a derived equivalence which induces an isomorphism of these two ı \imath Hall algebras, explaining the isomorphism of the q q -Onsager algebra under the two presentations. 

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2. The algebra of Schur operators

   https://doi.org/10.1016/j.ejc.2020.103130  

   Liu, Ricky Ini; Smith, Christian (June 2020, European Journal of Combinatorics)
3. Serverless linear algebra

   https://doi.org/10.1145/3419111.3421287  

   Shankar, Vaishaal; Krauth, Karl; Vodrahalli, Kailas; Pu, Qifan; Recht, Benjamin; Stoica, Ion; Ragan-Kelley, Jonathan; Jonas, Eric; Venkataraman, Shivaram (October 2020, SoCC '20: Proceedings of the 11th ACM Symposium on Cloud Computing)

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   Datacenter disaggregation provides numerous benefits to both the datacenter operator and the application designer. However switching from the server-centric model to a disaggregated model requires developing new programming abstractions that can achieve high performance while benefiting from the greater elasticity. To explore the limits of datacenter disaggregation, we study an application area that near-maximally benefits from current server-centric datacenters: dense linear algebra. We build NumPyWren, a system for linear algebra built on a disaggregated serverless programming model, and LAmbdaPACK, a companion domain-specific language designed for serverless execution of highly parallel linear algebra algorithms. We show that, for a number of linear algebra algorithms such as matrix multiply, singular value decomposition, Cholesky decomposition, and QR decomposition, NumPyWren's performance (completion time) is within a factor of 2 of optimized server-centric MPI implementations, and has up to 15% greater compute efficiency (total CPU-hours), while providing fault tolerance. 

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4. Extended BMS algebra of celestial CFT

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5. Students’ perspectives of Thinking With Algebra

   2. Feikes, D. (January 2023, Proceedings of the eighth annual Indiana STEM Education Conference. West Lafayette, IN.)

   W. S. Walker, III (Ed.)

   Thinking With Algebra (TWA) is a curriculum development project for college students needing introductory/intermediate algebra. Unique guiding principles of the project are a focus on algebraic structure, mixed review, equity, and a classroom approach emphasizing small-group work and whole- class discussion (Feikes et al., 2022). Results are derived from a survey given to one class of fifteen students taking an intermediate algebra summer course. The paper shares both Likert and open-ended responses. Data demonstrates that the students believed that the TWA curriculum was beneficial. 

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