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   Dancso, Zsuzsanna; Halacheva, Iva; Laplante-Anfossi, Guillaume; Robertson, Marcy (June 2025, Comptes Rendus. Mathématique)

   We show that solutions to the Kashiwara–Vergne problem can be extended degree by degree. This can be used to simplify the computation of a class of Drinfel’d associators, which under the Alekseev–Torossian conjecture, may comprise all associators. We also give a proof that the associated graded Lie algebra of the Kashiwara–Vergne group is isomorphic to the graded Kashiwara–Vergne Lie algebra. 

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2. Interpreting Degree Semantics

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   https://doi.org/10.1145/3427218.3427222  

   Härkönen, Marc; Hollering, Benjamin; Kashani, Fatemeh Tarashi; Rodriguez, Jose Israel (June 2020, ACM Communications in Computer Algebra)

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   The Macaulay2 [5] package AlgebraicOptimization implements methods for determining the algebraic degree of an optimization problem. We describe the structure of an algebraic optimization problem and explain how the methods in this package may be used to determine the respective degrees. Special features include determining Euclidean distance degrees and maximum likelihood degrees. To our knowledge, this is the first comprehensive software package combining different methods in algebraic optimization. The package is available at https://github.com/Macaulay2/Workshop-2020-Cleveland/tree/ISSAC-AlgOpt/alg-stat/AlgebraicOptimization. 

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4. Lifting sum-of-squares lower bounds: degree-2 to degree-4

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   Cao, Yan; Chen, Guantao; Jing, Guangming; Shan, Songling (September 2022, SIAM Journal on Discrete Mathematics)