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Creators/Authors contains: "Ormsby, Kyle"

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  1. ; ; (, Journal of the European Mathematical Society)
    We identify the motivicKGL/2-local sphere as the fiber of\psi^{3}-1on(2,\eta)-completed HermitianK-theory, over any base scheme containing1/2. This is a motivic analogue of the classical resolution of theK(1)-local sphere, and extends to a description of theKGL/2-localization of an arbitrary motivic spectrum. Our proof relies on a novel conservativity argument that should be of broad utility in stable motivic homotopy theory. 
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    Free, publicly-accessible full text available April 4, 2026
  2. ; ; (, Glasgow Mathematical Journal)
    We provide a general recursive method for constructing transfer systems on finite lattices. Using this, we calculate the number of homotopically distinct $$N_{\infty} $$ operads for dihedral groups $$D_{p^n}$$, p>2 prime, and cyclic groups $$C_{qp^n}$$, $$p \neq q$$ prime. We then further display some of the beautiful combinatorics obtained by restricting to certain homotopically meaningful $$N_\infty$$ operads for these groups. 
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    Free, publicly-accessible full text available January 1, 2026
  3. ; ; ; ; ; ; ; ; (, Tunisian Journal of Mathematics)
    We develop the theory of saturated transfer systems on modular lattices, ultimately producing a “matchstick game” that puts saturated transfer systems in bijection with certain structured subsets of covering relations. We also prove that Hill’s characteristic function χ for transfer systems on a lattice P surjects onto interior operators for P, and moreover, the fibers of χ have unique maxima which are exactly the saturated transfer systems. Lastly, after an interlude developing a recursion for transfer systems on certain combinations of bounded posets, we apply these results to determine the full lattice of transfer systems for rank two elementary abelian groups. 
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    Free, publicly-accessible full text available January 1, 2026
  4. ; ; ; (, Communications of the American Mathematical Society)
    We perform Hochschild homology calculations in the algebro-geometric setting of motives over algebraically closed fields. The homotopy ring of motivic Hochschild homology contains torsion classes that arise from the mod-p motivic Steenrod algebra and generating functions defined on the natural numbers with finite non-empty support. Under Betti realization, we recover Bökstedt’s calculation of the topological Hochschild homology of finite prime fields. 
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  5. ; ; (, European Journal of Combinatorics)
    We investigate the rich combinatorial structure of premodel structures on finite lattices whose weak equivalences are closed under composition. We prove that there is a natural refinement of the inclusion order of weak factorization systems so that the intervals detect these composition closed premodel structures. In the case that the lattice in question is a finite total order, this natural order retrieves the Kreweras lattice of noncrossing partitions as a refinement of the Tamari lattice, and model structures can be identified with certain tricolored trees. 
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  6. ; ; ; (, Mathematische Zeitschrift)
    Abstract We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics . In the case of a finite total order [ n ], we enumerate all model structures, exhibiting a rich combinatorial structure encoded by Shapiro’s Catalan triangle. This is an application of previous work of the authors on the theory of $$N_\infty $$ N ∞ -operads for cyclic groups of prime power order, along with new structural insights concerning extending choices of certain model structures on subcategories of [ n ]. 
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  7. ; ; (, Tunisian Journal of Mathematics)
    We isolate a class of groups — called lossless groups — for which homotopy classes of G-N∞ operads are in bijection with certain restricted transfer systems on the poset of conjugacy classes Sub(G)/G. 
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  8. ; ; ; (, Topology and its Applications)
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  9. ; ; ; ; (, Homology, Homotopy and Applications)
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  10. ; (, Pacific Journal of Mathematics)
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