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  1. ; ; (, International Mathematics Research Notices)
    null (Ed.)
    Abstract We study two kinds of categorical traces of (monoidal) dg categories, with particular interest in categories of Soergel bimodules. First, we explicitly compute the usual Hochschild homology, or derived vertical trace, of the category of Soergel bimodules in arbitrary types. Secondly, we introduce the notion of derived horizontal trace of a monoidal dg category and compute the derived horizontal trace of Soergel bimodules in type $$A$$. As an application we obtain a derived annular Khovanov–Rozansky link invariant with an action of full twist insertion, and thus a categorification of the HOMFLY-PT skein module of the solid torus. 
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  2. ; ; (, Advances in Mathematics)
    null (Ed.)
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  3. (, Selecta Mathematica)
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  4. ; ; (, Journal of Combinatorial Theory, Series A)
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  5. ; ; (, Mathematische Annalen)
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  6. ; ; ; (, Algebraic Combinatorics)
    null (Ed.)
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  7. ; ; (, Quantum Topology)
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  8. ; ; ; (, Selecta Mathematica)
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  9. (, Algebraic Geometry)
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  10. ; ; (, The Ramanujan Journal)
    We give an explicit recursive description of the Hilbert series and Gröbner bases for the family of quadratic ideals defining the jet schemes of a double point. We relate these recursions to the Rogers-Ramanujan identity and prove a conjecture of the second author, Oblomkov and Rasmussen. 
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