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Award ID contains: 1645877

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  1. (, Selecta Mathematica)
    Abstract We show that the wreath Macdonald polynomials for$$\mathbb {Z}/\ell \mathbb {Z}\wr \Sigma _n$$ Z / ℓ Z ≀ Σ n , when naturally viewed as elements in the vertex representation of the quantum toroidal algebra$$U_{\mathfrak {q},\mathfrak {d}}(\ddot{\mathfrak {sl}}_\ell )$$ U q , d ( sl ¨ ℓ ) , diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials. 
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    Free, publicly-accessible full text available July 1, 2026
  2. ; ; (, Forum of Mathematics, Sigma)
    Abstract We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath MacdonaldP-polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our operators arise from integral formulas for the action of the horizontal Heisenberg subalgebra in the vertex representation of the corresponding quantum toroidal algebra. 
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    Free, publicly-accessible full text available January 1, 2026
  3. (, Letters in Mathematical Physics)
    Abstract The goal of this paper is to better understand the quasimap vertex functions of typeANakajima quiver varieties. To that end, we construct an explicit embedding of any typeAquiver variety into a typeAquiver variety with all framings at the rightmost vertex of the quiver. Then, we consider quasimap counts, showing that the map induced by this embedding on equivariantK-theory preserves vertex functions. 
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  4. (, Mathematische Nachrichten)
    Abstract A Kodaira fibration is a non‐isotrivial fibration from a smooth algebraic surfaceSto a smooth algebraic curveBsuch that all fibers are smooth algebraic curves of genusg. Such fibrations arise as complete curves inside the moduli space of genusgalgebraic curves. We investigate here the possible connected monodromy groups of a Kodaira fibration in the case and classify which such groups can arise from a Kodaira fibration obtained as a general complete intersection curve inside a subvariety of parametrizing curves whose Jacobians have extra endomorphisms. 
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  5. ; (, Annales Henri Poincaré)
    Abstract We show that four-dimensional superconformal algebras admit an infinite-dimensional derived enhancement after performing a holomorphic twist. The type of higher symmetry algebras we find is closely related to algebras studied by Faonte–Hennion–Kapranov, Hennion–Kapranov, and the second author with Gwilliam in the context of holomorphic QFT. We show that these algebras are related to the two-dimensional chiral algebras extracted from four-dimensional superconformal theories by Beem and collaborators; further deforming by a superconformal element induces the Koszul resolution of a plane in $$\mathbb {C}^2 \cong {\mathbb {R}}^4$$ C 2 ≅ R 4 . The central charges at the level of chiral algebras arise from central extensions of the higher symmetry algebras. 
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  6. ; ; (, Sem. Lothar. Combin.)
    Accepted Manuscript Full Text Available
  7. ; ; (, Selecta Mathematica)
    Full Text Available 
  8. ; ; (, Pure and Applied Mathematics Quarterly)
    Full Text Available 
  9. (, manuscripta mathematica)
    Full Text Available 
  10. ; (, Higher Structures)
    Full Text Available