@article{20043,
  abstract     = {We establish an isomorphism of complex K-theory of the moduli space  M  of “SL n​ ”-Higgs bundles of degree d and rank n (in the sense of Hausel–Thaddeus) and twisted complex K-theory of the orbifold  M  of PGL n​ -Higgs bundles of degree e, where (n,d)=(n,e)=1. Along the way, we prove the vanishing of torsion for H ∗ ( M ) and certain twisted complex K-theory groups of  M . We also extend Arinkin’s autoduality of compactified Jacobian to a derived equivalence between SL n​ - and PGL n​ -Hitchin systems over the elliptic locus. In the appendix, we develop a formalism of G-sheaves of spectra, generalising equivariant homotopy theory to a relative setting.},
  author       = {Groechenig, Michael and Shen, Shiyu},
  issn         = {1435-9863},
  journal      = {Journal of the European Mathematical Society},
  publisher    = {EMS Press},
  title        = {{Complex K-theory of moduli spaces of Higgs bundles}},
  doi          = {10.4171/jems/1601},
  year         = {2025},
}

@article{14986,
  abstract     = {We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k). Let k be an algebraically closed field of characteristic p>n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod) of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles .},
  author       = {Shen, Shiyu},
  issn         = {1687-0247},
  journal      = {International Mathematics Research Notices},
  keywords     = {General Mathematics},
  number       = {7},
  pages        = {6176--6208},
  publisher    = {Oxford University Press},
  title        = {{Tamely ramified geometric Langlands correspondence in positive characteristic}},
  doi          = {10.1093/imrn/rnae005},
  volume       = {2024},
  year         = {2024},
}

@article{15248,
  abstract     = {Applying the technique of p-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups SLn and PGLn, building on previous work of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the E-polynomial of the smooth moduli space of parabolic GLn-Higgs bundles is independent of the degree of the underlying vector bundles.},
  author       = {Shen, Shiyu},
  issn         = {1090-2082},
  journal      = {Advances in Mathematics},
  number       = {5},
  publisher    = {Elsevier},
  title        = {{Mirror symmetry for parabolic Higgs bundles via p-adic integration}},
  doi          = {10.1016/j.aim.2024.109616},
  volume       = {443},
  year         = {2024},
}