Research Summary


    Categorical Heisenberg actions

  • Heisenberg categorification and Hilbert schemes (arXiv) with A. Licata, Duke Math Journal 161 (2012), no. 13, 2469--2547.
  • Vertex operators and 2-representations of quantum affine algebras (arXiv) with A. Licata.
  • Braid group actions via categorified Heisenberg complexes (arXiv) with A. Licata and J. Sussan, Compositio Math. 150 (2014), 105--142.
  • On a categorical Boson-Fermion correspondence (arXiv) with J. Sussan.




    Equivalences and categorical sl(2) actions

  • Coherent sheaves and categorical sl(2) actions (arXiv) with J. Kamnitzer and A. Licata, Duke Math Journal 154 (2010) no. 1, 135--179.
  • Categorical geometric skew Howe duality (arXiv) with J. Kamnitzer and A. Licata, Inventiones Math. 180 (2010) no. 1, 111--159.
  • Derived equivalences for cotangent bundles of Grassmannians via categorical sl(2) actions (arXiv) with J. Kamnitzer and A. Licata, J. Reine Angew. Math. 675 (2013), 53--99.
  • Equivalences and stratified flops (arXiv) Compositio Math. 148 (2012) no. 1, 185--209.
  • Flops and about: a guide (arXiv) EMS Congress Reports (2011), no. 8, 61--101.




    Quantum groups and higher representation theory

  • Braiding via geometric Lie algebra actions (arXiv) with J. Kamnitzer, Compositio Math. 148 (2012) no. 2, 464--506.
  • Coherent sheaves on quiver varieties and categorification (arXiv) with J. Kamnitzer and A. Licata, Math. Annalen 357 (2013) no. 3, 805--854.
  • Implicit structure in 2-representations of quantum groups (arXiv) with A. Lauda, Selecta Math (to appear).
  • Loop realizations of quantum affine algebras (arXiv) with A. Licata, J. Math. Phys. 53 (2012), no. 12, 18pp.
  • Webs and quantum skew Howe duality (arXiv) with J. Kamnitzer and S. Morrison, Math. Annalen (to appear)
  • Rigidity in higher representation theory (arXiv)




    Knot homologies via derived categories of coherent sheaves

  • Knot Homology Via Derived Categories of Coherent Sheaves I, sl(2) case (arXiv) with J. Kamnitzer, Duke Math Journal 142 (2008) no.3, 511--588.
  • Knot Homology Via Derived Categories of Coherent Sheaves II, sl(m) case (arXiv) with J. Kamnitzer, Inventiones Math. 174 (2008) no. 1, 165--232.
  • Clasp technology to knot homology via the affine Grassmannian (arXiv)




    The abelian monodromy extension property

  • The Abelian Monodromy Extension property for families of curves (arXiv) Math. Annalen 344 (2009) no. 3, 717--747.
  • The solvable monodromy extension property and varieties of log general type (arXiv) Clay Math. Proc.: A Celebration of Algebraic Geometry Clay Math. Proc. 18, (2013), 119--129.




    The geometric McKay correspondence in dimension three

  • A derived approach to geometric McKay correspondence in dimension three (arXiv) with T. Logvinenko, J. Reine Angew. Math. 636 (2009), 193--236.
  • Derived Reid's recipe for abelian subgroups of SL3(C) (arXiv) with A. Craw and T. Logvinenko, J. Reine Angew. Math. (to appear).