- 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,
*C.M.P.*336 (2015), 649--669. - W-algebras from Heisenberg categories
(arXiv)
with A. Lauda, A. Licata and J. Sussan,
*Jour. Inst. Math. Jussieu*(to appear) - The Elliptic Hall algebra and the deformed Khovanov Heisenberg category
(arXiv)
with A. Lauda, A. Licata, P. Samuelson and J. Sussan.
## Categorical Heisenberg 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. - Associated graded of Hodge modules and categorical sl(2) actions (arXiv) with C. Dodd and J. Kamnitzer.
- Categorical geometric symmetric Howe duality
(arXiv)
with J. Kamnitzer
## Equivalences and categorical sl(2) actions |

- 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*21 (2015), 201--244. - 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*360 (2014), 351--390. - Rigidity in higher representation theory (arXiv)
- Quantum K-theoretic geometric Satake (arXiv) with J. Kamnitzer.
- Exotic t-structures and actions of quantum affine algebras
(arXiv)
with C. Koppensteiner.
## Quantum groups and higher representation theory |

- 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)
*Math. Annalen*363 (2015), 1053--1115. - Knot homology via derived categories of coherent sheaves IV, coloured links
(arXiv)
with J. Kamnitzer,
*Quantum Topology*8 (2017) no. 2, 381--411. - Remarks on coloured triply graded link invariants
(arXiv)
*Algebr. Geom. Topol.*17 (2017), no. 6, 3811-3836.
## Knot homologies via derived categories of coherent sheaves |

- 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 abelian monodromy extension property |

- 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 SL(3)
(arXiv)
with A. Craw and T. Logvinenko,
*J. Reine Angew. Math.*727 (2017), 1--48.
## The geometric McKay correspondence in dimension three |