Nicholas Proudfoot

Email: njp - at -
Office: 322 Fenton Hall
Address: Department of Mathematics
1222 University of Oregon
Eugene, OR 97403


In the winter of 2017 I am teaching Calculus with Theory. My office hours are Monday 1:00 - 1:50 and Thursday 2:00 - 2:50.
Lecture Notes

Toric varieties (seven week course, fall 2010)
Geometric representation theory and categorification (three lecture minicourse, summer 2011)
Symplectic geometry (ten week course, fall 2013).

2010: Operator Algebras and Conformal Field Theory (with André Henriques)
2011: Cluster Algebras and Lusztig's Semicanonical Basis (with David Speyer)
2012: Categorical Representation Theory (with David Ben-Zvi)
2013: Quantum/Affine Schubert Calculus (with Allen Knutson)
2014: Kazhdan-Lusztig Theory and Soergel Bimodules (with Ben Elias)
2015: Positivity in Combinatorial Algebraic Geometry (with June Huh)
2016: Knot homologies, Hilbert schemes, and Cherednik algebras (with Jacob Rasmussen)
2017: Symplectic duality (the Abelian case) (with Ben Webster)

* Workshop on Algebra and Representation Theory Held on Oregonian Grounds


I am interested in symplectic algebraic varieties, which come up a lot in representation theory (e.g. quiver varieties, Hilbert schemes on ALE spaces, the Springer resolution, slices in the affine Grassmannian). The spaces with which I work the most are hypertoric varieties, which interact with combinatorial objects such as matroids, zonotopes, and hyperplane arrangements.

Recently I have been very interested in Kazhdan-Lusztig polynomials of matroids. Though these polynomials have a purely combinatorial definition, they have strong connections to algebraic geometry (compactifications of arrangement complements) and combinatorial representation theory (FI- and FS-modules).

Here is a list of my preprints.
  Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures
      With Katie Gedeon and Ben Young; to appear in Séminare Lotharingien Combinatoire (FPSAC 2017). pdf
  The equivariant Kazhdan-Lusztig polynomial of a matroid
      With Katie Gedeon and Ben Young; to appear in Journal of Combinatorial Theory, Series A. pdf
  The Orlik-Terao algebra and the cohomology of configuration space
      With Daniel Moseley and Ben Young; to appear in Experimental Mathematics. pdf
  Hypertoric varieties and zonotopal tilings
      With Matthew Arbo; to appear in Int. Math. Res. Not. pdf
  Intersection cohomology of the symmetric reciprocal plane
      With Max Wakefield and Ben Young; J. Alg. Comb. 43 (2016) 129-138. pdf
  The Kazhdan-Lusztig polynomial of a matroid
      With Ben Elias and Max Wakefield; Adv. Math. 299 (2016) 36-70. pdf
  Intersection cohomology and quantum cohomology of conical symplectic resolutions
      With Michael McBreen; Alg. Geom. 2 (2015) 623-641. pdf
  Quantizations of conical symplectic resolutions II: category O and symplectic duality
      With Tom Braden, Anthony Licata, and Ben Webster; Astérisque 384 (2016), 75-179. pdf
  Poisson-de Rham homology of hypertoric varieties and nilpotent cones
      With Travis Schedler; to appear in Selecta Math. pdf
  Hypertoric Poisson homology in degree zero
      Alg. Geom. 1 (2014) 261-270. pdf
  Quantizations of conical symplectic resolutions I: local and global structure
      With Tom Braden and Ben Webster; Astérisque 384 (2016), 1-73. pdf
  Hypertoric category O
      With Tom Braden, Anthony Licata, and Ben Webster; Adv. Math. 231 (2012) 1487-1545. pdf
  Localization algebras and deformations of Koszul algebras
      With Tom Braden, Anthony Licata, Chris Phan, and Ben Webster; Selecta Math. 17 (2011) 533-572. pdf
  Resolving toric varieties with Nash blow-ups
      With Atanas Atanasov, Christopher Lopez, Alexander Perry, and Michael Thaddeus; Experimental Math. 20 (2011) 288-303. pdf
  Gale duality and Koszul duality
      With Tom Braden, Anthony Licata, and Ben Webster; Adv. Math. 225 (2010) 2002-2049. pdf
  The hypertoric intersection cohomology ring
      With Tom Braden; Inv. Math. 177 (2009) 337-380. pdf
  A survey of hypertoric geometry and topology
      Toric Topology, Contemporary Mathematics 460, AMS, Providence, RI, 2006. pdf
  Moduli spaces for Bondal quivers
      With Aaron Bergman; Pacific J. Math. 237 (2008) 201-221. pdf
  Moduli spaces for D-branes at the tip of a cone
      With Aaron Bergman; Journal of High Energy Physics 03 (2006) 073. pdf
  All the GIT quotients at once
      Trans. Amer. Math. Soc. 363 (2011) 1687-1698. pdf
  A nonhausdorff model for the complement of a complexified arrangement
      Proc. Amer. Math. Soc. 135 (2007) 3989-3994. pdf
  Geometric invariant theory and projective toric varieties
      Snowbird Lectures in Algebraic Geometry,
      Contemporary Mathematics 388, AMS, Providence, RI, 2005. pdf
  Arithmetic and topology of hypertoric varieties
      With Ben Webster; J. Alg. Geom. 16 (2007) 39-63. pdf
  A broken circuit ring
      With David Speyer; Beitrage zur Algebra und Geometrie 47 (2006) 161-166. pdf
  Equivariant topology of real hyperplane arrangements
      Announcement of results. pdf
  Hyperplane arrangements and K-theory
      Top. Appl. 153 (2006) 2866-2875. pdf
  Hyperkahler analogues of Kahler quotients
      U.C. Berkeley Ph.D. thesis, Spring 2004. pdf
  Abelianization for hyperkahler quotients
      With Tamas Hausel; Topology 44 (2005) 231-248. pdf
  Hyperpolygon spaces and their cores
      With Megumi Harada; Trans. Amer. Math. Soc. 357 (2005) 1445-1467. pdf
  The equivariant Orlik-Solomon algebra
      J. Alg. 305 (2006) 1186-1196. pdf
  Properties of the residual circle action on a hypertoric variety
      With Megumi Harada; Pacific J. Math. 214 (2004) 263-284. pdf
  Brieskorn's construction of exotic spheres
      Harvard University senior thesis, Spring 2000. pdf
  Parallel connections and bundles of arrangements
      With Michael Falk; Top. Appl. 118 (2002) 65-83. pdf

In India, David Farris and I had small roles in the soap opera Kasauti Zindagi Ki; you can see the clip here.