Nicholas Proudfoot

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

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).
Workshops

I have an NSF CAREER grant that allows me to organize a workshop for postdocs and graduate students at the University of Oregon every summer, at least through 2014.

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)

Research

I am interested in the geometry of algebraic symplectic or hyperkahler varieties, which play a prominent role in many areas of mathematics. These include representation theory (Nakajima's quiver varieties, such as Hilbert schemes on ALE spaces and resolutions of Slodowy slices), string theory (moduli spaces of Higgs bundles), and low-dimensional topology (character varieties). The spaces with which I work the most are hypertoric varieties, which interact with combinatorial objects such as matroids and hyperplane arrangements.

Here is a list of my preprints.
  Quantizations of conical symplectic resolutions II: category O and symplectic duality
      With Tom Braden, Anthony Licata, and Ben Webster; preprint. pdf
  Poisson-de Rham homology of hypertoric varieties and other cones admitting symplectic resolutions
      With Travis Schedler; preprint. pdf
  Hypertoric Poisson homology in degree zero
      to appear in Alg. Geom. 2 (2014) 1-10. pdf
  Quantizations of conical symplectic resolutions I: local and global structure
      With Tom Braden and Ben Webster; preprint. pdf
  Hypertoric category O
      With Tom Braden, Anthony Licata, and Ben Webster; Adv. Math 231 (2012) 1487-1545. 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
  Localization algebras and deformations of Koszul algebras
      With Tom Braden, Anthony Licata, Chris Phan, and Ben Webster; Selecta Math. 17 (2011) 533-572. 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
      Journal of Algebra 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
Here is a bunch of pictures of me and my buddies.
In India, David Farris and I had small roles in the soap opera Kasauti Zindagi Ki; you can see the clip here.

With a little help from my friends, I founded the Harvard Folk Song Society (with Aaron Einbond) in the Spring of 1998, and the Many Cheerful Facts seminar at Berkeley (with André Henriques) in the Spring of 2001.