| Nicholas Proudfoot
Email: njp - at - uoregon.edu Office: 331 Fenton Telephone: (541) 346-0996 Address: Department of Mathematics 1222 University of Oregon Eugene, OR 97403 |
Teaching
In Winter 2009 I am teaching Math 411/511 (Complex Analysis) and Math 456/556 (Networks and Combinatorics).
My office hours are on Tuesdays and Thursdays from 2:30 - 3:30.
Colloquium
Here is the Colloquium schedule.
Workshop
I am organizing a workshop on operator algebras and conformal field theory, to be held at the University of Oregon from 16 August 2010 through 21 August 2010. The workshop will be led by André Henriques.
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.
My main research at the moment focuses on categories of representations of noncommutative deformations of the coordinate ring of an algebraic symplectic variety, and on categories of sheaves on the variety that one obtains by "localizing" these representations. Here is a description of this project, taken from a grant proposal. Everything described in these notes is joint with Tom Braden, Tony Licata, and Ben Webster.
Here is a list of my preprints.
Resolving toric varieties with Nash blow-ups
With Atanas Atanasov, Christopher Lopez, Alexander Perry, and Michael Thaddeus; preprint. pdf
Localization algebras and deformations of Koszul algebras
With Tom Braden, Tony Licata, Chris Phan, and Ben Webster; preprint. pdf
Gale duality and Koszul duality
With Tom Braden, Tony Licata, and Ben Webster; to appear in Advances in Mathematics. pdf
The hypertoric intersection cohomology ring
With Tom Braden; to appear in Inventiones Mathematicae. 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
To appear in the Transactions of the American Mathematical Society. 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. And here are some pictures from my travels in Japan, India, the Canadian Rockies, the Olympics, and Provence.
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In India, David Farris
and I had small roles in the
soap opera
Kasauti Zindagi Ki; you can see the clip
here.
(You may have to right click and download the file.) |
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.