| 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
This quarter I am teaching Math 346 - Number Theory. My office hour will be on Thursdays between 11:00 and 11:50. Anyone is welcome to look for me in my office at other times, or to email me to set up an appointment.
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 set of informal notes on symplectic duality, a subject that I am studying with Tom Braden, Tony Licata, and Ben Webster.
Here is a list of my preprints.
Gale duality and Koszul duality
With Tom Braden, Tony Licata, and Ben Webster; preprint. pdf
The hypertoric intersection cohomology ring
With Tom Braden; preprint. pdf
A survey of hypertoric geometry and topology
To appear in the proceedings of the Int. Conference on Toric Topology, Osaka 2006. pdf
Moduli spaces for Bondal quivers
With Aaron Bergman; to appear in the Pacific Journal of Mathematics. 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, Amer. Math. Soc., 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, No. 1 (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 Andre Henriques) in the Spring of 2001.