Nicholas Proudfoot
Email: njp - at - uoregon.edu
Office: 322 Fenton Hall
Address:
Department of Mathematics1222 University of Oregon Eugene, OR 97403 |

Toric varieties (seven week course, fall 2010)

Geometric representation theory and categorification (three lecture minicourse, summer 2011)

Symplectic geometry (ten week course, fall 2013).

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)

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.

Here is a list of my preprints.

With Travis Schedler; preprint. pdf

to appear in

With Tom Braden and Ben Webster; preprint. pdf

With Tom Braden, Tony Licata, and Ben Webster;

With Atanas Atanasov, Christopher Lopez, Alexander Perry, and Michael Thaddeus;

With Tom Braden, Tony Licata, Chris Phan, and Ben Webster;

With Tom Braden, Tony Licata, and Ben Webster;

With Tom Braden;

With Aaron Bergman;

With Aaron Bergman;

Contemporary Mathematics 388, AMS, Providence, RI, 2005. pdf

With Ben Webster;

With David Speyer;

Announcement of results. pdf

U.C. Berkeley Ph.D. thesis, Spring 2004. pdf

With Tamas Hausel;

With Megumi Harada;

With Megumi Harada;

Harvard University senior thesis, Spring 2000. pdf

With Michael Falk;

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.