Nicholas Proudfoot
Email: njp - at - uoregon.edu
Office: 322 Fenton Hall
Address:
Department of Mathematics1222 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.

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.

With Katie Gedeon and Ben Young; preprint. pdf

With Katie Gedeon and Ben Young; preprint. pdf

With Daniel Moseley and Ben Young; to appear in

With Matthew Arbo; to appear in

With Max Wakefield and Ben Young;

With Ben Elias and Max Wakefield;

With Michael McBreen;

With Tom Braden, Anthony Licata, and Ben Webster;

With Travis Schedler; to appear in

With Tom Braden and Ben Webster;

With Tom Braden, Anthony Licata, and Ben Webster;

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

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

With Tom Braden, Anthony 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;

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