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

I received my Ph.D. from Berkeley in 2004, under the supervision of Allen Knutson. I've had six students graduate so far; you can see them on my family tree. My current student is Patrick Durkin.

Toric varieties (seven week course, fall 2010)

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

Symplectic geometry (ten week course, fall 2013)

Kazhdan-Lusztig polynomials of matroids (20 minute AMS talk, spring 2018).

Category O, symplectic duality, and the Hikita conjecture (three lecture minicourse, summer 2018)

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)

2018: Deligne-Lusztig theory (with Olivier Dudas)

* Workshop on Algebra and Representation Theory Held on Oregonian Grounds

My work is somewhere in between algebraic geometry, combinatorics, representation theory, and algebraic topology. I work mostly with algebraic varieties that are built using the data of a hyperplane arrangement; examples include hypertoric varieties and various generalizations of (partial compactifications of) configuration spaces. I then study the relationship between the algebraic invariants of these spaces and the combinatorial invariants of the input data. The flow of information goes in both directions: sometimes I want to use combinatorics to compute objects of intrinsic geometric interest (categories of sheaves, cohomology rings, etc.), and sometimes I want to use geometric machinery to prove purely combinatorial theorems.

Here is a list of my preprints.

With Joel Kamnitzer and Michael McBreen; preprint. pdf

to appear in

With Yuan Xu and Ben Young;

With Ben Young;

With Katie Gedeon and Ben Young;

With Katie Gedeon and Ben Young;

With Daniel Moseley and Ben Young;

With Matthew Arbo;

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;

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. |