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

I am part of a Research Training Group in Combinatorics, Geometry, Representation Theory, and Topology (we run the RATCOW seminar), and also part of a Focused Research Group on Matroids, Graphs, and Algebraic Geometry.

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

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)

The wonderful geometry of matroids (ten week course, fall 2019)

Positivity theorems for hyperplane arrangements via intersection theory (UT Geometry Seminar, fall 2020)

Valuations for polytopes and matroids (BLT Seminar and FPSAC, spring and summer 2024)

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)

2019: Foundations of Tropical Geometry (with Diane Maclagan and Jeff Giansiracusa)

2022: Infinite-dimensional methods in commutative algebra (with Andrew Snowden)

2023: Categorical Coulomb Branches (with Sabin Cautis and Harold Williams)

2024: Coherent-constructible equivalences in local Geometric Langlands and Representation Theory (with Pramod Achar, Gurbir Dhillon, and Simon Riche)

* Workshop on Algebra and Representation Theory Held on Oregonian Grounds

Ben Elias and I wrote an article in the Notices of the AMS about our experiences organizing these workshops.

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, Schubert varieties, and wonderful varieties. 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 use combinatorics to compute objects of intrinsic geometric interest (categories of sheaves, cohomology rings, etc.) and sometimes I use geometric machinery to prove purely combinatorial theorems.

I make a lot of conjectures. Here are brief descriptions of what I regard as the most interesting of my conjectures that remain open.

Equivariant log concavity of Orlik-Solomon algebras

Roots of Kazhdan-Lusztig polynomials and Z-polynomials of matroids

Classification of abstract hypertoric varieties

Intersection cohomology and quantum cohomology of conical symplectic resolutions

The quantum Hikita conjecture

With Ben Young and Yuan Xu; preprint. pdf

With Ben Elias, Dane Miyata, and Lorenzo Vecchi; preprint. pdf

With Tom Braden and Jacob Matherne; preprint. pdf

With Alice L.L. Gao, Arthur L.B. Yang, and Zhong-Xue Zhang; to appear in

With Matt Larson, Shiyue Li, and Sam Payne;

With Galen Dorpalen-Barry and Jidong Wang;

With Trevor Karn, George Nasr, and Lorenzo Vecchi;

With Jacob Matherne, Dane Miyata, and Eric Ramos;

With Eric Ramos;

With Tom Braden, June Huh, Jacob Matherne, and Botong Wang; preprint. pdf

With Tom Braden, June Huh, Jacob Matherne, and Botong Wang;

With Eric Ramos;

With Eric Ramos;

With Joel Kamnitzer and Michael McBreen;

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 Matt 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;

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, my friend and I had small roles in the soap opera Kasauti Zindagi Ki; you can see the clip here. |