Nathan Reading

I am an assistant professor in the Department of Mathematics at North Carolina State University. Here is a cv which may or may not be up to date.

Research

My research area is algebraic and geometric combinatorics, particularly the combinatorics of Coxeter groups.

SUM Series

I organize the SUM Series, a series of informal, interesting talks on mathematical topics or issues of interest to math majors. These talks are sponsored by the NC State Society for Undergraduate Mathematics.

Papers

Sortable elements in infinite Coxeter groups (with David Speyer), Trans. Amer. Math. Soc, to appear.
Slides from my talk at Combinatexas 2008.
Chains in the noncrossing partition lattice, SIAM J. Discrete Math. 22 (2008), no. 3, 875-886.
Slides from my talk in the NCSU Algebra Seminar, November 2007.
Cambrian fans (with David Speyer), J. Eur. Math. Soc. (JEMS), 11 no. 2, 407-447.
Slides from my talk at the AMS Sectional Meeting in Fayetteville, AR, November 2006.
Slides from my talk at the AMS Sectional Meeting in Davidson, NC, March 2007.
Sortable elements and Cambrian lattices, Algebra Universalis 56 (2007) no. 3-4, 411-437.
Slides from my talk at the 2007 Winter Meetings in New Orleans.
Clusters, Coxeter-sortable elements and noncrossing partitions, Trans. Amer. Math. Soc. 359 (2007), 5931-5958.
Slides from my talk at FPSAC 2006. A rank-three example. The computer programs promised in the paper.
Generalized cluster complexes and Coxeter combinatorics (with Sergey Fomin), Int. Math. Res. Notices 2005, no. 44, 2709-2757.
The computer programs promised in the paper.
Root systems and generalized associahedra (with Sergey Fomin), Geometric combinatorics, 63-131, IAS/Park City Math. Ser., 13, Amer. Math. Soc., Providence, RI, 2007.
Cambrian lattices, Adv. Math. 205 (2006), no. 2, 313-353.
Slides from my talks at FPSAC 2004 and PCMI 2004.
Lattice congruences, fans and Hopf algebras, J. Combin. Theory Ser. A, 110 (2005) no. 2, 237-273.
Slides from my talk at Banff (Combinatorial Hopf Algebras, August 2004).
Lattice congruences of the weak order, Order, 21 (2004) no. 4, 315-344.
The order dimension of Bruhat order on infinite Coxeter groups (with Debra J. Waugh), Electron. J. Combin. 11(2) (2005), Research Paper 13, 26 pp. (electronic).
The order dimension of the poset of regions in a hyperplane arrangement, J. Combin. Theory Ser. A, 104 (2003) no. 2, 265-285.
The computer programs promised in the paper.
Lattice and order properties of the poset of regions in a hyperplane arrangement, Algebra Universalis, 50 (2003), 179-205.
The cd-index of Bruhat intervals, Electron. J. Combin. 11(1) (2004), Research Paper 74, 25 pp. (electronic).
Order Dimension, Strong Bruhat Order and Lattice Properties for Posets, Order 19 (2002) 73-100.
Non-negative cd-coefficients of Gorenstein* posets, Discrete Math 274, no. 1-3 (2004) 323-329.
Nim-Regularity of Graphs, Electron. J. Combin. 6 (1999), Research Paper 11, 8 pp.

Contact info

Some unpublished manuscripts

On the structure of Bruhat order, Doctoral Thesis, University of Minnesota, April 2002. Essentially all of this appears in the papers "Order Dimension, Strong Bruhat Order and Lattice Properties for Posets" and "The cd-index of Bruhat intervals" above. One important exception: the details of the order-dimension calculation for type B.
Bases for the Flag f-Vectors of Eulerian Posets, unpublished manuscript, 2000. This manuscript includes the material in the paper "Non-negative cd-coefficients of Gorenstein* posets" as well as a summary of the various bases and basis-change formulas for flag f-vectors of Eulerian posets. I don't intend to submit it for publication, but it has been useful for me to have all this material in one place, and I include it here in the hopes that others may find it useful.

Some Quotes

"The object of mathematical rigour is to sanction and legitimize the conquests of intuition, and there was never any other object for it." -Jacques Hadamard.

"Do not be bitter, deceptive or petty." -A fortune cookie I received twice during graduate school. This is excellent advice, which I try to follow, but apparently the fortune cookie people were worried about me.