Papers and Slides

Although most of these papers are available on the arXiv, the authoritative versions are the journal versions.

46. The fundamental theorem of finite semidistributive lattices (with David Speyer and Hugh Thomas). Preprint, 2019.
45. Dominance phenomena: mutation, scattering and cluster algebras. Trans. Amer. Math. Soc., to appear. Slides for a talk presented at the CIRM Luminy conference "Cluster Algebras: Twenty Years On," March, 2018.
44. A combinatorial approach to scattering diagrams. Algebraic Combinatorics, to appear.
Slides for a talk presented at the Seminario di Algebra e Geometria, Roma "La Sapienza" March, 2018.
43. Scattering fans. Int. Math. Res. Notices, to appear.
Slides for a talk presented at the conference "Combinatorics and beyond: the many facets of Sergey Fomin's mathematics", University of Michigan, 2018.
Slides for a talk presented at the conference "Cluster structures in geometry, physics, combinatorics, and representation theory", Jerusalem, 2018.
(These slides are similar to the Michigan slides, but these give no background on cluster algebras, and include material from the Rome talk above.)
42. Lattice homomorphisms between weak orders. Electron. J. Combin. 26, (2019), Article Number P2.23.
Slides for a talk presented at the CRM/LaCIM Workshop "Algebraic and Geometric Combinatorics of Reflection Groups" in Montreal, 2017.
41. Lattice theory of torsion classes (with Laurent Demonet, Osamu Iyama, Idun Reiten, and Hugh Thomas). Preprint, 2017.
40. An affine almost positive roots model (with Salvatore Stella), J. Comb. Algebra, to appear.
39. The action of a Coxeter element on an affine root system (with Salvatore Stella). Proc. Amer. Math. Soc., to appear.
38. Coxeter-biCatalan combinatorics (with Emily Barnard). J. Algebraic Combin. 47(2) (2018), 241-300.
37. Lattice structure of Weyl groups via representation theory of preprojective algebras (with Osamu Iyama, Idun Reiten, and Hugh Thomas). Compositio Mathematica 154, no. 6 (2018) 1269-1305.
35-36. Lattice Theory of the Poset of Regions. Chapter 9 of Lattice Theory: Special Topics and Applications, Volume 2, Editors: George Grätzer and Friedrich Wehrung, Springer 2016.
Finite Coxeter Groups and the Weak Order. Chapter 10 of Lattice Theory: Special Topics and Applications, Volume 2, Editors: George Grätzer and Friedrich Wehrung, Springer 2016.
Slides from my talk at TLC at Wake Forest University, 2019.

A Three-part lecture series (Part I Part II Part III) on Lattice congruences of the weak order, most of which was presented at the CRM/LaCIM Spring School "Algebraic and Geometric Combinatorics of Reflection Groups" in Montreal, 2017.
34. Universal geometric coefficients for the four-punctured sphere (with Emily Barnard, Emily Meehan, and Shira Viel). Ann. Comb. 22(1) (2018), 1-44.
33. A Cambrian framework for the oriented cycle (with David Speyer). Electron. J. Combin. 22(4) (2015), #P4.46, 21 pp.
32. Cambrian frameworks for cluster algebras of affine type (with David Speyer). Trans. Amer. Math. Soc. 370, Number 2, (2018), 1429-1468.
31. Coxeter arrangements in three dimensions (with Richard Ehrenborg and Caroline Klivans). Beitr. Algebra Geom. 57 (2016), 891-897.
30. Initial-seed recursions and dualities for d-vectors (with Salvatore Stella). Pacific J. Math. 293-1 (2018), 179-206.
29. Noncrossing arc diagrams and canonical join representations. SIAM J. Discrete Math. 29 (2015), no. 2, 736-750.
28. Universal geometric coefficients for the once-punctured torus. Sém. Lothar. Combin. B71e (2015), 30 pp.
27. Universal geometric cluster algebras from surfaces. Trans. Amer. Math. Soc. 366 (2014), 6647-6685.
26. Universal geometric cluster algebras. Mathematische Zeitschrift 277 (2014), no. 1-2, 499-547.
Slides from a talk on universal geometric cluster algebras.
Slides from my talk at FPSAC 2004 in Chicago. This talk also covers some of the material on surfaces (paper 28 here), and previews the material on combinatorial models of cluster algebras of affine type (papers 32 and 40) dominance phenomena (paper 45).
25. Combinatorial frameworks for cluster algebras (with David Speyer). Int. Math. Res. Notices. 2016, no. 1 (2016) 109-173.
Five-part lecture series (Part 1 Part 2 Part 3a Part 3b Part 4a Part 4b Part 5 ) that was presented at the MSRI Summer Graduate School "Cluster Algebras and Cluster Combinatorics" in August, 2011.
24. From the Tamari lattice to Cambrian lattices and beyond, in "Associahedra, Tamari Lattices and Related Structures", Tamari Memorial Festschrift. Progress in Mathematics 299 (Birkhauser, 2012) editors F. Mueller-Hoissen, J. Pallo and J. Stasheff, 293-322.
23. Generic rectangulations, European J. Combin. 33 (2012) 610-623. Slides from a talk at the AMS Eastern Sectional Meeting, Cornell University, 2011.
22. The Hopf algebra of diagonal rectangulations (with Shirley Law), J. Combin. Theory Ser. A. 119 (2012) no. 3, 788-824.
Slides of a talk on the Hopf algebra of rectangulations.
21. Coarsening polyhedral complexes, Proc. Amer. Math. Soc. 140 (2012), 3593-3605
20. Noncrossing partitions and the shard intersection order, J. Algebraic Combin. 33 (2011), no. 4, 483-530.
Slides of a talk on shard intersections.
19. Sortable Elements for Quivers with Cycles (with David Speyer), Electron. J. Combin. 17(1) (2010), Research Paper 90, 19 pp.
18. Sortable elements in infinite Coxeter groups (with David Speyer), Trans. Amer. Math. Soc. 363 (2011) no. 2, 699-761.
Slides from my talk at Combinatexas 2008.
17. Noncrossing partitions, clusters and the Coxeter plane, Sém. Lothar. Combin. 63 (2010), Article B63b.
The PostScript files promised in Section 1.3 are now posted with the paper on the Séminaire Lotharingien de Combinatoire site.
Slides from my talk at FPSAC 2007 in Tianjin, China.
16. 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.
15. Cambrian fans (with David Speyer), J. Eur. Math. Soc. (JEMS), 11 (2009) 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.
14. 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.
13. Clusters, Coxeter-sortable elements and noncrossing partitions, Trans. Amer. Math. Soc. 359 (2007) no. 12, 5931-5958.
A rank-three example. The computer programs promised in the paper.
Slides from my talk at FPSAC 2006 in San Diego.
12. 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.
11. Root systems and generalized associahedra (with Sergey Fomin), Geometric combinatorics, 63-131, IAS/Park City Math. Ser., 13, Amer. Math. Soc., Providence, RI, 2007.
10. Cambrian lattices, Adv. Math. 205 (2006), no. 2, 313-353.
Slides from my talks at FPSAC 2004 and PCMI 2004.
9. 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).
8. Lattice congruences of the weak order, Order 21 (2004) no. 4, 315-344.
7. 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).
6. 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.
Poster presented at FPSAC 2003, Vadstena, Sweden.
5. Lattice and order properties of the poset of regions in a hyperplane arrangement, Algebra Universalis, 50 (2003), 179-205.
4. The cd-index of Bruhat intervals, Electron. J. Combin. 11(1) (2004), Research Paper 74, 25 pp. (electronic).
3. Order Dimension, Strong Bruhat Order and Lattice Properties for Posets, Order 19 (2002) 73-100.
2. Non-negative cd-coefficients of Gorenstein* posets, Discrete Math 274, no. 1-3 (2004) 323-329.
1. Nim-Regularity of Graphs, Electron. J. Combin. 6 (1999), Research Paper 11, 8 pp.

Some unpublished manuscripts