Supported by NSF grant DMS 1500966
The algebra of conformal blocks, to appear in J. Eur. Math. Soc. (JEMS
Presentations of semigroup algebras of weighted trees, J. Alg. Comb. Vo. 31, 4, (2010) 467-489
Coordinate rings for the moduli of SL_2 quasi-parabolic principal bundles on a curve and toric fiber products, J. Algebra, Vo. 365, 1, (2011) 163-183.
The algebra of SL_3 conformal blocks, Trans. Groups, Vo. 18, 4, (2013) 1165-1187.
Cox rings of moduli of quasi parabolic principal bundles and the K-Pieri rule, J. Comb. Theory. A 136 (2016) 1-29.
Conformal blocks, Berenstein-Zelevinksy triangles, and group-based models, J. Alg. Comb. Vo. 40, 3, (2014) 861-886, joint with Kaie Kubjas.
The Gorenstein property for projective coordinate rings of rank 2 parabolic vector bundles on a smooth curve, joint with Theodore Faust.
Compactifications of character varieties and skein relations on conformal blocks, Geom. Dedicata. (2015), 179, 1, 335 - 376.
Newton-Okounkov polyhedra for character varieties and configuration spaces, Trans. Amer. Math. Soc. 368 (2016) 5979-6003.
Character varieties of free groups are Gorenstein but not always factorial, J. Algebra 456 (2016), 278-293, joint with Sean Lawton.
Semigroups of sl_3 tensor product invariants, J. Algebra, Vo. 400, 1, (2013) 94 -104, joint with Zhengyuan Zhou.
Gorenstein semigroup algebras of weighted trees, J. Algebra, Vo. 354, 1, (2012) 110-120.
Toric geometry of free group SL_2 character varieties from outer space, to appear in Canad. J. Math.
Ongoing large scale computation: Hilbert and Markov bases for value semigroups
Symplectic geometry of the Vinberg monoid and branching problems, Mathematisches Forschungsinstitut Oberwolfach Report No. 27/2014, 31-35.
Contraction of Hamiltonian K−spaces, to appear in Int. Math. Res. Notices. (IMRN), joint with Joachim Hilgert and Johan Martens.
The toric geometry of triangulated polygons in euclidean space, Canad. J. Math. 63, (2011), 878-937, joint with Ben Howard and John Millson.
he m−dissimilarity map and representation theory of SL_m, J. Alg. Comb. Vo. 33, 2, (2011) 199-213.
Dissimilarity maps on trees and the representation theory of GL_n, Elec. J. Combina- torics, Vo. 19, 3, (2012).
Phylogenetic trees and the tropical geometry of flag varieties, FPSAC 2012, DMTCS proc, AR (2012).
Toric degenerations and tropical geometry of branching algebras.
Gröbner theory and tropical geometry on spherical varieties, joint with Kiumars Kaveh.
Khovanskii bases, Newton-Okounkov polytopes and tropical geometry of projective varieties, joint with Kiumars Kaveh.
Algebra of Conformal Blocks
Character Varieties and Configuration Spaces
Tropical Geometry and Reductive Groups
Tropical Geometry and Newton-Okounkov Bodies
Rational Complexity-One T-Varietes are Well-Poised, joint with Nathan Ilten.