Publications of Shira Viel

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@article{fds350520,
   Author = {Barcelo, H and Bernstein, M and Bockting-Conrad, S and McNicholas, E and Nyman, K and Viel, S},
   Title = {Algebraic voting theory & representations of
             Sm≀Sn},
   Journal = {Advances in Applied Mathematics},
   Volume = {120},
   Year = {2020},
   Month = {September},
   Abstract = {We consider the problem of selecting an n-member committee
             made up of one of m candidates from each of n distinct
             departments. Using an algebraic approach, we analyze
             positional voting procedures, including the Borda count, as
             QSm≀Sn-module homomorphisms. In particular, we decompose
             the spaces of voter preferences and election results into
             simple QSm≀Sn-submodules and apply Schur's Lemma to
             determine the structure of the information lost in the
             voting process. We conclude with a voting paradox result,
             showing that for sufficiently different weighting vectors,
             applying the associated positional voting procedures to the
             same set of votes can yield vastly different election
             outcomes.},
   Doi = {10.1016/j.aam.2020.102077},
   Key = {fds350520}
}

@article{fds353793,
   Author = {Akin, V and Viel, S},
   Title = {Interpreting Student Evaluations of Teaching},
   Editor = {Maki, D and Bookman, J and Jacobson, M and Speer, N and Murphy,
             TJ},
   Year = {2019},
   Key = {fds353793}
}

@article{fds337147,
   Author = {Barnard, E and Meehan, E and Reading, N and Viel,
             S},
   Title = {Universal Geometric Coefficients for the Four-Punctured
             Sphere},
   Journal = {Annals of Combinatorics},
   Volume = {22},
   Number = {1},
   Pages = {1-44},
   Publisher = {Springer Nature},
   Year = {2018},
   Month = {March},
   Abstract = {We construct universal geometric coefficients for the
             cluster algebra associated to the four-punctured sphere and
             obtain, as a by-product, the g-vectors of cluster variables.
             We also construct the rational part of the mutation fan.
             These constructions rely on a classification of the
             allowable curves (the curves which can appear in
             quasi-laminations). The classification allows us to prove
             the Null Tangle Property for the four-punctured sphere, thus
             adding this surface to a short list of surfaces for which
             this property is known. The Null Tangle Property then
             implies that the shear coordinates of allowable curves are
             the universal coefficients. We compute shear coordinates
             explicitly to obtain universal geometric
             coefficients.},
   Doi = {10.1007/s00026-018-0378-0},
   Key = {fds337147}
}

@article{fds337148,
   Author = {Gilbert, S and Tymoczko, J and Viel, S},
   Title = {Generalized splines on arbitrary graphs},
   Journal = {Pacific Journal of Mathematics},
   Volume = {281},
   Number = {2},
   Pages = {333-364},
   Publisher = {Mathematical Sciences Publishers},
   Year = {2016},
   Month = {January},
   Abstract = {Let G be a graph whose edges are labeled by ideals of a
             commutative ring. We introduce a generalized spline, which
             is a vertex labeling of G by elements of the ring so that
             the difference between the labels of any two adjacent
             vertices lies in the corresponding edge ideal. Generalized
             splines arise naturally in combinatorics (algebraic splines
             of Billera and others) and in algebraic topology (certain
             equivariant cohomology rings, described by Goresky,
             Kottwitz, and MacPherson, among others). The central
             question of this paper asks when an arbitrary edge-labeled
             graph has nontrivial generalized splines. The answer is
             "always", and we prove the stronger result that the module
             of generalized splines contains a free submodule whose rank
             is the number of vertices in G. We describe the module of
             generalized splines when G is a tree, and give several ways
             to describe the ring of generalized splines as an
             intersection of generalized splines for simpler subgraphs of
             G. We also present a new tool which we call the GKM matrix,
             an analogue of the incidence matrix of a graph, and end with
             open questions.},
   Doi = {10.2140/pjm.2016.281.333},
   Key = {fds337148}
}