%% Papers Published
@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 = {333364},
Publisher = {Mathematical Sciences Publishers},
Year = {2016},
Month = {January},
url = {http://dx.doi.org/10.2140/pjm.2016.281.333},
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 edgelabeled
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}
}
@article{fds337147,
Author = {Barnard, E and Meehan, E and Reading, N and Viel,
S},
Title = {Universal Geometric Coefficients for the FourPunctured
Sphere},
Journal = {Annals of Combinatorics},
Volume = {22},
Number = {1},
Pages = {144},
Publisher = {Springer Nature},
Year = {2018},
Month = {March},
url = {http://dx.doi.org/10.1007/s0002601803780},
Abstract = {We construct universal geometric coefficients for the
cluster algebra associated to the fourpunctured sphere and
obtain, as a byproduct, the gvectors 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
quasilaminations). The classification allows us to prove
the Null Tangle Property for the fourpunctured 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/s0002601803780},
Key = {fds337147}
}
@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{fds350520,
Author = {Barcelo, H and Bernstein, M and BocktingConrad, 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},
url = {http://dx.doi.org/10.1016/j.aam.2020.102077},
Abstract = {We consider the problem of selecting an nmember 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≀Snmodule homomorphisms. In particular, we decompose
the spaces of voter preferences and election results into
simple QSm≀Snsubmodules 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}
}
