Faculty Advising Ph.D.s

Six faculty members are actively recruiting Ph.D students. Research expertise is in the broad areas of mathematical physics, control and inverse problems, geometry, and mathematical biology. For more detailed information, please see below, and visit the personal webpages.

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Elizabeth S. Allman
Professor of Mathematics
e.allman@alaska.edu
personal webpage

Research Interests: Phylogenetics, Modeling of sequence evolution, Algebraic Statistics, Applications of Computational Algebra

Select publications:

1. "Identifiability of parameters in latent structure models with many observed variables" by Elizabeth S. Allman, Catherine Matias, and John A. Rhodes, Annals of Statistics, 37 no. 6A (2009) 3099-3132.

2. "Trees, Fast and Accurate" by Elizabeth S. Allman and John A. Rhodes, Science, 327 (2010) 1334-1335.

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Sergei Avdonin
Professor of Mathematics
s.avdonin@alaska.edu
personal webpage
short CV

Research Interests: Control theory for partial differential equations, Inverse problems of mathematical physics, Nonharmonic Fourier series

Select publications:

1. "Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems" by S.A. Avdonin and S.A. Ivanov, Cambridge University Press, 1995, New York, London, Melbourne.

2. "Inverse problems for quantum trees" by S. Avdonin and P. Kurasov, Inverse Problems and Imaging, 2 no. 1 (2008) 1-21.

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Leah Wrenn Berman
Associate Professor of Mathematics
lwberman@alaska.edu

Research Interests: Study of configurations of points and lines with high degrees of incidence and/or symmetry, especially developing new construction techniques and examples; Study of abstract polytopes and their monodromy groups, with an emphasis on polytopes that are symmetric but not too symmetric; discrete geometry.

Select publications:

1. "Highly incident configurations with chiral symmetry" by Leah Wrenn Berman and Jill Faudree, Discrete and Computational Geometry, 49 no. 3 (2013) 671–694.

2. "Geometric constructions for 3-configurations with non-trivial geometric symmetry" by Leah Wrenn Berman, The Electronic Journal of Combinatorics, 20 no. 3 (2013).

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John A. Rhodes
Professor of Mathematics
j.rhodes@alaska.edu
personal webpage

Research Interests: Phylogenetics, Modeling of sequence evolution, Algebraic Statistics, Tensor decompositions

Select publications:

1. "Tensor Rank, Invariants, Inequalities, and Applications," with E.S. Allman, P. Jarvis, and J. Sumner, SIAM Journal on Matrix Analysis and Applications, 34 no. 3, (2013) 1014-1045.

2. "Species tree inference by the STAR method, and generalizations," with E.S. Allman and J.H. Degnan, Journal of Computational Biology, 20 no. 1 (2013), 50-61.

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Alexei Rybkin
Professor of Mathematics
arybkin@alaska.edu
personal webpage

Research Interests: Soliton theory and mathematical physics

Select publications:

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Gordon Williams
Associate Professor of Mathematics
giwilliams@alaska.edu
personal webpage

Research Interests: Study of the symmetry and combinatorial structure of polyhedra, convex polytopes and abstract polytopes, especially developing combinatorial representations of polytopes through the use of regular covers of polytopes and their monodromy (or connection) groups. Discrete geometry, mathematical art, and recreational mathematics.

Select publications:

1. "Minimal covers of the prisms and antiprisms," with M. Hartley, and D. Pellicer, Discr. Math., 312 no. 20, (2012) 3046-3058.

2. "The Tomotope," with B. Monson, D. Pellicer, Ars Math. Contemp., 5 (2012) 355–370.