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Algebra, Algebraic Geometry & Combinatorics

Mathematicians use algebra to represent symmetries and other patterns
and to perform calculations that reveal geometric and other structures.
Algebra research in the department includes programs involving
combinatorics, representation theory, Lie theory, algebraic geometry,
group theory, coding theory, and cryptography.

picture of a Julia set, in the complex plane

Research Advisors for Algebra, Algebraic Geometry & Combinatorics

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    Nick Loehr profile picture
    Nick Loehr , bio

    Professor Loehr conducts research in algebraic combinatorics. His work focuses on the combinatorics of symmetric functions, quasisymmetric functions, lattice paths, and tableau-like structures. These objects encode remarkable algebraic information about group representations, polynomial invariants, and Lie algebras.

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    Gretchen Mattews profile picture
    Gretchen Matthews , bio

    Professor Matthews' research is in applications of algebraic geometry to data storage, protection, and security, especially coding theory and cryptography.

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    Leonardo Mihalcea profile picture
    Leonardo Mihalcea , bio

    Associate Professor Mihalcea studies classical and quantum intersection rings for flag manifolds and related algebraic varieties, an area combining techniques from Algebraic Geometry, Combinatorics, and Geometric Representation Theory.

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    Travis Morrison , bio

    Professor Morrison's research is in algorithmic number theory and applications to cryptography.

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    Daniel Orr profile picture
    Daniel Orr , bio

    Daniel Orr conducts research in representation theory and algebraic combinatorics.

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    Eyvindur Paisson profile picture
    Eyvindur Ari Palsson , bio

    Assistant Professor Palsson conducts research in harmonic analysis, geometric measure theory, combinatorics, number theory and partial differential equations.

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    Mark Shimozono , bio

    Professor Shimozono works on combinatorial problems arising in enumerative algebraic geometry and representation theory.

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    Went Sun profile picture
    Wenbo Sun , bio

    Assistant Professor Wenbo Sun works on the problems lying at the interaction of ergodic theory, combinatorics, and number theory.

Researchers of Algebra, Algebraic Geometry & Combinatorics

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    Brian Cook profile picture
    Brian Cook , bio

    Visiting Assistant Professor Cook's research focuses on arithmetic harmonic analysis, extremal combinatorics & additive/analytic number Theory.

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    Garrett Fowler profile picture
    Garrett Fowler , bio

    Garrett Fowler's mathematical interests lay largely in combinatorics and algebra. His primary focus since graduating is teaching, but his previous research focused on Schubert Calculus.

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    Daniel Kim , bio

    Dr. Kim's research work has been in topological dynamics and discrete conformal geometry understanding Thurston maps, core entropy, and, briefly, hyperbolic expansion complexes.

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    Palanivel Manoharan profile picture
    Palanivel Manoharan , bio

    Research interest in Geometry of Manifolds and geometry of quantum states.

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    Aidan Murphy profile picture
    Aidan W. Murphy , bio

    Professor Murphy's research interest is in the theory of error-correcting codes, with particular focus on algebraic geometry codes and locally recoverable codes.

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    Ba Nguyen profile picture
    Ba Nguyen , bio

    Dr. Ba Nguyen conducts research in Cluster Algebra and Representation Theory, especially the connections between them.

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    Wellington Santos profile picture
    Welington Santos , bio

    Professor Santos' research is in algebra and coding theory.

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    photo of Eric Ufferman
    Eric Ufferman , bio

    Collegiate Assistant Professor Ufferman teaches classes in both Computational Modeling and Data Analytics and Discrete Mathematics.

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    Joseph Wells  profile picture
    Joseph Wells , bio

    Dr. Wells thinks about most things related to complex hyperbolic geometry. In particular, he is interested in (non-)arithmetic subgroups of SU(n,1) and, lately, spherical CR-uniformizations of 3-manifolds.

Recently Retired Faculty