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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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    Daniel Douglas's profile picture
    Daniel Douglas (starting Fall 2024) , bio

    Dr. Douglas works in the mathematical field of quantum topology. He is particularly interested in interactions with low dimensional geometry and topology, representation theory, combinatorics, and mathematical physics.

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    Leo Herr's profile picture
    Leo Herr (starting Fall 2024) , bio

    My work is in algebraic geometry. I study varieties using extra combinatorial data called logarithmic structures which enrich and compactify ordinary varieties as a middleman between schemes and tropical geometry. Log structures help to count curves, study intersections, and construct cohomology theories and invariants that behave well for singular varieties and normal crossings pairs.

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    Jason LeGrow's profile picture
    Jason LeGrow , bio

    Professor LeGrow's research is in the design, analysis, and optimization of isogeny-based cryptographic protocols.

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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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    Hiram Lopez Valdez profile picture
    Hiram López Valdez , bio

    Professor López researches connections of commutative algebra with coding theory and its applications, including quantum error correction, coding for post-quantum cryptography, and distributed storage systems.

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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 profile picture
    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

    Associate 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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    Eduardo Camps Moreno profile picture
    Eduardo Camps Moreno , bio

    Dr. Camps Moreno is a Presidential Postdoctoral Fellow working with Dr. Gretchen Matthews, with a research focus in algebraic coding theory.

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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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    Giuseppe Cotardo's profile picture
    Giuseppe Cotardo , bio

    Doctor Cotardo's research interest is in algebraic coding theory, with a focus on algebra, geometry, combinatorics, and their applications to the invariant theory of codes endowed with the rank metric.

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    Spencer Carey Cvitanov , bio

    Dr. Cvitanov's PHD is in Number theory, specifically Iwasawa Theory. Much of his work is concerned with non-Archimedean linear algebra.

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    Garrett Fowler profile picture
    Garrett Fowler , bio

    Garrett Fowler's mathematical interests lay largely in combinatorics and algebra.

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    Irit Huq-Kuruvilla profile picture
    Irit Huq-Kuruvilla , bio

    Dr. Huq-Kuruvilla is a postdoctoral scholar working on Gromov-Witten theory and related areas, with a particular focus on quantum K-theory and its relationship with the geometry of the Kontsevich moduli spaces of stable maps.

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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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    Ziqiang Li , bio

    Visiting Assistant Professor Dr. Li researches algorithms on the 2-sphere for the use of computational geometry, numerical methods, and analytical cartography. On the side, he studies flows in microfluidic systems.

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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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    Emily McMillon profile picture
    Emily McMillon , bio

    Dr. McMillon is an NSF Postdoctoral Scholar whose primary research interest is coding theory, with a focus on graph-based codes and iterative decoding algorithms.

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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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    Michael Schultz profile picture
    Michael T. Schultz , bio

    Dr. Schultz conducts research in the intersection of algebraic geometry and mathematical physics.

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    Eric Ufferman , bio

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

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    Daniel Valvo profile picture
    Daniel Valvo , bio

    Instructor Valvo's research is an exciting field of math called coding theory. Specifically he studies how to store data in ways that it can repair itself in the event of errors.

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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.

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    Weihong Xu's profile picture
    Weihong Xu , bio

    Dr. Xu studies combinatorial algebraic geometry, especially quantum Schubert calculus and questions concerning generalized flag varieties.

Recently Retired Faculty