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.
Research Advisors for Algebra, Algebraic Geometry & Combinatorics
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Sarah Arpin , bioDr. Arpin's research is in algebraic number theory and post-quantum cryptography, including the study of supersingular elliptic curves, isogeny-based cryptography, arithmetic geometry in characteristic p, and code-based cryptography.
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Giuseppe Cotardo , bioDr. Cotardo’s research interest is in algebraic coding theory, with a particular focus on algebra, geometry, combinatorics, and their applications to the invariant theory of rank-metric codes. He is also actively working on network communication and quantum error correction.
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Daniel Douglas , bioDr. 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 , bioMy 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 , bioProfessor LeGrow's research is in the design, analysis, and optimization of isogeny-based cryptographic protocols.
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Nick Loehr , bioProfessor 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 López Valdez , bioProfessor 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 Matthews , bioProfessor 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 , bioAssociate 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 , bioProfessor Morrison's research is in algorithmic number theory and applications to cryptography.
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Daniel Orr , bioDaniel Orr conducts research in representation theory and algebraic combinatorics.
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Eyvindur Ari Palsson , bioAssociate Professor Palsson conducts research in harmonic analysis, geometric measure theory, combinatorics, number theory and partial differential equations.
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Mark Shimozono , bioProfessor Shimozono works on combinatorial problems arising in enumerative algebraic geometry and representation theory.
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Wenbo Sun , bioAssistant 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 , bioDr. Camps Moreno is a Presidential Postdoctoral Fellow working with Dr. Gretchen Matthews, with a research focus in algebraic coding theory.
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Spencer Carey Cvitanov , bioDr. 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 , bioGarrett Fowler's mathematical interests lay largely in combinatorics and algebra.
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Irit Huq-Kuruvilla , bioDr. 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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Kelli Karcher , bioAdvanced Instructor Karcher conducts research in orderable group theory, studying the cardinality of a variety of solvable groups.
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Daniel Kim , bioDr. Kim is an instructor with research interests in symbolic dynamics and geometry.
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Palanivel Manoharan , bioResearch interest in Geometry of Manifolds and geometry of quantum states.
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Azam Mozaffarikhah , bioDr. Mozaffarikhah, Instructor in Mathematics, conducts research in infinite-dimensional algebras and coding theory, with a particular focus on noncommutative algebra, module theory, linear algebra, and their various applications.
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Zitong Pei , bioAs an instructor, I incorporate inclusive teaching practices to create a classroom environment where all students feel valued and included. Simultaneously, my research interests encompass a diverse range of topics in algebraic number theory and algebraic geometry.
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Michael T. Schultz , bioDr. Schultz conducts research in the intersection of algebraic geometry and mathematical physics.
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Timothy Smits , bioI have broad research interests in number theory and arithmetic geometry. I'm interested in the arithmetic of modular symbols and Massey products, Iwasawa theory, and arithmetic statistics.
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Eric Ufferman , bioCollegiate Assistant Professor Ufferman teaches classes in both Computational Modeling and Data Analytics and Discrete Mathematics.
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Daniel Valvo , bioInstructor 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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Milo Bechtloff Weising , bioDr. Bechtloff Weising is a postdoctoral associate working in algebraic combinatorics and representation theory with a primary focus on Macdonald polynomials and Hecke algebras.
Recently Retired Faculty
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