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

Bio ItemDaniel 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.

Bio ItemLeo 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.

Bio ItemJason LeGrow , bio
Professor LeGrow's research is in the design, analysis, and optimization of isogenybased cryptographic protocols.

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

Bio ItemHiram López Valdez , bio
Professor López researches connections of commutative algebra with coding theory and its applications, including quantum error correction, coding for postquantum cryptography, and distributed storage systems.

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

Bio ItemLeonardo 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.

Bio ItemTravis Morrison , bio
Professor Morrison's research is in algorithmic number theory and applications to cryptography.

Bio ItemDaniel Orr , bio
Daniel Orr conducts research in representation theory and algebraic combinatorics.

Bio ItemEyvindur Ari Palsson , bio
Associate Professor Palsson conducts research in harmonic analysis, geometric measure theory, combinatorics, number theory and partial differential equations.

Bio ItemMark Shimozono , bio
Professor Shimozono works on combinatorial problems arising in enumerative algebraic geometry and representation theory.

Bio ItemWenbo 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

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

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

Bio ItemGiuseppe 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.

Bio ItemSpencer Carey Cvitanov , bio
Dr. Cvitanov's PHD is in Number theory, specifically Iwasawa Theory. Much of his work is concerned with nonArchimedean linear algebra.

Bio ItemGarrett Fowler , bio
Garrett Fowler's mathematical interests lay largely in combinatorics and algebra.

Bio ItemIrit HuqKuruvilla , bio
Dr. HuqKuruvilla is a postdoctoral scholar working on GromovWitten theory and related areas, with a particular focus on quantum Ktheory and its relationship with the geometry of the Kontsevich moduli spaces of stable maps.

Bio ItemDaniel 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.

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

Bio ItemPalanivel Manoharan , bio
Research interest in Geometry of Manifolds and geometry of quantum states.

Bio ItemEmily McMillon , bio
Dr. McMillon is an NSF Postdoctoral Scholar whose primary research interest is coding theory, with a focus on graphbased codes and iterative decoding algorithms.

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

Bio ItemMichael T. Schultz , bio
Dr. Schultz conducts research in the intersection of algebraic geometry and mathematical physics.

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

Bio ItemDaniel 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.

Bio ItemJoseph 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 CRuniformizations of 3manifolds.

Bio ItemWeihong Xu , bio
Dr. Xu studies combinatorial algebraic geometry, especially quantum Schubert calculus and questions concerning generalized flag varieties.
Recently Retired Faculty

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