Permanent Faculty
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Johan Rosenkilde, Associate Professor
Keywords: discrete mathematics, algebra, computer algebra, error-correcting codes, coding theory, cryptography, number theory, finite fields, algebraic curves, algorithms, exact computation
I research in fast algorithms for exact computation in discrete algebra, with an emphasis on applications in digital communication, especially error-correcting codes and cryptography. These two serve opposite purposes in a sense: cryptography hides information from spying eyes, while error-correcting codes protects a message from errors that occur during storage or transmission. Central in all of this is efficient algebraic computation, such as solving special equations over finite fields or polynomials on the fly. I use algebraic curves and number theory as powerful tools for constructing good solutions. read more
Peter Beelen, ProfessorKeywords: algebra, discrete mathematics, algebraic varieties, finite fields, function fields, error-correcting codes
My research is in algebra with applications in discrete mathematics. The algebraic objects I study are algebraic varieties defined over a finite field, especially algebraic curves which can be described equivalently by their function fields. The study of function fields, is one of my main areas of research. The main application of algebraic varieties that I study, is within the area of algebraic coding theory. In the case of curves, these algebraic codes are known as algebraic geometry codes (AG codes). Studying properties of AG codes and finding fast decoders for them is another of my main areas of research. read more
Maria Montanucci, Assistant ProfessorKeywords: Algebra, Algebraic-Geometry, Algebraic Curves, Finite Fields, Coding Theory, Error-correcting Codes, Combinatorics, Galois geometries
Algebraic geometry is a branch of mathematics based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems and viceversa. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. The power of the connection between Algebra and Geometry shows itself in a number of applications. Leading examples are Coding theory and Cryptography. My research focuses on the investigation of the algebraic and geometric properties of algebraic curves that lead to good error-correcting codes as well as the construction of good curves for the purpose of error-correction. (1) Algebraic Geometry in positive characteristic (automorphism groups of algebraic curves, birational invariants, maximal curves, quotient curves), (2) Coding Theory (functional codes, AG codes, quantum codes, convolutional codes), (3) Linear sets and their applications (scattered polynomials, MRD codes). read more
PhDs, Postdocs and Research Assistants
Coming soon.