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• Algebraic Coding Theory
• Network Coding
• Rank Metric Codes
• +5 more

Assoc Professor Eimear Byrne is an academic at the School of Mathematics and Statistics, University College Dublin (UCD). She holds editorial roles, including membership on the editorial board of the Advances in the Mathematics of Communications . Her research focuses on algebraic coding theory, network coding, rank metric codes, and applications in wireless communications. She has been involved in grants such as the Discrete Mathematical Approach for Power Saving Coding Scheme of Wireless Body Area Networks (funded by Japan Society for the Promotion of Science) and the Renewable energy extraction from volcanoes project. Education: B.A. in Mathematics from Trinity College Dublin, M.Sc. from UCD, and Ph.D. from University College Cork (UCC). Academic positions include College Lecturer at UCD (2003–present), Postdoctoral Fellowships at National University of Ireland, Maynooth (2002–2003), and University College Cork (2000–2001), with a Visiting Professorship at the University of Notre Dame (2004). Research interests span algebraic coding theory, including codes over rings, linear codes, APN functions, and applications in network and wireless communications. She has supervised a PhD student (external advisor, 2015) and actively contributes to professional activities like peer-review for IEEE Transactions on Information Theory , Designs, Codes and Cryptography , and others. Teaching includes modules like Galois Theory , Coding Theory , Cryptography , Matrix Algebra , and Rank Metric Codes . Her work bridges theoretical mathematics with practical applications in information security and distributed computing.

• Algebraic Geometry
• Combinatorics
• Tropical Geometry
• +3 more

Marvin Anas Hahn serves as an Assistant Professor in the School of Mathematics at Trinity College Dublin, Ireland, with his office located at Trinity College, Dublin 2. His research bridges pure mathematics and applied fields through rigorous exploration of algebraic structures and combinatorial methods. Hahn's primary research focuses on the deep interplay between algebraic geometry and combinatorics, particularly in Hurwitz theory where he investigates piecewise polynomiality of curve enumeration, tropical realizations of moduli spaces, and combinatorial structures of double Hurwitz numbers. His work extends to tropical geometry applications in enumerative problems and has significant interdisciplinary reach into computer vision (rolling shutter camera models) and coding theory (rank-metric codes with valuation structures). The mathematical sophistication of his research manifests in connections to topological recursion, quantum curves, and non-archimedean geometry. Analysis of his 15 most recent publications reveals a cohesive trajectory where combinatorial frameworks solve geometric problems across diverse contexts—from toric surfaces and elliptic curves to camera geometry and coding theory. His articles demonstrate consistent innovation in applying tropical methods to classical algebraic geometry problems while expanding into computational domains, establishing him at the nexus of pure mathematics and practical applications. No scientific awards are documented in the available information. Hahn's academic advising activities and research funding sources remain unspecified in the provided materials, though his publication record suggests active supervision of graduate researchers in mathematical sciences.

• Discrete Mathematics
• Number Theory
• Algebraic Geometry
• +10 more

Professor Gary McGuire is a Full Professor in the School of Mathematics and Statistics at University College Dublin (UCD), specializing in discrete mathematics, number theory, algebraic geometry, and cryptography. He holds a PhD from the California Institute of Technology and has been a central figure in advancing research in finite fields and their applications. BSc, University College Dublin MSc, University College Dublin PhD, California Institute of Technology His research focuses on algebraic structures over finite fields, including Galois theory, permutation polynomials, error-correcting codes, and quantum codes. He has made significant contributions to the understanding of supersingular curves, L-polynomials, and lattice-based cryptanalysis. His work spans theoretical advances and practical applications in cryptography and computational mathematics. The recent publications reflect a strong trend in algebraic and computational number theory, with emphasis on Galois groups of linearized polynomials, quantum code construction, and discrete logarithm algorithms. His work often involves deep connections between algebraic geometry and coding theory, particularly in the construction of MDS and quantum codes from generalized monomial-Cartesian and algebraic geometry codes. Notable scientific awards and recognitions include: Best Paper Award at CRYPTO 2013 Invited Speaker at the 12th International Conference on Finite Fields (2015) Invited Speaker at the 25th British Combinatorial Conference (2015) Invited Session Speaker at the AAAS Annual Meeting (2014) Speaker at multiple international workshops on finite fields, cryptography, and polynomials Professor McGuire actively supervises PhD students and has coordinated key modules such as Galois Theory, Cryptography, and Numbers & Functions. He has secured research grants, including one on the simulation of photo-electronic excitation in nanofilms. His most famous contribution is the proof that no 16-clue Sudoku puzzle exists, achieved through a novel hitting set enumeration algorithm. He is a principal investigator in computational and theoretical mathematics with ongoing collaborations across Europe. He is a member of research teams focused on finite field applications, cryptographic protocols, and algebraic coding theory. His lab-like collaborative environment involves work with postdocs and researchers on projects related to discrete logarithm computation, polynomial factorization, and quantum code design.