معرفی
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.
