Brief Summary of Accomplishments
Tel: 410-455-2338
Fax: 410-455-3969
E-Mail: Lomonaco@umbc.edu
Web Page: http://www.cs.umbc.edu/~lomonaco
1985 - Present
University of Maryland Baltimore County (UMBC),
Baltimore, MD, Computer Science & Electrical Engineering
Department, Full Professor. (Chair, 1985-1991.) (1991-92,
while on sabbatical leave from UMBC, Academic Visitor at
Center for Computing Sciences (CCS), Bowie, MD.)
Fall Semester 2003, Visiting Key Senior Research Scientist,
Mathematical Sciences Research Institute (MSRI), Berkley, California
Academic Year 2004/2005, On sabbatical leave, visting the
Institute for Scientific Interchange (ISI) in
Turin, Italy as a
Senior LaGrange Fellow.
1983-1985
Army Research Laboratories (ARL), Adelphi, MD, Research
computer scientist/mathematician (signal processing).
1981-1983
Institute for Defense Analyses (IDA), Alexandria, VA,
Science & Technology, Computer Scientist/Mathematician
(Design & Development of Ada.)
1971-1981
State University of New York at Albany (SUNYA), Albany, NY,
Computer Science Department, Associate Professor. (1974-76,
while on leave from SUNYA, Academic Visitor at Center for
Communications Research (CCR), Princeton, NJ.)
(1979-80,
while on sabbatical leave from SUNYA, Visiting Associate
Professor of Mathematics and Computer Science, Unversity
of British Columbia,
Vancouver, B.C., Canada.)
1969-1971
Texas Instruments, Dallas, TX, Research Computer
Scientist/Mathematician (Advanced Scientific Computer (ASC)
Development.)
1965-69
Florida State University, Tallahassee, FL, Mathematics
Department, Assistant Professor.
1964-65
St. Louis University, Mathematics Department, Assistant
Professor
Brief Summary of Accomplishments
Dr. Lomonaco is internationally known for his many contributions both in Mathematics and in Computer Science.
In mathematics, Dr. Lomonaco provided a solution to problem 36 of R.H. Fox, a problem that resisted solution for over 15 years. In doing so, he created the hyperbolic section representation of four dimensional knots, and a homology theory for systems of groups connected by morphisms. The latter was accomplished by inventing a generalization of Eilenberg-Mac Lane complexes, called GEM complexes. He also demonstrated that Saunders Mac Lane's algebraic 3-type completely classifies a large class of four dimensional knots. Moreover, he created the movie-movie representation of five dimensional knots. Recently, Dr. Lomonaco has shown how knot theory can be applied to solve some outstanding problems in electrodynamics. He also serves as an associate editor of the Journal of Knot Theory.
In computer science, Dr. Lomonaco has used group representation theory to develop the theory of non-abelian error-correcting codes. He has developed a symbolic algorithm for factoring integers that reduces integer factoring to the task of solving boolean equations. For his many contributions to the development of the programming language Ada, Dr. Lomonaco received an award from the United States Under Secretary of Defense for Research and Engineering, Dr. Richard DeLauer. In quantum cryptography, he has shown how quantum information theory can be used to gain a better understanding of eavesdropping with quantum entanglement. In quantum computation, he has shown how Lie groups can be used to solve problems arising in the study of quantum entanglement. He is currently working on the development of new quantum algorithms based on the quantum hidden subgroup paradigm.
Dr. Lomonaco was the first to formally introduce to the American Mathematical Society (AMS) the new and emerging discipline of quantum information science. He did so by organizing and giving at the Annual Meeting of the AMS held in Washington, DC in January 2000, the first AMS Short Course on Quantum Computation and the first AMS Special Session on Quantum Computation and Information. These two events (AMS Short Course and AMS Special Session) were recorded as two AMS books:
- Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, PSAPM/58, AMS, (2002)
- Quantum Computation and Information
, CONM/305, AMS, (2002)
These books were written with the purpose of enticing and daring the mathematical community into participating in the many mathematical research opportunities arising from the “Grand Challenge of Quantum Information Science.”
For the fall semester of 2003, Dr. Lomonaco was a visiting member of the Mathematical Sciences Research Institute (MSRI) in Berkeley, California, and participated in the MSRI semester-long program on quantum Information Science in the invited role of Key Senior Research Scientist.
Dr. Lomonaco has also given many invited one hour lectures on quantum computation and quantum cryptography at various institutions and professional meetings. Recently, Dr. Lomonaco gave four invited one hour lectures at the University of Virginia NSF Conference and Workshop on Coding Theory and Quantum Computing.
At the University of Maryland Baltimore County (UMBC), he teaches a graduate level course CMSC 643 on quantum computation, and currently has two PhD students working under his direction. He also serves as Associate Editor of the Journal of Knot Theory and Its Ramifications. Dr. Lomonaco is also PI (with Co-PI Louis Kauffman) of the Quantum Algorithms Research Group which currently receives support from DARPA. This group has for example created six new quantum hidden subgroup (QHS) algorithms, namely the Wandering Shor algorithm, the Lifted Shor algorithm, the Quantum Circle algorithm, the Dual Shor algorithm, and a Quantum Algorithm for Functional Integrals.
Quantum Computation, Quantum Cryptography, Entangled States, Quantum Eavesdropping; Knots, Electrodynamics, Energy, Magnetic Knots, Electrostatic Knots, Minimal Energy Knots, Fluid Dynamics, Plasmas, Vortices, Gauge Theory; Error-Correcting Codes, Algebraic Codes, Non-abelian Codes, Metacyclic Groups, Group Representations; Symbolic Computation, Boolean Rings, Factoring, Algebraic Ring Extensions; Homotopy Groups, Higher Dimensional Knot Theory, Homology of Group Systems, Covering Spaces, Morse Theory
Publications
For publications, please link to Representative Publications
