Dr. Davis is interested in questions that require algebraic techniques to solve combinatorial problems. He has done work in difference sets and related objects, bent functions, and error correcting codes with an emphasis on finding new constructions with optimal or near-optimal structure. He has also worked in an industrial research lab (Hewlett-Packard) and served as a testifying expert in a patent dispute between Apple and Samsung.
He has 15 granted patents including:
K.K. Smith, J. Jedwab, J.A. Davis, D. Banks and S.R. Wyatt, System for error correction coding and decoding, U.S. Patent No. 7418644, 26 Aug 2008.
D. Banks, J. Davis, and J. Jedwab, Identifying uncorrectable codewords in a Reed-Solomon decoder for errors and erasures, US Patent No. 7278086, 2 October 2007.
J. Davis, K. Eldredge, J. Jedwab, G. Seroussi, and K. Smith, MRAM with controller, US Patent No. 7266732, 4 September 2007.
National Security Agency Grant, 2015
National Science Foundation, LURE, 2007-2011, $1,500,000.
National Security Agency Grant, salary, travel expenses, and support for undergraduate research, January 2003-December 2005.
University of Richmond Undergraduate Research Commmittee Collaborative Grant, salary and travel for me and two students, summer 2002.
Hewlett-Packard Grant for Leave of Absence, academic year 2000-2001, paying salary, moving expenses, cost of living expenses, and benefits.
Apple-Samsung: the codes in 3G communication, Finite Fields conference, Magdeburg, Germany, July 25, 2013.
Apple-Samsung: a personal story, University of Richmond, August 2012.
Science Scholar Committee, 1994-present
Davis, J., & Xiang, Q. (2000) A Family of partial difference sets with Denniston parameters in nonelementary abelian 2-groups. The European Journal of Combinatorics, Vol. 00, 1-8.
Davis, J., & Jedwab, J. (1999) "Some recent developments in difference sets," in K. Quinn, B. Webb, F. Holroyd and C. Rowley, eds., Pitman Research Notes in Mathematics,Combinatorial Designs and their Applications, Addison Wesley Longman, 83-102.