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Dan Baczkowski's research interests include elementary and analytic number theory, yet he has dabbled in other areas like algebraic combinatorics, design theory, and algebra. In particular, he has explored Diophantine equations involving factorials, applications of counting lattice points close to smooth curves, distribution of fractional parts of powers of rational numbers, applications of covering systems to problems in number theory, and Hadamard matrices problems.
Some recent projects with student collaboration include finding intersections between classical sequences such as the Fibonacci numbers, Lucas numbers, Sierpiński numbers, Riesel numbers, triangular numbers, etc. These works have involved some concepts from elementary number theory and computer programming and algorithm writing. The long term goal is to discover more about the Sierpiński and Riesel numbers for which the vast majority of research utilizes the covering systems of Paul Erdős.
For some of my math papers, see my preprints folder.
See my formal research statement which includes many of the topics I have investigated.
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