His research interests lie mainly in the fields of geometric knot theory and discrete and computational geometry, though he also has peer-reviewed work in sustainable service learning and relationships between knot theory and musical rhythm. The primary goal of his research is to collaborate with students. Thus, finding projects accessible by undergraduates is always his top priority and has resulted in multiple co-authored peer-reviewed articles.
Beyond the classroom, Neil is North Central College's Faculty Athletic Representative (FAR) to the NCAA and serves as advisor the NCC Cycling & Multisport Club. He chairs the Faculty Elections Committee as well as the informal faculty Fermentation Committee, has served as a Director-at-Large for the Illinois Section of the Mathematical Association of America, and has served as a Coleman Foundation Faculty for his weaving of entrepreneurial approaches into his general education courses.
Dr. Neil has been very active in the M3 math modeling competition, serving as a grader for their national competition and having written multiple problems for their monthly dialogues. He was the primary author of the 2016 national competition question, partnering with the National Park Service to write, "From Sea to Shining Sea: Looking ahead with the National Park Service."
Beyond North Central, Dr. Neil spends much of his time devoted to his passions of running (not fast but far), ultra-distance mountain bike racing and bikepacking. He is also the founder of DTS (Dream, Train, Succeed) Coaching and works with athletes of all levels to achieve their running goals. And last, but certainly not least, Dr. Nicholson, along with his amazing wife Elizabeth and fantastic son Zeke, spends ample time addressing the needs of Gordon and Gus, his two cats.