Dr. Daniel M Look

I received my PhD from Boston University in 2005 working under Robert L. Devaney. I work in an area of mathematics called Complex Dynamics. This area studies the behavior of iterated functions of the complex plane. Essentially, I try to discover the long-term behavior of points that are run through a feedback loop of sorts. This often involves studying the Julia set for a function, where the Julia set is a (usually very stunning) fractal picture that acts as a type of graph. In terms of teaching, my dream class is one where no student is afraid to ask questions and all students feel challenged, yet not overwhelmed, by the material. I do my best with each class I teach to create such an environment. 

Current Research:

I am currently working on a few research projects. In the field of Complex Dynamics I am looking at the dynamics of perturbed complex polynomials as well as a map derived from a form of multiple circle inversion in the complex plane. Outside of Complex Dynamics I have research involving text mining and stylometry (a mathematical/statistical study of linguistic style) as well as the use of mathematics in comic books and other pop culture media.

Publications:

2024: "Sequence of complex radius values that yield capture Sierpiński curve Julia sets for n-circle inversion", Topology Proceedings, Vol. 64

Additional Contributions to Mathematics and Popular Culture:

• 2024: Wrote a review of "Intersections between boundaries of bounded hyperbolic components of cubic polynomials" by Qui and Wang (Math. Z. 305 (2023), no. 4, Paper No. 55) for the American Mathematical Society’s Mathematics Review
• 2024: Co-PI on a successfully funded MAA Tensor Grant to host Math and Everything: Inspiring College Math Study in Women High School Students in Northern NY at St. Lawrence University (bringing ~200 high school women to campus for mathematical programming).
• 2023-Present: Area Co-Chair for the Pulp Studies section of the national PCA Conference
• 2023-Present: MAA Seaway Section Randolph Lecture Committee (Chair)

Talks & Workshops:
• October 4-5, 2024: MAA Seaway Section, Rochester Institute of Technology
Talk: Can Circle Inversions be Interesting?
• April 19-20, 2024: MAA Seaway Section, SUNY Fredonia
Workshop (Invited): Exploring Alternatives to Traditional Grading (Section NExT Workshop)
• March 27-30, 2024: Joint Meeting of the PCA/ACA, Chicago, IL
Talk: Klein & Möbius: Twisted Surfaces in the Pulps

Personal Webpage