The thesis, old interests as well as publication and preprints and seminar page or the last chapter in my probability book illustrate earlier work in ergodic and spectral theory. Having always done what is now called "experimental mathematics" (initially got hooked with additive number theory), I have a passion for mathematical problems in computer science, with discrete structures, geometry or probability. Always having been fascinated by almost periodicity, (like packings, fluids, operators, walks, matrices,cellular automata), or Dirichlet series. A particular question on Birkhoff sums or the Birkhoff sum of the cotangent function. (Some notes (43 pages PDF) for a talk). A couple of years ago, playing with polyhedra led to a paper in graph theory which continues to interest me and fits well into quantum calculus. Teaching got me interested also in pedagogical questions, especially in web pedagogy and the use of technology in teaching. I love movies, especially if they contain math. In that context, a central interest is calculus and especially quantum calculus (which has a dedicated blog). About the history: here [PDF] is a course developed and ran first in the spring of 2010 and is now taught for the 9th time.

Some work highlights: Here is some more unpublished work (most of it is not even submitted once as writing down ideas currently has priority). This is ordered according my personal current preferences:

Oliver Knill, Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA. SciCenter 432 Tel: (617) 495 5549, Email: Quantum calculus blog, Twitter, Youtube, TikTok, Vimeo, Linkedin, Scholar Harvard, Academia, Harvard Academia, Google Scholar, ResearchGate, Slashdot, Ello, Webcam, Spring 2020 office hours: Tentative: Mon-Fri 9-10 AM and 5-6 PM and by appointment.