Oliver Knill Homepage

Spring, 2020: I teach Single Variable this spring. A bit more about index expectation in diff geometry related to Hopf conjectures. About the picture to the right.
Fall, 2019: I teach Math 21a this fall. New in graph geometry: Energized complexes [ArXIV]. (A few slides.) Some notes from Professional norms in math. A simple sphere theorem ArXiv). A PDE lecture. Poincare-Hopf for vector fields [ArXIV] and more [ArXIV] and Constant curvature [ArXiv]. Hopf conjectures [ArXiv] and fall photos and Marthas Vineyard.
Summer, 2019: I teach Maths21a. New: Numbers and Graphs and slides. A Parametrized Poincare-Hopf and slides. Travel: I, II and III, IV and V. Summer: I. The energy of a simplicial complex [PDF]. Tech: Povray is great. New in graph geometry: Counting Matrix [PDF].
Spring, 2019: I teach Math 22b. Winter photos: Nantucket I, and II. New in graph geometry: A Reeb sphere theorem in Graph theory. Winter Harvard I, II, III. Some Plumber stories. New graph geometry: the average simplex cardinality and Dehn-Sommerville from Gauss-Bonnet and slides and blog entry and Gauss-Bonnet. Spring photos.
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Oliver Knill, Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA. SciCenter 432 Tel: (617) 495 5549, Email: knill@math.harvard.edu 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.