Spring, 2024: Upper level coordination, Spring 2024. Math 1a, Spring 2024. Manifolds from Partitions [ArXiv]. Stuff from the fall: Differential geometry, Fall 2024. Tutoral 99R Fall 2024.
Fall, 2023: Math 1b, Fall 2023, Upper level coordination. Three tree theorem [ArXiv] and Arboricity of manifolds [ArXiv] and Arboricity and Acyclic Chromatic Number and Morse-Sard II [PDF].
Summer, 2023: Math S 21a, Summer 2023, May 21: Cohomology of open sets and a bit of dynamics: May 28: Mandelbulbs, Jun 18: Weierstrass and the Pendulum, and Jul 23: Cohomology of measurable sets.
Spring, 2023: I'm teaching a section in Math 21b this spring. Upper level coordination. A sphere formula. And A higher Characteristics. April 3: Spectral Monotonicity. Some stable diffusion experiments.
Fall, 2022: I'm teaching a section in Math 21a this fall. Upper level coordination. Something about topology.
Summer, 2022: Math S 21a, Summer 2022 Spectra of Kirchhoff Laplacian, Tree-Forest Ratio, Graphs, Groups and Geometry, Babylonian graph. Summer travels 2022.
Spring, 2022: I teach Math 22b Analysis and Math E-320 Math with a Historical Perspective. Upper level coordination. Some pictures from Martha's Vineyard winter break. About analytic torsion ArXiv. Summer 2022 Website.
Fall, 2021: I'm teaching a section in Math 1b this fall. Updates on Graph geometry. Some work in progress [PDF]. Some pictures December 2021.
Summer, 2021: Maths21a. Graph arithmetic[ArXIv], Coloring manifolds [ArXiv], Curvature of products [ArXiv], Chess, DNA etc. (ArXiv). Recent Videos.
Spring 2021: Math 1a, Single Variable and MathE320, Math with a historical perspective". graph complements and ArXiv. May talks: homotopy manifolds, graph I, manifolds, graph II, coloring I, II.
Winter 2020: Graph geometry news. Math movies updates. Fall photos: I, II, III, IV. Winter photos: I and II. and III.
Fall, 2020: Sweet complexes [PDF] in the Graph geometry. (see also a present, slides, code, ArXiv). Also: Quantum calculus updates. Section page 1A. Fall photos: I, II, III. IV. On simplicial complexes with code.nb and Shannon capacity.
Summer, 2020: Maths21a. About the pic to the right. Summer photos I, II, III, IIIa, IV, V, VI, VII, VIII, IX. On Positive curvature. and graph geometry, Life in a Day.
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. The Energy article is up. A bit on diff geometry. Spring photos
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.
Fall, 2018: I teach Math 22a this fall (Catch 22!). More Summer photos (I), (II), (III). Eulerian Edge refinements, geodesics, billiards and sphere coloring [ArXiv], see also the blog entry on the Euler Game. In the Mathtable talk on Goldbach, showed also a clip from Fermat's room. Fall photos: (I), (II) with Bacow inauguration, (III). Cartan's Magic Formula [ArXiv]. Fall/Winter photos (IV) with khipus. (IV) with CS50 fair.
Summer, 2018: I teach Maths21a. New in graph geometry: the paper Combinatorial manifolds are Hamiltonian. See also the Blog entry or Slides. Summer photos (I). (II). (III). Something about creativity and computer algebra. Some fundamental theorems [PDF].
Spring, 2018: Math 21b Winter photos: I, II, and III. January photos (with Vermont): I, II, and III. Dyadic zeta [ArXiv] with Blog. Hear cohomology [ArXiv]. Euler's day 2/7/18: [PDF], Talk [Youtube], Slides [Youtube]. Hydrogen [ArXiv]. AMS Apr 21-22, Notes [PDF] slides and cohomology. Summer 2018. Syntax Spring photos I, II, III.
Fall, 2017: I teach Math 21a Multivariable calculus and Teaching Math with a historical perspective (Canvas). ArXiv: "The strong ring" and as a follow up: discrete Atiyah-Singer (and blog entry), for graph geometry. Travel photos: I, II, III. Energy of a complex. Chandra (1920-2017). Fall photos: I, II, III, IV. One can hear the Euler characteristic of a complex [ArXiv].
Summer, 2017: I teach the Maths21a this summer. Some Barycentric refinement. Summer photos: I, II, III, IV. Clips: 10-2=20, 12% > 11%. Updates graph geometry: Dehn-Sommerville [ArXiv], arithmetic of graphs [ArXiv], Strong ring of simplicial complexes [PDF], Slides: Hardy-Littewood race and Middlesex canal with Slides. Some amazing identities by Monisharan Maheswaran.
Spring, 2017: Math21b. Quantum Calc. Block Island, Boston library. Winter: I, II, III, IV, V, office, lab. The algebra adventure. Sphere geometry with slides, and Helmholtz free energy. Entropy in film. Spring I. II. III. 50 years SJF.
Fall, 2016: Math21a at college and Math E320 at extension. Update graph geometry: graphs related to counting and particles and primes. Fall 2016 Photos. SIAM talk 9/30, 2016, slides. Also SIAM resources. Related: and Rocky run. Mystic run. Mathtable [PDF]. More Fall 2016 Photos, Swiss movies and River panoramas. Apropos: On time and the river and Goodwill problem revisited. Unimodularity theorem and slides.
Summer, 2016: I teach the multivariable course Maths21a. A HCRP PDE project. A 15 min Calculus refresher. Some experiments with primes and matrices as seen here or in this animation. Summer 2016 panoramas and a new google earth experiment. Travel photos:Rheinfall, Salmenfee, Uhwiesen and Israel.
Spring, 2016: I teach the linear algebra course Math21b (Canvas admin), this spring semester. Providence end of year. New in graph geometry: Gauss-Bonnet for multi-linear valuations and some slides on Wu characteristic with miniblog, a row reduction, determinant, and PDE song. Some winter 2016 and spring 2016 panoramas. Ecdysis Spring 2016.
Fall, 2015: I teach multivariable Math21a (Canvas)), this fall as well as Math 320E in the Extension school (Canvas)). New in graph geometry: Spectra of barycentric refinements:ArXiv (miniblog) as well as a a discrete Sard result (miniblog) and more Chladni pictures. Photos of Summer 2015 travels, a Freshmen advising lunch, and November river panoramas. A rewrite of universality. On Barycentric characteristic numbers.
Summer, 2015: I teach the multivariable course this summer. New in graph geometry: a Cartesian product (ArXiv). During a Santorini 2015, wrote on Jordan-Brouwer-Schoenflies theorem. Techno demos: Double pendulum and Chirikov or Game of Life demo in JS or Chladni figures for a graph. Projects in Maths21a. Run in Baltschiedertal.
Spring, 2015: After Nantucket end of year, February blizzards and snow affected also teaching. Math E320, needing some online lecture. Since I teach 21b something about Eigenvalues. Jan 12: Graphs with Eulerian Unit spheres, in graphgeometry, mini blog. Curliecue and Buffon javascript demo. Feb 15 talk at BU [PDF].
Fall, 2014: I teach the Harvard Multivariable calculus course this fall. Advising Lunch Aug 27. Tracing walks of Jean Piaget and Georges de Rham during visit in Salmenfee. Oct 5: a graph geometry update: Curvature from Graph Colorings and some variational problems in graph theory. Dec 22: some work on graph coloring [ArXiv] with mini blog [HTML], illustration [HTML], animation [YouTube] and slides [YouTube], [PDF].
Summer, 2014: I teach the Summer 2014 multivariable course this summer (Summer syllabus [PDF]) and work on a HCRP project with research page, in geometric graph theory. Update to Cauchy-Binet with miniblog. About descriptive geometry. Summer splash.
Spring, 2014: I teach Math 1a and Math E-320 this spring. A graph geometry update. A landscape inverse problem. Slides orbital networks and AMS meeting Baltimore slides. A Charles river and Bike run. Chinese remainder update and javascript demo. Summer 2014 website and syllabus [PDF]. About calculus on graphs. Sinai won Abel prize, see Sinai billiard.
Fall, 2013: I teach the Harvard Multivariable calculus course this fall. Advisees lunch Aug 28. The beauty of networks. Syllabus for Math E-320, Spring 2014 [PDF], Interesting work on an older paper with Hof and Simon, Calabi-Yau on Thingiverse, AMS session January. Sad to hear that Oscar Lanford passed away November 16. Work on the Zeta function of circular graphs.
Summer, 2013: I teach multivariable calculus this summer. Various updates on graph theory: Cauchy-Binet with a forest theorem, and an integrable system. Slides [PDF] from ILAS 2013 [PDF] and notes. Monthly problem. with code for experimentation. The Math in movies page appeared in a podcast [MP3] (starts at 11:20) made by Jamillah Knowles. 3D printed objects arrived.
Spring, 2013: I teach Math 1a and Math E-320 this spring. Over the break, a new update on graph theory and a paper with Liz [PDF] [ArXiv]. student projects from the fall printed. Links: Trieste (see book, slides [PDF]), ILAS 2013 and SIC 2013 (outline [PDF], slides [PDF]). A PechaKucha. A spring break zeta flight.
Fall, 2012: I teach Math21a this fall. The 3D printing thesis of Liz is finished. Update on graph theory. Bridgewater Slides [PDF] from a MAA Fall 2012 Section Meeting. Course website for Math E320, Spring 2013.
Summer, 2012: More update on graph geometry, more on Birkhoff sums and update on CRT and the 3D printing project. The Math21a Summer school page and already a Math21a fall page. Our chicken.
Spring, 2012: I teach Math1a and Math E-320 this spring. There are some updates on graph geometry. The Summer 2012 website. A lecture in creativity, [Youtube].
Fall, 2011: I teach the multivariable calculus course this fall and Math1a and Math E-320 in spring 2012 which will be also part of distance learning. This fall also: Liz 3D printing project, updates on graphgeometry, and a bird project.
Summer, 2011: This summer I teach Multivariable calculus in the Harvard summer school. A collection of Math novels started this summer. A Revision of the paper with Tangerman which is going to appear in Nonlinearity. Panoramas and nonpanoramas from the summer. Here is the multivariable calculus course website of Fall 2011/2012.
Spring, 2011: This spring I teach Math 19b and Math 1a, as well as Math E-320 at the extension school.
Fall, 2010: I teach linear algebra this fall. Some recent panoramas: Freshmen convocation, of August 31, 2010, Columbus day, the Cape and a Locke farm near our home.
Summer, 2010: I taught Multivariable calculus this summer. June 27 was the Charles river run 2010. Some summer panoramas from Ausserberg, Uhwiesen in Switzerland and from Acre to Cesarea in Israel.
Spring, 2010: I teach 21b this spring as well as a new course Teaching Math with a historical perspective at the Harvard extension school. Jose's thesis is now finished and won a prize photo. Here is the link to the summer school multivariable course site of 2010. A paper written this spring. On the project page, you find more pictures.
Fall, 2009: I teach 21a in the fall. A start of the semester with some remarkable talks and Math riddles which is part of theMath movie collection. Panoramas from a Vermont weekend. Slides from a math circle talk on polytopes. See also a youtube clip. recorded on a new imac, which also helped to test new Google earth experiments. More Work with Jose Ramirez on Computer vision is in the process of being wrapped up. We went to Martha's Vineyard for the last days of the year. The colder winter allowed a new Charles river crossing.
Summer, 2009: As usual, I taught multivariable in the summer school. It was a rather large (52) but great class this summer and I would have loved to continue an other 6 weeks. Besides teaching, I continued to bike this summer (additional 300 Km/Mth to the 200 Km/Mth to work) as a running complement (running is also about the usual 300 Km/Mth). Early in the summer, I ran theCharles river run. A lot of programming work on vision with Jose. Boring twitter details about the summer.
Spring, 2009: I teach linear algebra and applications this semester. Here are some notes from a Mathtable talk: treasure hunting perfect Euler bricks. This semester, we continue a HCRP project in elementary differential geometry and focus on caustics as well as continue to work with Jose on computer vision. Here is problem which killed a few spring semester hours. And here are some technology in the classroom demos for example with now with Java source from 2002 applets. Check out 3430 mathematicians on a 360 degree wall. The power of perl ...
Fall, 2008: Taught multivariable calculus in the fall semester. Besides helping out Otto Bretscher a bit for the solution manual of his new edition, the beginning of the semester was also used to finalize with John Lesieutre a project on Dirichlet series with almost periodic coefficients of the summer. John had been working with me as a PRISE fellow on this exciting project during the summer. In the second half of the semester, I started with Michael Teodorescu a beautiful HCRP project in elementary differential geometry. Here is the project page. We spent the last days of the year on Cape Ann.
Summer, 2008: Quite a bit of training for a triathlon in Switzerland, a re-run of the 1987 "transswiss". Instead of roller blading, I biked 1000 km/month for 3 months often tripling or quadrupling my bike time to/from work. Highlights were trips to Gloucester(5h) or Wachusetts(7h). Even so I had been swimming competitively as a teenager and swam almost daily during my California and Arizona years, swimming needed a refresh (1-2 km/week for 4 months and two 4K full distance tests). I continued to run 10-20 km/day as usual. Also the summer school course and a KAM project were fun. The summer ended with travels to Switzerland and Israel: Wallis, Uhwiesen, and Haifa/TelAviv. Twitter details.
Spring, 2008: I'm teaching Math21b, linear algebra this semester. The semester with a presentation organized by SCI. 2008 is the year of mathematics. In Germany, the "year of mathematics" produces quite a bit of hype, the German TV for example shows a report. Apropos movies: the "math in movies" page got a bit updated this year. Google also built the science center.
Fall, 2007: Math21a was fun as always. Students liked Mathematica 6. A talk at Colby on SFM and a talk on perfect numbers were fun. See the handout. On the gadget side, the "Ipod touch" changed my life. The touch is exactly what I needed. As a constant companion, I can read email after the gym or surf the web on the chair of the dentist. I also got OS X Lepard when it arrived and all eligible Macs run it. Ubuntu upgrades to Gutsy. And there were the last days of the year.
Summer, 2007: Here are some links to a Summer 2007 diary I maintained from June 1 to September 3 2007: The Summer school course was great fun to teach. We had a project Mathematica 6. Also the Summer project with Jose in computer vision was a blast. Some 360 panoramas got added to to this page: like the Potter night at Harvard square and the summer trip from the alps in Switzerland to the Mediterranean sea. I also got a new Piano.

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,