Adventures with Manifolds
The work on Sard is wrapped up in : https://people.math.harvard.edu/~knil... See also https://www.quantumcalculus.org/adven... for more comments and screenshots. A typo on the left side chalk board only noticed after editing: the standard map is T(x,y) = (2x-y+c sin(x), x) (see https://people.math.harvard.edu/~knil... for a javascript animation from 2015) or https://dynamical-systems.org/twist from 1999.
Time line:
0:00 Avata footage taken in Winchester and Stoneham near Fells reservation
1:00 a quick look back on Sard and how to continue
2:20 about manifolds. for me it started with a problem in ergodic theory
3:30 changing research fields
4:00 structure of motion (work with Jose Ramirez-Herran) in 2007-2009
4:45 some footage with Insta X3 on avata in Cambridge commons
8:30 something about 3D printing (work with Liz Slavkovsky in 2013)
10:00 integral geometry (work with Barry Tng, 2015)
11:00 flying avata in my office with the insta 360 X3 on top.
In this end of the year recording, some other stories are mentioned, like 3d printing, integral geometry, the entropy problem and most prominently the structure of motion problem, where manifolds play an important role. To a combination of hobbies: flying drones and panorama photography: a insta X3 is placed on top of the DJI avata and flown around in my office. The drone footage at the beginning and end were from runs this week done in the Fells: a longer run was a Arlington-Winchester-Woburn-Stoneham-Medford-Sommerville, Arlington round. The second shorter crossed the fells along the 93. Both runs together were a marathon. I made lots of stops however to photo. I also carried my laptop with me in both runs (did finish up some writing in coffee shops).