Convex polytopes, selected chapters (in Russian)
IUM website: here (in Russian)
Instructor: Igor Pak (UCLA)
Schedule: starting Feb 9, 2021, Zoom lectures will be on Tuesdays, 17:30-19:10.
Location: Zoom link (meeting ID: 981 2462 9796).
Passcode: number of faces of icosahedron.
I plan to follow chapters 14-18 of my book (not in this order).
I will also mention some more recent work which I will also post here.
- L1: Bolyai-Gerwien, Bricard and Dehn theorems (Chapter 15 in the book)
Part-1, Part-2, Whiteboard (all unedited)
Original papers by Bricard (in French), Dehn (in German), and
Kagan (in Russian)
Additional reading: §9-11 in the Hilbert's Third Problem by V.G. Boltyansky (in Russian)
and Hinged Dissections Exist by T. Abbott et al.
- L2: Polytope algebra, Sydler and Zylev theorems (Chapter 16 in the book)
Video, Whiteboard (all unedited)
Original papers by Sydler: first
and best (in French), by Jessen (in Danish), Zylev:
and second (in Russian).
Additional reading: Lagarias-Zong paper
on tetrahedral packing and Aristotle's mistake, and this clarification
on spider legs and Aristotle's non-mistake.
- L3: Valuations, Dehn invariant, and Ludwig-Reitzner theorem (Chapter 17 in the book)
Whiteboard (all unedited)
Original sources: Ludwig-Reitzner paper
Additional reading: Valuations and Dissections, a survey
by P. McMullen.
E-mail: click here (delete .zzz)
Return to Igor Pak Home Page.
Last updated: 2/25/2021