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. (Moscow time).

Location: Zoom (link expired).
Passcode: number of faces of icosahedron.

Content:

Over the course of six lectures, 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.

Lectures:

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: first 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)
Video, Whiteboard (all unedited)
Original sources: Ludwig-Reitzner paper
Additional reading: Valuations and Dissections, a survey by P. McMullen.
L4: Spherical tetrahedra, Monge equivalence, geometric RSK (Chapter 18 in the book)
Video, Whiteboard (all unedited)
Original sources: Henriques-Pak paper, Kuperberg's paper, Pak's geometric RSK paper, Kolpakov-Robins paper.
Additional reading: Dupont's Notices article
L5: Space tilings with congruent polyhedra
Video, Whiteboard (all unedited)
Original sources: Alexandrov paper, Niven paper, Erickson paper.
Additional reading: Grunbaum -- Mani-Levitska -- Shephard paper.
L6: Domino tilings and plane triangulations (Chapter 14 in the book)
Video, Whiteboard (all unedited)
Original sources: Thurston's lectures, Pak's old survey on tilings.
Additional reading: Pak-Sheffer-Tassy paper on fast domino tileability.

Contact information:

E-mail: click here (delete .zzz)
Telegram: @IP_LA

Return to Igor Pak Home Page.

Last updated: 4/17/2021