Lectures
The following is a preliminary list of the lecture in the course and topics covered each time. Lectures are on Tuesdays 8.15-10.00.
Given the current high spread of omicron and the recommendations to diminish risk of spreading the virus, we have decided that the first lecture will be given over zoom. But I will sit in the assigned room Q15 and give the lecture. Those of you that want to come to the lecture room are welcome to do so.
Zoom room: https://kth-se.zoom.us/j/63098396988
Course literature will be the following three books that should all be available online to KTH and SU students via the library..
Lectures on Polytopes, Günter Ziegler, Springer Verlag. GTM (2012)
Computing the continuous discretely, (BR) Matthias Beck and Sinai Robins, Springer UTM, (2015)
| Lecture | Day | Room | Content | Literature | Lecturer | Preliminary |
Notes |
| 1 | 18/1 | Q15 | Introduction and Examples of Polytopes | Ziegler, chap 0 | Svante | Slides 1 Download Slides 1 | |
| 2 | 25/1 | D41 | More examples and Fourier-Motzkin elimination, Homogenization | Ziegler chap 0-1 | Svante | Slides 2 Download Slides 2 | |
| 3 | 1/2 | D41 | Carathéodory's thm, Faces of a polytope. | Ziegler chap 1-2 | Svante | Slides 3 Download Slides 3 | |
| 4 | 8/2 | Q15 | Face lattice, simplical polytopes | Ziegler chap 2 | Svante | Slides 4 Download Slides 4 | |
| 5 | 15/2 | Q17 | Shellability | Ziegler chap 8 | Alex | Slides 5 Download Slides 5 | |
| 6 | 22/2 | D41 | Brugesser-Mani and h-Vectors | Ziegler chap 8 | Alex | HW1 handed out | Slides 6 Download Slides 6 |
| 7 | 1/3 | V21 | Dehn-Sommerville and UBT | Ziegler chap 8 | Alex | Slides 7 Download Slides 7 | |
| 8 | 8/3 | 3721 | Kruskal-Katona and g-Theorems | Ziegler chap 8 | Alex | HW1 due | Slides 8 Download Slides 8 |
| 9 | 15/3 | 3721 | Polytopes and Linear Programming | Benjamin | Solutions HW1 Download Solutions HW1 | Slides 9 Download Slides 9 | |
| 10 | 22/3 | D41 | Examples of Triangulations | DRS 2.2 | Benjamin | Slides 10 Download Slides 10 | |
| 11 | 29/3 | D41 | Secondary Polytopes | DRS 5.1 | Benjamin | HW2 handed out Download HW2 handed out | Slides 11 Download Slides 11 |
| 12 | 5/4 | V01 | More on Secondary Polytopes | DRS 5.2 | Benjamin | Slides 12 Download Slides 12 | |
| 13 | 12/4 | E52 | Ehrhart polynomial | BR 2.2,2.3,3.3,3.4 | Lorenzo | HW2 due | Slides 13 Download Slides 13 |
| 14 | 26/4 | D41 | Stanley nonnegativity and reciprocity | BR 3.5,4.1,4.2 | Lorenzo | HW2 solutions Download HW2 solutions | Slides 14 Download Slides 14 |
| 15 | 3/5 | D41 | The degree of a polytope, Gorenstein and reflexive polytopes | BR 4.3, 4.4 | Lorenzo | Slides 15 Download Slides 15 | |
| 16 | 10/5 | D41 | Gorenstein and reflexive polytopes (continued). Magic squares | BR 4.4, 6.1-6.3 | Lorenzo | HW3 handed out Download HW3 handed out | Slides 16 Download Slides 16 |
| 10/5 | 3721 | PhD presentations 13-15 | Petter Restadh Danai Deligeorgaki |
Slides Petter Download Slides Petter | |||
| 17/5 | 3721 3721 |
PhD - presentations 8-10 and 13-15 |
Joel Frisk Gärtner |
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| 24/5 | 3721 | PhD presentations 13-16 | Philippe Moreillon Leo Saud Maia Leite Aryaman Jal |
HW3 due | Slides Leo Download Slides Leo | ||
| Exam | 7/6 | ||||||