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Discrete Geometry: Lattice Polytopes (VL im Wintersemester 2015/16)

Modul MA5215 4V+
Termin (VL) Montags 10:15–11:45 im 02.10.011
Freitags 10:15–11:45 im 02.10.011
Termin (TÜ) Montags 12-14 im 02.06.011
Dozent Carsten Lange
Übungsleiter Carsten Lange

Aktuelles

2016-01-08
The SFB-TRR 109 applied for a second funding period. The review process is due January 13-15. Therefore, the lecture on Friday, January 15
is cancelled.
2015-11-13
We re-evaluated the time slots for the tutorial. The official tutorial is monday after the lecture in room 02.06.011 (12-14). There is an inofficial tutorial that I offer
on request (wednesday 12-14 also in 02.06.011)
2015-11-13
My Email had the correct time for yesterday's tutorial,below I was in a different time zone, I wanted to write 1200hrs and 1215 hrs! Please accept my apologies!
2015-11-12
Tutorial today starts at 1415hrs in MW 3707. We can meet at 1400hrs in front of 02.10.011and walk together to MW 3707.
2015-11-09
We meet in front of 02.10.011 at 1415hrs for the tutorial.
2015-10-12
The poll during the first lecture resulted in a tie between tutorials on monday 14-16 and thursday 12-14. Please check your time table carefully, there will be an online poll soon.
2015-10-12
Unfortunately, I am on sick leave until November 8, but I will update reading assignments and exercises on this webpage regularly. Do not hesitate contacting me (by email) in case of questions, problems, suggestions, etc. I will reply by mail. Additional skype sessions are possible.

Vorlesungen

You can download Lecture Notes (updated: feb 15, 2016; including lecture 23) for this course. The notes are not complete and are updated during the term.

Nr. Datum Thema Skriptum
01. - 02. 12.-16.10.15 motivation, basic problems and examples Section 1
03. - 04. 19.-23.10.15 basics on lattices Section 2
05. - 06. 26.-30.10.15 basics on cones Section 3
07. - 08. 02.-06.11.15 basics on polytopes to be done
09. - 10. 09.-13.11.15 Erhart Theory (first examples and tools) Section 5
11. - 12. 16.-20.11.15 Erhart Theory (lattice points of cones) Section 5
13. - 14. 23.-27.11.15 Erhart Theory (lattice points of polytopes) Section 6
15. - 16. 30.11.-04.12.15 Erhart Theory (lattice points of interior of polytopes) Section 6
17. 07.12.15 Erhart Theory (lattice points of polytopes via tangent cones) Section 6
18. 11.12.15 Algorithmic aspects (shortest lattice vectors) Section 7
19. - 20. 14.-18.12.15 Algorithmic Aspects (LLL-algorithm) Section 7
21. 21.12.15 Algorithmic aspects (Barvinok's algorithm) Section 7
22. 08.01.16 Geometry of numbers (Minkowski's Theorems) Section 8
23. 11.01.16 Geometry of numbers (Lagrange's Theorem) Section 8
24. - 25. 18.-22.01.16 Geometry of numbers (lattice packing and covering) Section 8
26. 25.01.16 Geometry of numbers (flatness theorem) to be done
27. 29.01.16 applications (integer programming) to be done
28. - 29. 01.-05.02.16 applications (toric varieties) to be done

Tutorials

We meet once a week for two hours for the tutorials: Monday 12:15-13:45 hrs in 02.06.011

Exercises

Exercises are available for download. We discuss solutions and approaches in the tutorial, the is no marking of exercises.

Nr. date Blatt
1 14.10.2015 Blatt 1
2 21.10.2015 Blatt 2
3 28.10.2015 Blatt 3
4   enfällt wegen Krankheit
5   entfällt wegen Krankheit
6 18.11.2015 Blatt 6
7 25.11.2015 Blatt 7
8 02.12.2015 Blatt 8
9 09.12.2015 Blatt 9
10 16.12.2015 Blatt 10
11 23.12.2015 Blatt 11
12 13.01.2016 Blatt 12
13 20.01.2016 Blatt 13
14 27.01.2016 Blatt 14

Literatur

Links