Topics
This seminar continues along the lines of the Discrete Mathematics III course titled "Designs and Codes". The seminar will explore various topics related to design theory and extremal combinatorics, including:
- Codes: maximum distance separable codes, spherical codes, Shannon capacity
- Discrete Geometry: Borsuk's Conjecture, points in convex position
- Graph Theory: bootstrap percolation, rainbow matchings
References
Links to some source material, from which you should prepare your talks, can be found below. You should also feel free to read around the topic and find other references that may be of use.
| Topic | Adviser | First source | Further reading |
|---|---|---|---|
| Borsuk's Conjecture | Anurag | Bondarenko | Cameron, Chen, Spielman |
| Points in convex position | Tibor | Suk | |
| The MDS Conjecture | Anurag | Ball | Ball, Chowdhury |
| Equiangular lines | Shagnik | Balla et al. | Jiang-Polyanskii |
| Shannon capacity | Tibor | Aigner-Ziegler (§41) | Alon-Orlitsky, Alon |
| Rainbow matchings | Shagnik | Keevash-Yepremyan | Pokrovskiy |
| Bootstrap percolation | Tibor | Hambardzumyan et al. | Morrison-Noel |
Course Details
Instructor
The seminar will be run by
Tibor Szabó
Arnimallee 3, Rm 211a
szabo at math dot fu-berlin dot de
Prerequisites
A general prerequisite is familiarity with combinatorics.
A formal prerequisite is the successful completion of the Designs and Codes (Discrete Mathematics III) course taught in the Summer 2017 semester, or the consent of the instructor (please contact if necessary).
Credits
This course can be used as a Forschungsmodul or an Ergänzungsmodul in the Masters curriculum of the Freie Universität, or as an advanced seminar course in the curriculum of the Berlin Mathematical School.
Schedule
The seminar will meet on Mondays, 10:15 to 11:45, in Arnimallee 3, SR 119.
| Date | Speaker | Title |
|---|---|---|
| Nov 13 | Ander | Borsuk's Conjecture |
| Nov 20 | JD | Points in convex position |
| Nov 27 | Sebastian | Shannon capacity I |
| Dec 4 | Tim | Shannon capacity II |
| Dec 11 | Mingyang | Equiangular lines and spherical codes I |
| Dec 18 | Eric | Equiangular lines and spherical codes II |
| Jan 8 | Patrick | Rainbow matchings |
| Jan 15 | Simona | The MDS Conjecture I |
| Jan 22 | Evgeniya | The MDS Conjecture II |
| Feb 12 | Alexandra | Bootstrap percolation |