Meeting time
Tuesdays 2-4 in A3.019
upon popular request, select meetings will be available at
https://fu-berlin.webex.com/meet/c.haase
Contents
We talk about the connection between the Kähler package in algebraic geometry on the one hand and the Alexandrov-Fenchel inequality in convex geometry on the other.
The goal is to understand the method of normal complexes from [NR] to prove the Kähler package for matroids, and our first step is to prove the classical Alexandrov-Fenchel inequality according to [SvH].
preliminary schedule
| Date | Topic | References | Speaker |
|---|---|---|---|
| 25.04.23 | Overview | Christian | |
| 02.05.23 | --- no talk --- | ||
| 09.05.23 | convex bodies & support functions; mixed volume and mixed discriminants 1 | [SvH, §2], [S] | Sophie |
| 16.05.23 | mixed volume and mixed discriminants 2 | [SvH, §2], [S] | Esme |
| 23.05.23 | Alexandrov-Fenchel inequality | [SvH, §3] | Sophía |
| 06.06.23 | Mixed discriminant inequality | [SvH, §4] | Kyle |
| 13.06.23 | Alexandrov-Fenchel via polytopes | [SvH, §5], [C-EKMS] | Raman |
| 20.06.23 | normal complexes 1 -- definitions | [NR, §2.1-2.4] | Moritz (Sophie weg) |
| 27.06.23 | normal complexes 2 -- volumes & triangulation | [NR, §§3&4] | Christian |
| 03.07.23 | normal complexes 3 -- Chow ring computations | [NR, §5&6] | Kyle |
| 10.07.23 | normal complexes 4 -- Alexandrov-Fenchel (Lorentzianness, big picture) | [NO'MR, §3.3&5] | Sofía |
| 17.07.23 | --- no talk --- | ||
| 23.07.23 |
Newton-Okounkov bodies and Alexandrov-Fenchel (sketch) |
[KK] |
Christian -------- N.N. |
| matroids & Bergman fan | |||
| Newton-Okounkov bodies and Alexandrov-Fenchel (sketch) | |||
References
[NR] Nathanson, Ross: Tropical Fans and Normal Complexes; arXiv:2110.08647
[NO'MR] Nowak, O'Melveny, Ross: Mixed volumes of normal complexes; arXiv:2301.05278
[R] Ross: Lorentzian fans; arXiv:2304.13176
[SvH] Shenfeld, van Handel: Mixed Volumes and the Bochner Method; arXiv:1811.08710
[D-CKMS] Cordero-Erausquin, Klartag, Merigot, Santambrogio: One more proof of the Alexandrov-Fenchel inequality; arXiv:1902.10064
[S] Schneider: Convex Bodies: the Brunn-Minkowski Theory; Cambridge University Press, 2014
[BL] Branden, Leake
[KK] Kavee, Khovanskii