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
30.05.23 Alexandrov-Fenchel inequality 2 [SvH, §3] Kyle
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)
-------------------------------------------
Lorentzian on cones and interlacing

[KK]
-------
[BL, Prop. 2.4]

 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