Reading seminar on the work of June Huh
We will study papers by June Huh,
who received Fields Medal this year for his work in combinatorics. If
necessary, we will give a short introduction to matroid theory. We plan
to concentrate on the solution of Top-Heavy Conjecture of Dowling and
Wilson.
Date, time and place
Tuesdays, 12,20, seminar room of KA
Literature and further information
- June Huh's talk at ICM2022
- June Huh's paper in the Proceedings of ICM2022
- proof of Top-Heavy Conjecture (2022) for representable matroids
- proof of Top-Heavy Conjecture (2022) for general matroids
- short survey paper (2017) about proofs of log-concavity of various combinatorial sequences
- 18.10.22 linear algebra proof of de Bruijn - Erdös Theorem, formulation of Theorem 1 proving general Top-Heavy Conjecture, short introduction to matroids with emphasis on the lattice of flats
- 25.10.22 Chow rings and augmented Chow rings of a matroid, origins of Chow rings, more on combinatorial background of Chow rings
- 1.11.22 Bergman fan and augmented Bergman fan as in section 2 of the proof of Top-Heavy conjecture for representable matroids
- 8.11.22 Stellar constructions
- 15.11.22 Short introduction to toric varieties, speaker Aniket Shah
- 22.11.22 More on Bergman fans and augmented Bergman fans and complexes, connectedness in codimension 1
- 29.11.22 Building sets and nested subsets in meet-semilattices, according to Feichtner-Kozlov
- 6.12.22 Stellar subdivisions in meet-semilattices, intro to Chow rings of matroids
- 13.12.22 More on Chow rings
- 3.1.23 Abstract framework, combinatorial fans
- winter break
- 7.3.23 Combinatorial fans and Chow rings of the Bergman fan of a matroid
- 14.3.23 Homology and cohomology of Chow rings, Poincaré duality for the Chow ring of a matroid
- 21.3.23 Hard Lefschetz and Hodge-Riemann conditions for graded Artinian rings satisfying Poincaré duality