The Inaugural Seminar

Ana Botero & Alex Fink

18–19 July 2024

Speakers

• Ana Botero (Bielefeld University)
  

• Alex Fink (Queen Mary University of London)
  

Location and Schedule

All talks will take place in the Center for Interdisciplinary Research at the University of Bielefeld.

Thursday
9:30 – 10:30	The Tutte polynomial as a character on a coalgebra
10:30 – 11:00	Coffee Break
11:00 – 12:00	Preliminaries on toric varieties and toric schemes over a DVR
12:00 – 13:00	Lunch Break
13:00 – 14:00	The arithmetic Tutte polynomial and “matroids over rings”
14:00 – 14:30	Coffee Break
14:30 – 15:30	Toric vector bundles over a field as piecewise linear maps to spherical Tits buildings
15:30 – 18:00	Open Discussion

Friday
9:30 – 10:30	Toric vector bundles over a DVR as piecewise affine maps to affine Bruhat-Tits buildings
10:30 – 11:00	Coffee Break
11:00 – 12:00	Lattice point counting and tautological classes
12:00 – 13:00	Lunch Break
13:00 – 14:00	Characteristic classes of toric vector bundles
14:00 – 14:30	Coffee Break
14:30 – 15:30	Coxeter matroids
15:30 – 18:00	Open Discussion

Topics & Background Reading

Ana Botero:

• Preliminaries on toric varieties and toric schemes over a DVR
  • References: Chapter 3 of arXiv:1105.5584

• Toric vector bundles over a field as piecewise linear maps to spherical Tits buildings
  • References: arXiv:2304.11211

• Toric vector bundles over a DVR as piecewise affine maps to affine Bruhat-Tits buildings
  • References: arXiv:2304.11211

• Characteristic classes of toric vector bundles
  • References: arXiv:2304.11211 and arXiv:2402.18712

---

Alex Fink:

• The Tutte polynomial as a character on a coalgebra
  • Following Dupont, Fink, Moci, Universal Tutte characters via combinatorial coalgebras. The paper of Krajewski, Moffatt, Tanasa that this one is based on may also be useful reading.

• The arithmetic Tutte polynomial and “matroids over rings”
  • The key papers would be Moci, A Tutte polynomial for toric arrangements; D’Adderio, Moci, Arithmetic matroids, the Tutte polynomial and toric arrangements; and Fink, Moci Matroids over a ring and Polyhedra and parameter spaces for matroids over valuation rings.

• Lattice point counting and tautological classes
  • This would start from my work with Amanda Cameron, The Tutte polynomial via lattice point counting, which was motivated by Kálmán and Postnikov, Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs. We will also discuss the Berget–Eur–Spink–Tseng way (Tautological classes of matroids), which reinterprets my and Amanda’s proof.

• Coxeter matroids
  • The centre of this would be Eur, Fink, Larson, Spink, Signed permutohedra, delta-matroids, and beyond and Eur, Larson, Spink, K-classes of delta-matroids and equivariant localization, which investigate the type BC case.