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.