- Ana Botero (Bielefeld University)
- Alex Fink (Queen Mary University of London)

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

Thursday | |
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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 | |
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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 |

**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.

- Following Dupont, Fink, Moci,

*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*.

- The key papers would be Moci,

*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.

- This would start from my work with Amanda Cameron,

*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.

- The centre of this would be Eur, Fink, Larson, Spink,