- Series
- Algebra Seminar
- Time
- Monday, March 2, 2026 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Spencer Backman – University of Vermont – https://www.uvm.edu/~sbackman/
- Organizer
- Donggyu Kim
Please Note: There will be a pre-seminar at 10:55-11:25 in Skiles 005.
Shellability is a fundamental concept in combinatorial topology and algebraic combinatorics. Two foundational results are Bruggesser–Mani’s line shellings of polytopes and Björner’s theorem that the order complex of a geometric lattice is shellable.
Inspired by Bruggesser–Mani’s line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given a normal complex for a Bergman fan of a matroid induced by a building set, we show that the lexicographic order of the coordinates of its vertices is a shelling order. This yields a new geometric proof of Björner’s classical result and establishes shellability for all nested set complexes for matroids.
This is joint work with Galen Dorpalen-Barry, Anastasia Nathanson, Ethan Partida, and Noah Prime.