MacPhersonians and Pseudocircle Arrangements

Series
Algebra Seminar
Time
Monday, September 22, 2025 - 1:00pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Dobbins – Binghamton University – https://www2.math.binghamton.edu/p/people/dobbins/start
Organizer
Donggyu Kim, Julia Lindberg

Please Note: There will be a pre-seminar 10:55-11:15 in Skiles 005.

MacPhersonians are a combinatorial analog of real Grassmannians defined by oriented matroids.  A long standing conjecture says that each MacPhersonian is homotopy equivalent to the corresponding Grassmannian.  Pseudolinear Grassmannians are spaces of topological representations of oriented matroids, and these are each homotopy equivalent to the corresponding Grassmannian in rank 3.  I will present a good cover of the rank 3 pseudolinear Grassmannian with nerve complex isomorphic to the order complex of the corresponding MacPhersonian, confirming the conjecture in rank 3.