### Matroids, Matrices, and Partial Hyperstructures

- Series
- Dissertation Defense
- Time
- Wednesday, July 5, 2023 - 02:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 006
- Speaker
- Tianyi Zhang – Georgia Tech – tzhang358@gatech.edu

**Please Note:** Zoom Link: https://gatech.zoom.us/j/7776548887?pwd=SFEySmpVUW9FckxJVEZRY2hUbUVOQT09
Committee Members:
Matt Baker (Co-advisor)
Oliver Lorscheid (Co-advisor)
Anton Leykin
Josephine Yu
Xingxing Yu

I will talk about the application of algebra and algebraic geometry to matroid theory. Baker and Bowler developed the notions of weak and strong matroids over tracts. Later, Baker and Lorscheid developed the notion of foundation of a matroid, which characterize the representability of the matroid. I will introduce a variety of topics under this theme. First, I will talk about a condition which is sufficient to guarantee that the notions of strong and weak matroids coincide. Next, I will describe a software program that computes all representations of matroids over a field, based on the theory of foundations. Finally, I will define a notion of rank for matrices over tracts in order to get uniform proofs of various results about ranks of matrices over fields.