### A stronger Torelli theorem for graphs

- Series
- Algebra Seminar
- Time
- Monday, October 2, 2023 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Sarah Griffith – Brown University – sarah_griffith-siqueira@brown.edu

There will be a pre-seminar (aimed toward grad students and postdocs) from 11:00 am-11:30 am in Skiles 006.

Recent research trends have explored curious analogies between the theory of graphs and Riemann surfaces. To each graph we can associate a real metric torus, known as its Jacobian. It was previously known that isomorphisms of graph Jacobians yield isomorphisms of the associated graphic matroids, partially mirroring a classical algebraic geometry result known as the Torelli theorem. However, the result on graphs is not as strong as a direct analogue of the Riemann surface result would be, nor does it use as much data. I will discuss how the graph Torelli theorem can be refined to incorporate additional data as with Riemann surfaces, in which case it produces isomorphisms of graphs. If time permits, I will describe further recent work in this direction.