- Series
- Algebra Seminar
- Time
- Monday, September 8, 2025 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Tianran Chen – Auburn University at Montgomery – https://www.tianranchen.org/
- Organizer
- Donggyu Kim, Julia Lindberg
Please Note: There will be a pre-seminar 10:55-11:15 in Skiles 005.
Power-flow equations model the intricate balancing conditions in electric power grids and are central to analysis and control. They can be reformulated as Laurent polynomial systems, which makes algebraic and polyhedral techniques applicable. In this talk, we first explore different ways in which this can be done.
However, certain algebraic formulations may be deficient: the actual number of isolated solutions (counting multiplicity) may fall below the Bernshtein–Kushnirenko–Khovanskii (BKK) bound predicted from Newton polytopes. By choosing a proper parametrization one uncovers that this deficiency exhibits a certain toric structure. Recognizing that structure reframes the deficit as a geometric feature rather than a numerical anomaly. In the second part of this talk, we explore variations of polyhedral homotopy methods designed to respect and exploit this structure.
====(Below is the information on the pre-talk.)====
Title: Mixed volume, mixed cells, and stable self intersections
Abstract: This talk provides an introduction to mixed volume, mixed cells, and their connections to the Bernshtein–Kushnirenko–Khovanskii bound, as well as stable intersections of tropical hypersurfaces.