AMS Special Seminar Series | Julia Lindberg

Location: Clark 110

When: January 28th at 3:30 p.m.

Title: Leveraging Algebraic Structures for Innovations in Data Science and Complex Systems

Abstract: Many modern challenges in engineering and data science require understanding the solution sets of systems of polynomial equations. An important recurring task in this area is solving the steady-state equations of a polynomial dynamical system. For instance, the power flow equations—a system of quadratic equations—model the nonlinear relationship between voltage magnitudes and power injections in electric power networks. Real solutions to these equations correspond to operating points for the network. Traditionally, a single operating point is found using Newton’s method, but there is little theory to support that this solution is optimal, or even satisfactory.

This talk will survey the history of the power flow problem and outline heuristics used in practice as well as optimization techniques that have been popularized via competitions like the ARPA-E GO competition. We will then turn to recent work which extends the applicability of globally convergent methods for solving power flow systems using techniques like monodromy and parameter continuation. Much of this work relies on recent results characterizing the combinatorial geometry associated to the power flow equations for families of networks. We will conclude by discussing practical considerations when solving the power flow equations as well as variations often important for practical grid operation.

Bio: Julia Lindberg is a Bing Postdoctoral Instructor in the Department of Mathematics at the University of Texas at Austin. Previously, she was a postdoctoral researcher in the Nonlinear Algebra group at the Max Planck Institute in Leipzig, Germany. She earned her Ph.D. in Electrical and Computer Engineering from the University of Wisconsin–Madison (UW) in May 2022. Her research is broadly in applied algebraic geometry and has focused on applications in statistics, optimization, and power systems engineering.  Julia’s research has been supported by grants from the NSF and SIAM. She has received several honors, including the John Nohel Award for an outstanding thesis in applied mathematics, the Excellence in Mathematical Research Prize, the Grainger Graduate Student Fellowship, and the Sarah and Dave Epstein Fellowship. She also holds an M.S. in mathematics and a B.S. in both mathematics and dance, all from UW.

Zoom link: https://wse.zoom.us/j/91341349436