Taylor Brysiewicz
My background is in numerical algebraic geometry. I develop algorithms for solving and analyzing polynomial systems and apply existing tools to solve problems in applications.
Some common themes in my research group include
-Monodromy: How can one use ideas from monodromy to improve algorithms?
-Verification/Certification: Given a result coming from numerical algebraic geometry, how can one increase their confidence that the result is correct? Can one prove correctness?
-Enumerative Problems in Applications: Find and study enumerative problems coming from applications. What are their degrees, monodromy groups, and reality-features?
-Software Development: How much of the study of enumerative problems can be automated, or semi-automated? See Pandora.jl (logo below)
News:
Solving the area-length systems in discrete gravity using homotopy continuation was recently accepted in Classical and Quantum Gravity
I recently gave a talk about Monodromy Coordinates
Short bio:
I received my PhD in mathematics from Texas A&M University under the guidance of Frank Sottile. Afterwards (2020), I traveled to the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany to be part of their software group led by Michael Joswig. In 2021 I traveled back to the United States and became a postdoctoral researcher at the University of Notre Dame, working with Jonathan Hauenstein. I am now an assistant professor in London Ontario at Western University.