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Explore the intricate mathematical structures of polynomial automorphisms in complex two-dimensional space through this 50-minute conference talk delivered by Tanya Firsova from Kansas State University at the Fields Institute. Delve into the advanced concepts of critical loci and complex solenoids as they relate to polynomial automorphisms of $\mathbb{C}^2$, examining how these mathematical objects interact and influence the behavior of dynamical systems in complex analysis. Investigate the geometric and topological properties that emerge from these polynomial transformations, gaining insights into the sophisticated mathematical frameworks used to understand nonlinear dynamical processes. Learn about the theoretical foundations and current research developments in this specialized area of mathematics, presented as part of the Fields-CNAM Nonlinear Days 2025 conference focusing on dynamical, geometric, and random structures and processes.
