Invited Talks
We are proud to present the invited speakers of CASC conference:
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Prof. Carsten Schneider, Director of Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria
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Dr. Joseph Tooby-Smith, University of Bath, UK
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Thi Xuan Vu - Université de Lille, France
Title of the talk: Symbolic Homotopy Techniques for Structured Multivariate Polynomial Systems
Abstract: In the context of solving systems of polynomial equations, homotopy refers to the process of deforming a simple system G(X), where X is a sequence of variables, whose solutions are known, into a target system F(X) that we aim to solve. There are two main approaches to homotopy methods: numerical and symbolic. While the core mathematical idea, by using the continuous transformation H(t, X) = (1-t) G(X) + t F(X), is the same, the way we handle that transformation differs between the symbolic and numerical worlds.
Numerical homotopy methods approximate solutions by tracking solution paths as the parameter t varies from 0 to 1, using predictor-corrector techniques. In contrast, symbolic homotopy methods treat t as an algebraic parameter and study the structure of the ideal generated by the homotopy system in order to obtain a parametric description of the solutions for all values of t simultaneously. Then specilizing this formula at t = 1 gives a parametrization for the solution set of the target system F(X).
In this talk, we focus on symbolic homotopy techniques for solving multivariate polynomial systems, with a particular emphasis on determinantal systems arising from minors of polynomial matrices, illustrating how exploiting algebraic structure can lead to efficient solution methods.