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- Indico Weeks View
October 9 to 13, 2023
Tuesday 2pm-5:30pm, Wednesday 10am-12pm, Thursday 10am-12pm and 2pm-5:30pm.
Monday 10am-12pm, Tuesday 10am-12pm.
Wednesday 4pm.
October 16 to 20, 2023
Organisers: C. D’Andrea, P. Lairez, M. Safey El Din, É. Schost, L. Zhi
Polynomial systems encode a wide range of non-linear (but static) phenomena which arise in many applications. Non-linearity makes them non-trivial to handle, both from complexity and reliability viewpoints. Still, because of their importance for key applications e.g. in mechanism design and optimization amongst many others, various algorithmic approaches have been developed. During the last decades, tremendous achievements have been accomplished to design faster algorithms for polynomial system solving, extend their capabilities to tackle topological issues and understand their complexities. For instance, let us mention new families of algorithms to exploit algebraic and geometric properties of polynomial systems and their solution sets such as sparsity or weighted and multi-homogeneity, algorithms for understanding the topology of semi-algebraic sets (Betti numbers, connectivity queries), the raise of sums-of-squares certificates to certify emptiness over the reals of polynomial systems through symbolic-numeric approaches, and last but not least, the stellar solution to 17th Smale problem by Lairez following previous works from Beltrán, Cucker and Pardo.
Many challenges remain to be addressed to pave the way towards high performance polynomial system solvers tackling large scale applications. Topical issues lie in the combination of efficiency and certification, computing exact certificates of emptiness, understanding the geometry of polynomial systems and their solution sets to exploit better their properties algorithmically. This workshop will cover broadly all these topics.
Invited speakers
October 24, 2023
Organizer: J. Schicho
Speakers: Maria Alberich-Carraminana, Didier Henrion, Johanna Frischauf Hans-Peter Schröcker, Josef Schicho