Prezada comunidade,

Nesta semana teremos a palestra do professor Zbigniew Jelonek (Instytut Matematyczny PAN, Polônia).

Título: On the Arnold corank problem
Data: 27 de março de 2026
Horário: 14h
Local: Auditório do DM

Resumo: In this lecture, we approach the Arnold corank problem, posed by Arnold in 1975, which asks whether the corank of holomorphic functions is an ambient topological invariant. Here, we obtain a complete positive answer to the metric Arnold corank problem, which asks whether the corank of holomorphic functions is an ambient bi-Lipschitz invariant. Consequently, we show that for complex hypersurfaces, the multiplicity equal to two is an ambient bi-Lipschitz invariant. We also prove that the Arnold corank problem holds true for holomorphic functions of three variables. Other topological invariants are also presented.