Friday, November 15, 2024, 12 o’clock, we invite you to participate in the following Lecture:

Invited guest: Francisco Braun (Federal University of São Carlos, Brazil)

The global invertibility problem and the Jacobian conjecture

Abstract: The problem of finding conditions guaranteeing a local invertible map is globally invertible goes back at least to the works of Hadamard, in the early 19th century. Maybe the most known open problem here is the Jacobian conjecture, raised by Keller in 1939, claiming that a polynomial map F : 𝕂ⁿ → 𝕂ⁿ, where 𝕂 is a field of characteristic 0 and n ≥ 2, becomes an automorphism provided its Jacobian determinant is a nonzero constant. If 𝕂 = ℝ, the claim that F is invertible if its Jacobian determinant is different from zero throughout ℝⁿ was disproved by a celebrated counterexample provided by Pinchuk in 1994.

The abstract is also available in pdf format here.

The lecture will be online, via Microsoft Teams at this access link.

Alternatively, one can use:

Meeting ID: 340 972 436 501
Passcode: UjpNyi