Patrick Bishop

Patrick Cavanagh

Patrick Cavanagh graduated in Communications Engineering from McGill University in 1968. An interest in artificial intelligence led to a Ph.D. in cognitive psychology from Carnegie-Mellon in 1972. He taught at the Université de Montréal in Psychology until 1989, when he moved to Harvard as a Professor of Psychology. Along with Ken Nakayama, he founded the Vision Sciences Laboratory at Harvard i...

Patrick Lemaire

Patrick Lemaire grew up in Orsay, close to Paris. He graduated from the Ecole Polytechnique and did his PhD at the EMBL (Heidelberg) and ENS (Paris) with Patrick Charnay (1985–1990); he then joined, as a post-doc, the laboratory of John Gurdon in Cambridge (1991–1994), where he identified a crucial Xenopus organizer gene, Siamois. He has been heading a CNRS research group in Marseille since 199...

A Bishop surface with a vanishing Bishop invariant

We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant s < ∞ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real...

The Mergelyan-Bishop Theorem

We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...

Patrick Graves