Connected Sets in Global Bifurcation Theory

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<p style="text-align: justify;"><strong><span style="font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-ansi-language: EN-IN; mso-bidi-font-style: italic;">Boris Buffoni</span></strong><span style="font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-ansi-language: EN-IN; mso-bidi-font-weight: bold; mso-bidi-font-style: italic;"> works at the Institute of Mathematics at EPFL (Ecole Polytechnique Fédérale de Lausanne, Switzerland), where he has taught since 1998. His doctorate, under the supervision of Charles Stuart at EPFL, focused on nonlinear problems in the presence of essential spectrum. He was a postdoctoral researcher at the University of Bath and the Scuola Normale Superiore in Pisa, and, from 1995 to 1998, a lecturer at the University of Bath. His research interests include calculus of variations, bifurcation theory, partial differential equations and applications to hydrodynamics. He is currently a senior scientist at EPFL.</span></p> <p style="text-align: justify;"><strong><span style="font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-ansi-language: EN-IN; mso-bidi-font-style: italic;">John Toland</span></strong><span style="font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-ansi-language: EN-IN; mso-bidi-font-weight: bold; mso-bidi-font-style: italic;"> is Emeritus Professor of Mathematics at the University of Bath where he was professor for 32 years before being appointed Director of the Isaac Newton Institute in Cambridge.</span></p> <p><span style="font-size: 11.0pt; line-height: 107%; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA; mso-bidi-font-weight: bold; mso-bidi-font-style: italic;">His PhD, under the supervision of Charles Stuart at Sussex University,<span style="mso-spacerun: yes;"> </span>was on global bifurcation theory for </span><em style="mso-bidi-font-style: normal;"><span style="font-size: 11.0pt; line-height: 107%; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA; mso-bidi-font-weight: bold;">k</span></em><span style="font-size: 11.0pt; line-height: 107%; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA; mso-bidi-font-weight: bold; mso-bidi-font-style: italic;">-set-contractions after which, with collaborators, he<span style="mso-spacerun: yes;"> </span>developed topological methods<span style="mso-spacerun: yes;"> </span>to prove the existence of large amplitude solitary waves, including the famous singular Stokes-wave-of-greatest-height. Since then he has developed aspects of convex analysis, harmonic analysis, duality theory, Nash-Moser theory and variational methods, to address nonlinear problems arising in applications.</span></p>

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