BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:About the shape maximizing the gradient of the torsion function - 
 Ilias Ftouhi (Nîmes University)
DTSTART:20260206T103000Z
DTEND:20260206T111500Z
UID:TALK239833@talks.cam.ac.uk
DESCRIPTION:In this talk\, we consider the functional\\[J(\\Omega) = \\fra
 c{\\|\\nabla u_\\Omega\\|_\\infty}{\\sqrt{|\\Omega|}}\,\\]where $\\Omega$ 
 is an open subset of the plane\, $u_\\Omega$ is its torsion function\, and
  $|\\Omega|$ denotes its area.\nWe prove that the functional $J$ admits a 
 maximizer among convex planar domains. We then show that any optimal domai
 n is regular (of class $C^1$) and that its boundary contains a segment on 
 which the function $|\\nabla u_\\Omega|$ attains its maximum value. The pr
 oofs rely on probabilistic approaches\, whose main intuitions and usefulne
 ss will be highlighted. Finally\, we present numerical simulations and sta
 te some conjectures.\nThis talk is based on works in collaboration with Kr
 zysztof Burdzy (University of Washington\, USA)\, Chiu-Yen Kao (Claremont 
 McKenna College\, USA)\, Xuefeng Liu (Tokyo Woman's Christian University\,
  Japan)\, and Phanuel Mariano (Union College\, USA).
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR