Colloquium: "Twistor theory of the Mobius group and Weingarten surfaces in hyperbolic 3-space"

Michael Deutsch, Federal University of Rio de Janeiro

Abstract: During the last 50 years, twistor techniques have been implemented in a variety of geometric problems with considerable success [1]. In this talk, we will compute the basic twistorial objects associated to the complex 3-fold SL2C, and indicate how a projection map from the moduli space of Bryant surfaces in H3 to that of flat surfaces arises in the process of reducing the full twistor space to the mini-twistor space. Time permitting, we will describe some applications, such as a complex-geometric interpretation of the Galvez-Martinez-Milan deformation for linear Weingarten surfaces of Bryant type [2], a characterization of the local correspondence between flat surfaces in H3 and minimal Ribaucour pairs in R3 [3], an analogous correspondence for superminimal Ribaucour pairs in R4, and a method for constructing examples with prescribed symmetry.

[1] Atiyah, Dunajski, Mason, "Twistor theory at fifty: from contour integrals to twistor strings." arXiv:1704.07464
[2] Galvez, Martinez, Milan, "Complete linear Weingarten surfaces of Bryant type. A Plateau problem at infinity." Trans AMS 356 (9), 3405-3428, 2004.
[3] Martinez, Roitman, Tenenblat. "A connection between flat fronts in hyperbolic space and minimal surfaces in Euclidean space." Ann. Global Anal. Geom., 48(3):233-254, 2015.


Host: Renato Feres

Tea @ 3:45pm in Cupples I, room 200