"On De
Giorgi's Conjecture"
By
(University of Alberta)
Abstract: De Giorgi's conjecture
(1978) brings together three groups of mathematicians: one specializing in
nonlinear partial differential equations, another in differential geometry,
more specially on minimal surfaces and constant mean curvature surfaces, and in
mathematical physics on phase transitions. Classifying solutions of PDEs
has been a very interesting topic. We begin by various celebrated
classification results for solutions of elliptic PDEs
such as Lane-Emden conjecture and De Giorgi's conjecture. These conjectures have attracted many
experts in the field for a few decades. Later
in this talk, we state counterparts of these conjectures to systems of
equations and we provide idea of proofs in lower dimensions. To provide such
counterparts we need to introduce a few novel concepts. Part of this talk is
based on joint works with Nassif Ghoussoub..
Date: Wednesday, May 7, 2014
Time: 15.40 – 16:30
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served after the
seminar.