**UBC Mathematics Department**

*http://www.math.ubc.ca*

## Colloquium Abstract: Dr. Changfeng Gui, Department of Mathematics, UBC

*Maximum principles and symmetries of Partial Differential Equations*

Like the physical problems they are trying to model, many partial
differential equations possess certain symmetries, i.e. they are
invariant under various group actions. A natural and important
question is: should the solutions inherit some or all of these
symmetries? The answers to these questions are often as varied
as the equations themselves and are often quite surprising and
unexpected: Even scalar-valued ground states of basic energy
functionals need not be symmetric even when the geometry
of the domain allows them to be so. The only general principle
that comes out of the literature seems to be: Symmetry properties
of solutions need a proof.

In this talk, I will discuss various aspects of this question.
In particular, I will explain *why* and *how*
maximum principles play an important role here. I will also
mention some recent results in this field, including my recent
solution with Nassif Ghoussoub of the DeGiorgi conjecture in
dimensions two and three.

Calculus (Math 200) is the only prerequisite for this talk.

Return to this week's seminars