3:00 p.m., Friday
Pacific Institute of the mathematical sciences
Department of Mathematics, UBC
Phase transitions, Domain walls and minimal surfaces
I shall describe how a 25 year-old conjecture of DeGiorgi, which originated
from problems in phase transitions, is closely related to Gibbons'
conjectures on scalar field theories and to the Bernstein problem for
minimal graphs. So far, the conjecture has only been solved in low
dimensions and the progress (one dimension at a time) seems to be slow in
spite of a fierce international competition for a complete resolution. I
will also describe how UBC is keeping in the lead, thanks to major
contributions by Martin Barlow, Changfeng Gui and their collaborators. The
mathematics involved are basic, varied and great!