Name Shin Satoh Department of Mathematics, Kobe University Plenary Jan 9 09:10~10:00 E11-304 Virtual graph presentations of ribbon surface-knots In our previous study, we introduced a method to describe a ribbon $S^2$- or $T^2$-knot by use of a virtual arc or knot diagram, respectively. We generalize this method to a ribbon surface-knot with a virtual graph diagram, and study the stable equivalence of ribbon presentations in terms of virtual graph diagrams. 304-1-9/satoh.pdf