Vertex operator algebras and local conformal nets (of operator algebras) are two mathematical frameworks to study chiral conformal field theory. Many analogies between the two have been known, but no directi relations were known so far. With Carpi, Longo and Weiner, we have proved that we can construct a local conformal net from a strongly local vertex operator algebra and we can also recover the original vertex operator algebra from this resulting local conformal net. We have further given a simple sufficient condition for strong locality. This gives a solution to an important problem studied over more than ten years. We have also shown that the automorpshim group of a vertex operator algebra and that of the corresponding local conformal net coincide. This result applies to many examples including the Moonshine vertex operator algebra. (The case of the Moonshine vertex operator algebra was known before.)
Gapped domain walls between topological phases of matters have been studied in condensed matter physics. We have given their mathematical definition and proved that a conjecture of Lan, Wang and Wen in 2015 is not true.