arXiv subjects
Publications and source records attributed to Dongwen Liu.
We explicitly study Kato's residue homomorphisms in Milnor $K$-theory, which are closely related to Contou-Carrère symbols. As applications we establish several reciprocity laws for certain locally defined maps on $K$-groups that are associated to arithmetic surfaces.
We investigate the large phase shifts of the bi-color spatial soliton pair in a cylindrical lead glass rod. The theoretical study suggests a synchronous propagation of a strong pump beam and a weak signal beam under the required initial condition. We experimentally obtain a $π$ phase shift of the signal beam by changing the power of the pump beam by about 14 mW around the soliton critical power, which agrees qualitatively with our theoretical result. The ratio of the phase shift rate of the signal soliton to that of the pump soliton shows a close match to the theoretical estimation.
In this paper we observe that isomorphism classes of certain metrized vector bundles over P^1-{0,infinity} can be parameterized by arithmetic quotients of loop groups. We construct an asymptotic version of theta functions, which are defined on these quotients. Then we prove the convergence and extend the theta functions to loop symplectic groups. We interpret them as sections of line bundles over an infinite dimensional torus, discuss the relations with loop Heisenberg groups, and give an asymptotic multiplication formula.
We classify twisted conjugacy classes in loop groups, restricted to classical groups. The main tool we used is the so-called D_q module, an object which is related to vector bundles over elliptic curves.