In his monumental book, Arthur gave a complete description of the automorphic discrete spec-

tra of quasi-split orthogonal groups and symplectic groups. Following Arthur, Mok obtained same

results for quasi-split unitary groups. To generalize these results to non quasi-split groups, one way

is to use the stable trace formula. In the 2014 paper of Kaletha-Minguez-Shin-White, they carried

out some results for inner forms of unitary groups in this way.

However, there is a much more cheaper way to “transport” these results from one group to another

group, which is provided by the theta lifts. In this talk, I will describe how we use the

theta lifts to get some results for non quasi-split even orthogonal or unitary groups.

Locally, we obtain a local Langlands correspondence; and globally, we obtain a multiplicity formula

for the tempered part of discrete spectra. The idea comes from Gan-Ichino’s paper "The Shimura-Waldspurger correspondence for $Mp_{2n}$" . If time permits, I will also briefly describe some related works.