[File : ConjCharTh.dvi] Conjectures on character degrees for the simple Thompson group Authors' name: Katsuhiro Uno email addresses and institutions: Department of Mathematics, Osaka University, Toyonaka, Osaka, 560-0043 Japan A short abstract of the paper: We prove an alternating sum version of Isaacs-Navarro conjecture, which treats radical $p$-chains and characters of any defect, for the simple Thompson group. Current status: a preprint