Studis on local signature and monodromy of degenerate families of algebraic carves

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The aim to obtain an explicit formula of local signature for the contribution of semi-stable reduction coas completed by applying Atiyah-Singer's G-signature theovem, The main termof the formula consists of Pedeking sams of Nielsen-Matsumoto-Moutesions' monodromy data, and I wrote it in Kokyuroku RIMS1345(2003), PP.203-237.The aim to compare Furuta's local signature and Yoshikawa's local signature was almost settled, and I wrote it in the previous RIMS report. But Yoshikawa critacize a cerlain part of the argument, and my study in still on the way at this point.On the other hand, I also obtained a formula for the contribution of semi-stavle reduction to Yoshikawa's local signature by using Atiyah-Botl-Segal-Singer's fixed point formula, and I gave a lecture forit at the symposium "Algobraic Geomety and Topoloy of Hodge Theory, Degnerations and Complex Sarface", I am preparing the full paper of these results.