K. İLHAN İKEDA


FIELDS OF SPECIALIZATION-- Algebraic number theory, automorphic forms and representation theory.

RESEARCH--

I am especially interested in the local-global Langlands functoriality and reciprocity principles, in the local-global non-abelian class field theory (local case: Fesenko-Laubie theory, global case: WA-idèles); their relationship with each other via higher ramification theory and Howe theory in the local case, and WA-parameters in the global case. Their multi-dimensional generalizations to the K-theoretic setting (that is, the non-abelianization of the class field theory of Kato and Parshin, where the 1-dimensional theory is the local-global Langlands functoriality and reciprocity principles, and the Fesenko-Laubie theory and WA-idèles), i.e., to n-dimensional local fields, to semi-global fields and to schemes (that is, local-global Kapranov-Kontsevich functoriality and reciprocity principles, and the K-theoretic Fesenko-Laubie theory in the local case and Lichtenbaum-Weil-Arthur idèles in the global case), their relationship with each other via Zhukov's and Abbes-Saito’s higher ramification theories and higher-dimensional Howe theory in the local case, and Lichtenbaum-Weil-Arthur parameters in the global case. Geometrization of Kapranov-Kontsevich functoriality (that is, muti-dimensional Beilinson-Drinfel'd theory). The place of Arthur trace formula, Eisenstein series and spectral decomposition in these general higher-dimensional settings following Garland and Kapranov. I am also interested in the DG versions (that is, possible extensions of the above theories to the NC schemes and to the NC motives), and in the applications and possible analogues of these very general theories in algebraic topology (tmf theory), mathematical physics and in string theory (quantum Langlands program).

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