K. İLHAN İKEDA
26 Ağustos Yerleşimi İnönü Mah., Kayışdağı Cad., 34755 Kadıköy, İstanbul, Turkey
Tel. +902165781782 (office) Fax. +902165780671 email. ilhan.ikeda@yeditepe.edu.tr

FIELDS OF SPECIALIZATION
Algebraic number theory, automorphic forms and representation theory.
RESEARCH
(1) Ktheoretic class field theory, arithmetic and geometric Langlands functoriality principles and nonabelian class field theory.
(2) The theory of Eisenstein series and Arthur trace formula.
(3) Conformal field theory and topological quantum field theory.
I am especially interested in the localglobal Langlands functoriality and in the nonabelian localglobal class field theory (local case: FesenkoLaubie theory, global case: FesenkoLaubie adèles), their relationship with each other via higher ramification theory and Howe theory. Their multidimensional generalization to the Ktheoretic setting (that is, the nonabelianization of the class field theory of Kato and Parshin, where the 1dimensional theory is the Langlands functoriality and the FesenkoLaubie theory), i.e., to nlocal fields, to semiglobal fields and to schemes (that is, KapranovKontsevich functoriality and the Ktheoretic Fesenko theory), their relationship with each other via Zhukov's and AbbesSaito’s higher ramification theories and higherdimensional Howe theory. Geometrization of KapranovKontsevich functoriality (that is, mutidimensional BeilinsonDrinfel'd theory). The place of Arthur trace formula, Eisenstein series and spectral decomposition in these general higherdimensional settings following Garland and Kapranov. I am also interested in the applications and possible analogues of this very general theory in mathematical physics and in string theory (quantum Langlands program).
PUBLICATIONS
Thesis :
Thesis : Linear equivalence of Eisenstein series. Princeton University, Department of Mathematics (November 1993).
Thesis supervisor: Goro Shimura.
Refereed Journal Papers :
(1) A formal theory of Eisenstein series, C. R. Acad. Sci. Paris Sér. I Math. 321, (1995), pp. 4550. (MR1340080/ 96h:11037 and Zbl 0840.11022) (pdf)
(2) On the standard Lfunctions of centralsimple algebras, Bull. Sci. Math. 124, (2000), pp. 147157. (MR1752107/ 2001h:11065 and Zbl 1017.11024) (pdf)
(3) Two lemmas on formal power series, (with Masatoshi Ikeda), Turk. J. of Math. 23, (1999), pp. 435440. (MR1773548/ 2001f:13032 and Zbl 0999.11072) (pdf)
(4) On the local Artin conductor ƒ_{Artin}(χ) of a character χ of Gal(E/K) 1: Basic definitions, Turk. J. of Math. 23, (1999), pp. 519530. (MR1780938/ 2001i:11137 and Zbl 1006.11067). (pdf)
(5) On the metabelian local Artin map 1: Galois conjugation law, Turk. J. of Math. 24, (2000), pp. 2558. (MR1792243/ 2001g:11185 and Zbl 0976.11054) (pdf)
(6) On the local Artin conductor f_{Artin}(χ) of a character χ of Gal(E/K) 2: Main results for the metabelian case, Proc. Indian Acad. Sci. (Math. Sci.) 113 (2003), pp. 99137. (MR1983746/ 2004c:11224 and Zbl 0204.0287) (pdf)
(7) Genelleştirilmiş Fesenko karşılıklılık ilkesi : Abelyenolmayan lokal sınıf cisim kuramı (Erol Serbest ile), 18. Ulusal Matematik Sempozyumu Bildiri Kitabı, Istanbul Kültür Üniversitesi Yayınları, 2005, pp. 147187 (English : Generalized Fesenko reciprocity law : Nonabelian local class field theory, with Erol Serbest). (pdf)
(8) Langlands karşılıklılık ilkesi (Sevan Bedikyan ile çağrılı makale), İTÜ/C Dergisi 5 (2007), pp. 318 (English : Langlands reciprocity principle, with Sevan Bedikyan, invited paper). (pdf)
(9) Fesenko reciprocity map (with Erol Serbest), Algebra i Analiz : St. Petersburg Math. Journal 20(3) (2008), pp. 112162. (pdf)
(10) Generalized Fesenko reciprocity map (with Erol Serbest), Algebra i Analiz : St. Petersburg Math. Journal 20(4) (2008), pp. 118159. (pdf)
(11) Nonabelian local reciprocity law (with Erol Serbest), Manuscripta Math. 132 (2010), pp. 1949. (pdf)
(12) Ramification theory in nonabelian local class field theory (with Erol Serbest), Acta Arithmetica, 144 (2010), pp.373393 . (pdf)
(13) 2boyutlu Langlands karsiliklilik ilkesi : M. M. Kapranov'un çalismasi üzerine notlar, Fizik Dünyasi Dergisi, Ankara Üniversitesi, Cilt 1 (1), 2012, 17. (pdf)
(14) On the nonabelian global class field theory, accepted by Annales mathématiques du Québec, 37 (2) in 2013,pp. 129172. (pdf).
(15) ''Basic properties of the nonabelian global reciprocity map'' , Mathematics in the 21st Century, Springer Proceedings in Mathematics& Statistics Volume 98, 2015, pp 4592. (pdf)
Submitted Papers :
(16) Local class field theory in the sense of TateSen theory (with Sevan Bedikyan and Erol Serbest), submitted.
(17) Problems in nonabelian local class field theory (with Erol Serbest), submitted.
(18) Kapranov reciprocity principle for GL(n), submitted.
(19) Basic functorial properties of the Kapranov reciprocity principle for GL(n), submitted.
(20) On the relationship between the generalized Fesenko and the Laubie reciprocity maps (with Serdar Kazancioglu and Erol Serbest), preprint (pdf).
(21) On the epsilonfactor of Weil Deligne representations, submitted. (pdf)
Books :
Multidimensional Langlands functoriality, to appear in Series on Number Theory and Applications, World Scientific, in progress.
Kisa Ders : Fonktörsellik ve Esleme (30 Mart  27 Nisan 2011 Galatasaray Üniversitesi)
Conferences :
Turing çalistayi 45 Mayis 2012
IWASAWA 2012, Univ Heidelberg, July 23Aug 03 2012
XXV. Ulusal Matematik Sempozyumu, Nigde Üniversitesi 58 Eylül 2012, Nigde
6th World Conference of 21st Century Mathematics held by Abdus Salam School of Mathematical Sciences (ASSMS) at Lahore on March 2013.
Representation Theory and Applications, Yeditepe University, Istanbul, June 1117 2013.
Istanbul Summer School in Algebraic Geometry, Istanbul Center for Mathematical Sciences, June 1721 2013
26. Ulusal Matematik Sempozyumu, Dicle Universitesi, Diyarbakir, 47 Eylül 2013.
Japanese Turkish Joint Geometry Meeting, Galatasaray University, Istanbul, November 2124 2013