**K.
İLHAN İKEDA**

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

**RESEARCH--**

Langlands functoriality and reciprocity principles, non-abelian class field theory.

The theory of Eisenstein series and Arthur trace formula.

Higher-dimensional (

-theoretic) class field theory, theory of motives.**K**Conformal field theory and topological quantum field theory.

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

**WORKS--**

**Thesis
:**

Thesis
: *Linear
equivalence of Eisenstein series*.
Princeton University, Department of Mathematics (November 1993).
Thesis advisor: Goro Shimura.

**Journal
Papers :**

*A formal theory of Eisenstein series*, C. R. Acad. Sci. Paris Sér. I Math.**321**, (1995), pp. 45-50.*On the standard***L***-functions of central-simple algebras*, Bull. Sci. Math.**124**, (2000), pp. 147-157.*Two lemmas on formal power series*, (with Masatoshi Ikeda), Turk. J. of Math.**23**, (1999), pp. 435-440.*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. 519-530.*On the metabelian local Artin map 1: Galois conjugation law*, Turk. J. of Math.**24**, (2000), pp. 25-58.*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. 99-137.*Genelleştirilmiş**Fesenko karşılıklılık ilkesi : Abelyen-olmayan lokal sınıf cisim kuramı*(Erol Serbest ile), 18. Ulusal Matematik Sempozyumu Bildiri Kitabı, Istanbul Kültür Üniversitesi Yayınları, 2005, pp. 147-187 (English :*Generalized Fesenko reciprocity law : Non-abelian local class field theory*, with Erol Serbest).*Langlands**karşılıklılık ilkesi*(Sevan Bedikyan ile çağrılı makale),**İTÜ/C**Dergisi**5**(2007), pp. 3-18 (English :*Langlands**reciprocity principle*, with Sevan Bedikyan, invited paper).*Fesenko**reciprocity map*(with Erol Serbest), Algebra i Analiz : St. Petersburg Math. Journal**20**(3) (2008), pp. 112-162.*Generalized Fesenko reciprocity map*(with Erol Serbest), Algebra i Analiz : St. Petersburg Math. Journal**20**(4) (2008), pp. 118-159.*Non-abelian local reciprocity law*(with Erol Serbest), Manuscripta Math.**132**(2010), pp. 19-49.*Ramification theory in non-abelian local class field theory*(with Erol Serbest), Acta Arithmetica,**144**(2010), pp.373-393.*2-boyutlu Langlands karşılıklılık**ilkesi : M. M. Kapranov'un çalışması**üzerine notlar*, Fizik Dünyası Dergisi, Ankara Üniversitesi, Cilt 1 (1), 2012, 1-7.*On the non-abelian global class field theory*, Annales mathématiques du Québec,**37**(2) (2013),pp. 129-172.*Basic properties of the non-abelian global reciprocity**map*, Mathematics in the 21st Century, Springer Proceedings in Mathematics & Statistics Volume 98, 2015, pp 45-92.*On a group closely related with the automorphic Langlands group*, J. Korean Math. Soc.,**57**(1) (2020), pp. 21—59.

**Preprints**
**:**

*A note on Arthur's**construction of**the automorphic Langlands group,*preprint.*On the**ε**-factors of Weil- Deligne representations,*preprint.*On the relationship between the generalized Fesenko and the Laubie reciprocity maps (with Serdar Kazancı**oğ**lu and Erol Serbest),*preprint*.**Arf symbols and the absolute Galois group of a local field (with Buse Fırat and Erol Serbest),*preprint*.*

**Ongoing
works :**

*On**the Langlands**reciprocity and**functoriality principle**s**,*in progress.*2-trace formulas on finite groups**(with Serdar Nair),*in progress.*Local n**on-abelian Kato-Parshin reciprocity map (with Erol Serbest),*in progress.*Multi-dimensional Langlands functoriality:**Notes on M. M. Kapranov's work*, to appear in Series on Number Theory and Applications, World Scientific, in progress.

**SEMINARS--**