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## GeneralMy mathematical research interest lies in algebraic number theory. I am now working on Iwasawa theory, which is regarded as the best way to understand the arithmetic meaning of zeta andL-values of various motives. Especially, Iwasawa main conjectures give the precise connection between the congruence properties of the special values of L-functions (p-adic L-functions) and the (dual of) Selmer groups of a given motive. Many interesting arithmetic properties are encoded in Selmer groups; for example, in the case of elliptic curves, Selmer groups contain the information of the rational points of elliptic curves (Mordell-Weil groups) and the failure of the local-global principle (the p-primary part of Tate-Shafarevich groups).
## Research Themesp-adic L-functions.
p-adic variation of Euler and Kolyvagin systems.
## Math WritingsThe arXiv version would be different from the published one. Please send me an email if you want to check the published version (and you do not have subscription).A refined Birch and Swinnerton-Dyer type conjecture for Selmer groupspreprint, available upon request. Refined applications of Kato's Euler systems for modular formssubmitted, available upon request. On the Iwasawa invariants of Kato's zeta elements for modular formswith Jaehoon Lee and Gautier Ponsinet submitted On the quantitative variation of congruence ideals and integral periods of modular formswith Kazuto Ota submitted; video lecture at Padova An anticyclotomic Mazur-Tate conjecture for modular formssubmitted A proof of Perrin-Riou's Heegner point main conjecturewith Ashay A. Burungale and Francesc Castella Algebra \& Number Theory, to appear (It's the revised version of this article.)Indivisibility of Kato's Euler systems and Kurihara numbers (expository)with an appendix by Alex Ghitza RIMS K\^{o}ky\^{u}roku Bessatsu, to appear;
the relevant Sage code is available.
On the indivisibility of derived Kato's Euler systems and the main conjecture for modular forms (arXiv)with Myoungil Kim and Hae-Sang Sun Selecta Mathematica, New Series, 2020, Vol. 26, Issue 2, Article Number 31, published online (16 April, 2020)Remarks on Kato's Euler systems for elliptic curves with additive reduction (arXiv)with Kentaro Nakamura Journal of Number Theory, 2020, Vol. 210, pp. 249--279On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction (arXiv)with Masato Kurihara International Mathematics Research Notices, rnz129, published online (5 July, 2019)Overconvergent quaternionic forms and anticyclotomic (arXiv)p-adic L-functionsPublicacions Matem\`{a}tiques, Vol. 63 (2019), No. 2, pp. 727--767Variation of anticyclotomic Iwasawa invariants in Hida families (pdf)with Francesc Castella and Matteo Longo Algebra \& Number Theory, Vol. 11 (2017), No. 10, pp. 2339--2368On the freeness of anticyclotomic Selmer groups of modular forms (pdf)with Robert Pollack and Tom Weston International Journal of Number Theory, July 2017, Vol. 13, No. 06, pp. 1443--1455Anticyclotomic Iwasawa invariants and congruences of modular forms (pdf) (This is my thesis.)Asian Journal of Mathematics, June 2017, Vol. 21, No. 3, pp. 499--530## EditedLecture note on local class field theory (99 pages)written by 9 Korean graduate students for the preparation of the instructional workshop on class field theory non-refereed and not intended for publication; available upon request ## In preparation (to push myself..)in progress in progress Remarks on the mod , with Sujathap Iwasawa theory for elliptic curves with supersingular reductioncoming soon in progress in progress in preparation ## List of talks I've given:## Interesting math and non-math stuff on the internet |