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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 local Langlands correspondence
(ref. Repr\'{e}sentations p-adiques de groupes p-adiques
One,
Two,
and Three).
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).My Erd\"{o}s number is 4 (Chan-Ho Kim - Tom Weston - Chantal David - Antal Balog - Paul Erd\"{o}s). A user's guide to Beilinson-Kato's zeta elements (expository)submitted to the proceedings of the ICTS program "Elliptic curves and the special values of L-functions" On the adjoint Selmer groups of semi-stable elliptic curves and Flach's zeta elementssubmitted The refined Tamagawa number conjectures for GL_2with an appendix in collaboration with Robert Pollack preprint available upon request On the anticyclotomic Mazur-Tate conjecture for elliptic curves with supersingular reductionsubmitted to Bertolini's 60th birthday conference proceedings The structure of Selmer groups and the Iwasawa main conjecture for elliptic curvessubmitted; video lecture at ICTS Refined applications of Kato's Euler systems for modular formssubmitted On the Iwasawa invariants of Kato's zeta elements for modular formswith Jaehoon Lee and Gautier Ponsinet submitted An anticyclotomic Mazur-Tate conjecture for modular formssubmitted On the mod p Iwasawa theory for elliptic curveswith R. Sujatha ICCGNFRT (International Conference on Class Groups of Number Fields and Related Topics) conference proceedings, to appear.
A higher Gross-Zagier formula and the structure of Selmer groups (arXiv)Transactions of the American Mathematical Society, Vol. 377, No. 5, May 2024, pp. 3691--3725On the quantitative variation of congruence ideals and integral periods of modular forms (arXiv)with Kazuto Ota Research in the Mathematical Sciences, 2023, Vol. 10, Article number 22Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg (arXiv)L-values in Hida familieswith Matteo Longo Journal of Number Theory, September 2023, Vol. 250, pp. 183--205An explicit comparison of anticyclotomic (arXiv)p-adic L-functions for Hida familieswith Matteo Longo International Journal of Number Theory, 2023, Vol. 19, No. 9, pp. 2021--2050On the soft (arXiv)p-converse to a theorem of Gross-Zagier and KolyvaginMathematische Annalen, 2023, Vol. 387, pp. 1961--1968A proof of Perrin-Riou's Heegner point main conjecture (arXiv)with Ashay A. Burungale and Francesc Castella Algebra \& Number Theory, Vol. 15 (2021), No. 7, pp. 1627--1653 (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, 2021, B86, pp. 63--86;
the relevant Sage code is available.
On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction (arXiv)with Masato Kurihara International Mathematics Research Notices, Volume 2021, Issue 14, July 2021, pp. 10559--10599On 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 31Remarks on Kato's Euler systems for elliptic curves with additive reduction (arXiv)with Kentaro Nakamura Journal of Number Theory, 2020, Vol. 210, pp. 249--279Overconvergent 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 in progress in progress in progress in progress in progress ## List of talks I've given:## Interesting math and non-math stuff on the internet |