General
My 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 and Lvalues of various motives. Especially, Iwasawa main conjectures give the precise connection between the congruence properties of the special values of Lfunctions (padic Lfunctions) and the (dual of pprimary part 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 (MordellWeil groups) and the failure of the localglobal principle (ShafarevichTate groups).
Research Themes
Anticyclotomic Iwasawa theory for modular forms à la BertoliniDarmon, Gross, and Vatsal.
Overconvergent construction of anticyclotomic padic Lfunctions.
A bit more explicit computation of BlochKato's exponential and dual exponential maps.
Kato's Euler systems.
Integral periods of modular forms
Arithmetic applications of modularity lifting theorems.
Refined Iwasawa theory and the structure of Selmer groups.
Hida and Coleman families.
padic variation of Euler and Kolyvagin systems.
Kato's epsilon conjecture.
Applications of machine learning (any ``applied mathematics") to number theory (Hope I can do this soon..)
Math Writings
The 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).
On the Iwasawa invariants of Kato's zeta elements for modular forms
with Jaehoon Lee and Gautier Ponsinet
submitted
A proof of PerrinRiou's Heegner point main conjecture
with Ashay Burungale and Francesc Castella
submitted (It's the new version of this paper.)
On the quantitative variation of congruence ideals and integral periods of modular forms
with Kazuto Ota
submitted;
video lecture at Padova
Indivisibility of Kato's Euler systems and Kurihara numbers (survey)
with an appendix by Alex Ghitza
submitted to RIMS K\^{o}ky\^{u}roku Bessatsu;
the relevant Sage code is available.
On the indivisibility of derived Kato's Euler systems and the main conjecture for modular forms
with Myoungil Kim and HaeSang Sun
under revision
An anticyclotomic MazurTate conjecture for modular forms
submitted
Remarks on Kato's Euler systems for elliptic curves with additive reduction (arXiv)
with Kentaro Nakamura
Journal of Number Theory, to appear
On 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 padic Lfunctions (arXiv)
Publicacions Matem\`{a}tiques, Vol. 63 (2019), No. 2, pp. 727767
Variation of anticyclotomic Iwasawa invariants in Hida families (pdf)
with Francesc Castella and Matteo Longo
Algebra \& Number Theory, Vol. 11 (2017), No. 10, pp. 23392368
On 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. 14431455
Anticyclotomic Iwasawa invariants and congruences of modular forms (pdf) (This is my thesis.)
Asian Journal of Mathematics, June 2017, Vol. 21, No. 3, pp. 499530
Edited
Lecture 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
nonrefereed and not intended for publication; available upon request
In preparation (to push myself..)
(title undecided, something on eigencurves)
in progress
(title undecided, something on control theorem)
in progress
(title undecided, something on the simplest case of Selmer groups)
in progress
(title undecided, something on Heegner and Gross points)
in progress
(title undecided, something on Eisenstein series and theta series), with Ick Sun Eum
in progress
(title undecided, something on the integral nature in Iwasawa theory)
in preparation
(title undecided), with Jaehoon Lee
in preparation
List of talks I've given:
2019/10/09, Kyushu University, Fukuoka, Japan
2019/08/08, KIAS
2019/05/31, Padova school on Serre conjectures and the $p$adic Langlands program, Padova, Italy
2019/05/16, Korea University, Seoul, Korea
2019/05/14, Yonsei University, Seoul, Korea
2019/03/15, SNU, Seoul, Korea
2019/02/12, National Taiwan University, Taipei, Taiwan
2018/12/04, KeioYonsei Joint Workshop, Keio, Yokohama, Japan
2018/11/27, Algebraic number theory and related topics 2018, RIMS, Kyoto, Japan
2018/10/05, Advances on automorphic forms and related topics, COEX, Seoul
2018/06/26, Workshop on Number Theory and Algebra, Yeosu, Korea
2018/04/09, KAIST, Daejeon, Korea
2018/03/22, Shanghai Center for Mathematical Sciences, Fudan University, China
2018/02/12, The 7th Number Theory Festival, UNIST, Korea
2018/02/07, The 7th East Asia Number Theory Conference, TIMS, Taiwan
2017/11/03, UNIST, Ulsan, Korea
2017/11/01, Postech, Pohang, Korea
2017/09/14, Workshop on $p$adic $L$functions and algebraic cycles, Taipei, Taiwan
2017/04/19, UNIST
2017/04/17, UNIST
2017/04/13, KIAS
2017/02/21, The 6th Number Theory Festival, Sungkyunkwan University, Korea
2017/01/20, Tokyo Institute of Technology, Japan
2017/01/13, Waseda University, Japan
2016/11/14, Keio University, Japan
2016/09/21, UNIST
2016/04/28, Shanghai Center for Mathematical Sciences, Fudan University, China
2016/02/15, The 5th Number Theory Festival, Kyungnam University, Korea
2016/02/02, 2016 KoreaJapan Joint Number theory Seminar, Postech, Korea
2016/01/29, Sendai International Conference on Arithmetic Geometry in 2016, Tohoku University, Japan
2015/11/27, Industrious Number Theory, KIAS
2015/09/21, Postech
2015/08/25, Arithmetic of Euler systems, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain
2015/07/28, KAIST
2015/07/23, Pan Asian Number Theory 2015, Sanya, China
2015/04/09, Caltech
2015/03/16, Universit\'{e} Laval, Qu\'{e}bec, Canada
2014/12/23, KIAS
2014/11/04, University of Chicago
2014/11/03, Northwestern University
2014/08/29, Postech
2014/04/17, UCSD
2014/03/03, UCLA
2013/10/01, UC Irvine
2013/09/12, Qu\'{e}becVermont Number Theory Seminar, Montreal, Canada
2013/01/08, Workshop on modular forms and Galois representations, KIAS
2012/12/17, Keio University, Japan
2012/11/05, BU
Interesting math and nonmath stuff on the internet
Thinking Space
How to study spectral sequences
Geometric vs. Arithmetic Frobenii
The topology of the Robba ring
BSD, padic BSD, and Iwasawa main conjecture
Flatness in algebraic geometry
Almost purity theorem
Vanishing cycles
Computing hypercohomology
Monodromy
Computing monodromy
Monodromy and global cohomology
Pontryagin dual and mu invariants
Ring homomorphisms
*Ordinary* Galois representations
Ordinary local Galois invariants
Welldefinedness of modular Jacobians
On the module structure of local systems
Characteristic complexes in Iwasawa theory
The difference between an etale finite group scheme and a finite group
Why does the Section Conjecture exclude curves of genus 1?
Prime 2 and 3
Prime 2
Various topologies in algebraic geometry
Flat topology
Local properties of schemes
MayerVietoris
Timeline of class field theory
Finding the Zariski closure of a set
Around locally ringed spaces. See also *Enlightning Exercise 4.3.A* in Vakil's book
Intuition for etale morphisms
5/8 bound in group theory
Are there Maass forms where the expected Galois representation is ladic?
Reference book for Galois Representations
Frobenius weights on etale cohomology and purity
Semisimplicity of Frobenius on *integral* Tate module
Psi operator on PhiGamma modules
Refereeing a Paper
Demonstrating that rigour is important
What is the motivation for a vertex algebra?
Heuristic argument that finite simple groups _ought_ to be "classifiable"?
Reading the mind of Prof. John Coates (motive behind his statement)
etale cohomology of an abelian variety and its dual
Why do we care about dual spaces?
Counterexamples for the quasiunipotence of monodromy over an annulus?
Torsors in Algebraic Geometry?
What does the Lefschetz principle (in algebraic geometry) mean exactly?
Avoiding Minkowski's theorem in algebraic number theory
Do Tamagawa numbers of Galois representations stabilise in the cyclotomic tower?
How to avoid any wrong elementary ``proofs" of Fermat's last theorem
