Joint Head of Oxford Number Theory Research Group (with Ben Green)

Fellow of Merton College

Address:

Mathematical Institute

Woodstock Road

Oxford

OX2 6GG

Tel: +44 (0)1865 273525

I am a mathematician working in the area of arithmetic geometry, which explores the interaction between structures of number theory and geometry with particular emphasis on the study of schemes of finite type over the integers. I am especially interested in applications of homotopy theory to number theory. Recently, I have started exploring the possibility of connections between arithmetic geometry and quantum field theory. In my spare time, I work rather seriously on educational outreach, including adult education, teacher training, and motivational talks for students. I have published four books in Korean on mathematics written for the general public.

Curriculum vitae

List of Publications

Mathematical Genealogy

Teaching blog

Outreach Page (page under construction)

Arithmetic Gauge Theory: A Brief Introduction

Modern Physics Letters A, Volume 33, Issue 29 (2018)

Mirror Symmetry, Mixed Motives, and \zeta(3)

(with Wenzhe Yang) Preprint, 2018

A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves.

(with J. Balakrishnan, I. Dan-Cohen, and S. Wewers) Mathematische Annalen, October 2018, Volume 372, Issue 1-2, pp 369-428

Principal Bundles and Reciprocity Laws in Number Theory

in Algebraic Geometry: Salt Lake City 2015, Proceedings of Symposia in Pure Mathematics, Volume 97 (2018)

Abelian Arithmetic Chern-Simons Theory and Arithmetic Linking Numbers.

(with H.-J. Chung, D. Kim, G. Pappas, J. Park, and H. Yoo) International Mathematics Research Notices, Published electronically, November, 2017

Arithmetic Chern-Simons Theory II.

(with H.-J. Chung, D. Kim, J. Park, and H. Yoo) To be published in

Arithmetic Chern-Simons Theory I. Preprint, 2016

Diophantine Geometry and non-abelian reciprocity laws I.

in Elliptic Curves, Modular Forms and Iwasawa Theory: In Honour of John H. Coates' 70th Birthday, Cambridge, UK, March 2015, Loeffler, David, Zerbes, Sarah Livia (Eds.).

A p-adic nonabelian criterion for good reduction of curves.

(with F. Andreatta and A. Iovita) Duke Math. J. 164 (2015), no. 13, 2597--2642.

On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication.

(with J. Coates, Z. Liang, and C. Zhao) Muenster J. Math. 7 (2014), 83--103.

Tangential localization for Selmer varieties.

Duke Math. J. 161 (2012), no. 2, 173--199.

A remark on fundamental groups and effective Diophantine methods for hyperbolic curves.

Selmer varieties for curves with CM Jacobians.

(with John Coates) Kyoto J. Math. 50 (2010), no. 4, 827--852.

Massey products for elliptic curves of rank 1.

J. of Amer. Math. Soc. 23 (2010), 725--747.

Appendix and erratum to "Massey products for elliptic curves of rank 1''.

(with J. Balakrishnan and K. Kedlaya) J. Amer. Math. Soc. 24 (2011), no. 1, 281--291.

p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication.

Annals of Math. 172 (2010), no. 1, 751--759.

The unipotent Albanese map and Selmer varieties for curves.

Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 89--133.

The l-component of the unipotent albanese map.

(with Akio Tamagawa) Math. Ann. 340 (2008), no. 1, 223--235.

The motivic fundamental group of the projective line minus three points and the theorem of Siegel.

Invent. math. 161 (2005), no. 3, 629--656.

The Hyodo-Kato theorem for rational homotopy types.

(with Richard Hain) Math. Res. Lett. 12 (2005), no. 2-3, 155--169.

(Korean) Influential Inc., Seoul (2018)

The Learning of Mathematics

(Korean) Eunhaeng-namu Publishing, Seoul (2016)

Father's Mathematical Journey

(Korean) Eunhaeng-namu Publishing, Seoul (2014)

Prime Fantasy

(Korean) Banni Publishing, Seoul (2013)

Automorphic Forms and Galois Representations I, II

(co-edited with Fred Diamond and Payman Kassaei)

Non-abelian fundamental groups and Iwasawa theory

(co-edited with John Coates, Florian Pop, Mohamed Saidi, and Peter Schneider)

Autour des motifs I

(with R. Sujatha, L. Lafforgue, A. Genestier, and B.-C. Ngo)

(2002)

A vanishing theorem for Fano varieties in positive characteristic.

(2002)

Torsion points on modular curves and Galois theory

(with Ken Ribet, 1999)

(January, 2019)

IUTT Workshop, Oxford, December, 2015: A Brief Summary

(12 December, 2015)

Brief superficial remarks on Shinichi Mochizuki's Interuniversal Teichmueller Theory, version 1.

(16 November, 2015)

On relative computability for curves.

Asia Pac. Math. Newsl. 3 (2013), no. 2, 16--20.

Dietrich Fischer-Dieskau in Seoul

(June, 2012)

Mathematical Journeys

(2011, contribution to Korean edition of `Les Dechiffreurs')

On number and space

(September, 2010, lecture in memory of Yunsan Lee Won-Guk)

Non-abelian fundamental groups in arithmetic geometry

(for INI administration, 2009)

Galois Theory and Diophantine geometry

in

Fundamental groups and Diophantine geometry

Cent. Eur. J. Math. 8 (2010), no. 4, 633--645.

Mathematical vistas

(2007)

Diophantine geometry as Galois theory in the mathematics of Serge Lang.

Notices Amer. Math. Soc. 54 (2007), no. 4, 476--497.

Motivic L-Functions

in

Physical mathematics: the case of number theory, Perimeter Institute, Colloquium, March, 2019.

Some arithmetic path integrals, Simons Center, February, 2019.

Arithmetic geometry for physicists, KIAS, August, 2017.

A superficial introduction to Langlands functoriality, KIAS, August, 2016.

Tunisian Journal of Mathematics, Member of Editorial Board

International Centre for Mathematical Sciences, Edinburgh, Board Member (2012-)

Pan-Asian Number Theory Conference Series , Member of Scientific Committee (2010-)

International Workshop on Arithmetic Geometry and Quantum Field Theory, Co-organiser (with Philip Candelas, Xenia de la Ossa, and Sergei Gukov), Korea Institute for Advanced Study, August, 2017

Thematic Programme on Arithmetic Geometry and Quantum Field Theory II, Organiser, Korea Institute for Advanced Study, 2018

Thematic Programme on Arithmetic Geometry and Quantum Field Theory I, Organiser, Korea Institute for Advanced Study, 2017

Workshop on Motives and Automorphic Forms, Co-organizer (with Peter Scholze), Clay Mathematical Institute, September, 2015

International Congress of Mathematicians 2014, Member of Organising Committee

Durham Mathematical Symposium: Automorphic Forms and Galois Representations, Co-organizer (with Fred Diamond and Payman Kassaei), July, 2011

Workshop on non-abelian fundamental groups in arithmetic geometry, Co-organizer (with John Coates, Richard Taylor, and Andrew Wiles), Newton Institute for Mathematical Sciences, July, 2009

Newton Institute Program on Non-Abelian Fundamental Groups in Arithmetic Geometry, 2009, Co-organiser (with John Coates, Florian Pop, Mohamed Saidi, and Peter Schneider)

Workshop on Non-commutative Constructions in Arithmetic and Geometry, Organiser, University College London, 2008

Plenary Lecture, LMS Midlands Regional Meeting Leicester, 2018

Philosophy of Physics Seminar, University of Oxford, 2018

Logic Seminar, University of Oxford, 2018

Quantum Field Theory Seminar, University of Oxford, 2018

Iwasawa Theory and Related Topics University of Heidelberg, 2018

Simons Symposium on Periods and L-values of Motives 2018

Simons Conference on Number Theory, Geometry, Moonshine & Strings II, 2018

Joint Mathematics and Physics Colloquium University of Heidelberg, November, 2017

Simons Symposium on p-adic Hodge Theory 2017

Simons Conference on Number Theory, Geometry, Moonshine & Strings, 2017

The Amsterdam Math-Physics Colloquium, May 2017

Plenary Lecture, SIAM Conference on Applied Algebraic Geometry. 2015

p-adic Methods in Number Theory: A Conference Inspired by the Mathematics of Robert Coleman, Berkeley, 2015

Plenary Lecture, Bridges 2014: Mathematics, Music, Art, Architecture, Culture

Plenary Lecture, Canadian Number Theory Association XII Meeting, 2012

Lecture Series, McGill University Bellairs Research Institute, Barbados 2012

Fondation Jacques Hadamard Lecture Series, IHES 2012

Lorentz Centre Workshop on the Motivic Fundamental Group Leiden, 2011

British Mathematical Colloquium, 2011

ETH Zureich and EPF Lausanne Number Theory Days 2010

Plenary Lecture, Joint Meeting of the Korean Mathematical Society and the American Mathematical Society, 2009

Martin Taylor 60 (July, 2012)

CNTA Lethbridge (June 2012)

Lorentz Center workshop (May, 2011)

Essen workshop (February, 2010)

Heidelberg workshop (February, 2010)

Bordeaux workshop (January, 2010)

AMS-KMS joint meetings, Seoul (December, 2009)

Paris number theory seminar (November, 2009)

Oxford number theory seminar (November, 2009)

Colloquia at Leicester and Sheffield (Fall, 2009)

Cambridge anabelian workshop (August, 2009)

Cambridge workshop (July, 2009)

Heidelberg seminar (April, 2009)

Regensburg workshop on 'Finiteness for Motives and Motivic Cohomology' (February, 2009)

Pan Asian Number Theory, Pohang (January, 2009)

Cambridge number theory seminar (November, 2008)

Lille colloquium (November, 2008)

Fields lecture on Selmer varieties (October, 2008)

Muenster lecture (June, 2008)

Exeter colloquium (March, 2008)

Kings colloquium (March, 2008)

Bangalore lecture (March, 2008)

IMSc Chennai (January, 2008)

London-Paris number theory seminar (November, 2007)