Webpage of Minhyong Kim
Professor of Number Theory
Joint Head of Oxford Number Theory Research Group (with Ben Green)
Fellow of Merton College
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.
List of Publications
Outreach Page (page under construction)
Some Recent Publications
Some of the manuscripts below may be different from the published versions.
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) Preprint, 2017
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.
Number Theory, Analysis, and
Geometry, in memory of Serge Lang. D. Goldfeld et. al. (ed.), Springer-Verlag (2012).
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.
The Moment You Need Mathematics
(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)
(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)
Some Unpublished Papers
A note on Szpiro's inequality for curves of higher genus.
A vanishing theorem for Fano varieties in positive characteristic.
Torsion points on modular curves and Galois theory
(with Ken Ribet, 1999)
Some Expository Essays
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
(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 Non-abelian fundamental groups and Iwasawa theory, 162--187, Cambridge Univ. Press, Cambridge, 2012.
Fundamental groups and Diophantine geometry
Cent. Eur. J. Math. 8 (2010), no. 4, 633--645.
Diophantine geometry as Galois theory in
the mathematics of Serge Lang.
Notices Amer. Math. Soc. 54 (2007), no. 4, 476--497.
in Autour des motifs-- Volume I, 1--25, Panor. Syntheses, 29, Soc. Math. France, Paris, 2009.
Current Editorial Duties
Springer Monographs in Mathematics, Co-Editor-in-Chief (with Isabelle Gallagher)
Tunisian Journal of Mathematics, Member of Editorial Board
Some Recent Professional Service
AMS Leonard Eisenbud Prize for Mathematics and Physics, Member of Prize Committee (2019-)
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
Some Recent Presentations
Simons Symposium on p-adic Hodge Theory 2019
Plenary Lecture, LMS Midlands Regional Meeting
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
Lecture Series, Cours d'Arithmetique et de Geometrie Algebrique, 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