Shinichi Mochizuki

Shinichi Mochizuki
Born (1969-03-29) March 29, 1969[1]
Tokyo, Japan[1]
Nationality Japanese
Alma mater Princeton University
Known for

The author of the first proof of a conjecture of Grothendieck in anabelian geometry,
the author of several theories extending anabelian geometry and its aspects,
the author of inter-universal Teichmuller theory,

the author of a proof of abc conjecture.
Awards JSPS Prize, Japan Academy Medal[1]
Scientific career
Fields Mathematics
Institutions Kyoto University
Doctoral advisor Gerd Faltings

Shinichi Mochizuki (望月 新一, Mochizuki Shin'ichi, born March 29, 1969) is a Japanese mathematician working in number theory and geometry. He is the leader of, originator and one of the main contributors to the branch of modern number theory called anabelian geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry about hyperbolic curves over number fields. He initiated and developed several other developments in that area: absolute anabelian geometry, mono-anabelian geometry, and combinatorial anabelian geometry. Among other theories, Mochizuki introduced and developed Hodge–Arakelov theory, p-adic Teichmüller theory, and etale theta function theory.

Shinichi Mochizuki is the author of the inter-universal Teichmüller theory (IUT), also referred to as the arithmetic deformation theory or Mochizuki theory. This theory uses anabelian geometry and his mono-anabelian geometry and etale theta function theories. Due to its nature and applications, IUT has attracted a high level of attention of non-mathematicians.[2] IUT supplies a new conceptual view on numbers by using non-commutative groups of symmetries, such as the full absolute Galois groups and arithmetic fundamental groups and by restoring ring structures.

Biography

Early life

Shinichi Mochizuki was born to parents Kiichi and Anne Mochizuki.[3] When he was five years old, Shinichi Mochizuki and his family left Japan to live in the USA. His father was Fellow of Center for International Affairs and Center for Middle Eastern Studies at Harvard University (1974-76).[4] Mochizuki attended Phillips Exeter Academy and graduated in 1985.[5] He entered Princeton University as an undergraduate at age 16 and graduated salutatorian in 1988.[5] He then received a Ph.D. under the supervision of Gerd Faltings at age 23.[1] After his PhD, Mochizuki spent two years at Harvard and then in 1994 moved back to Japan to join the Research Institute for Mathematical Sciences in Kyoto University (RIMS) in 1992 and was promoted to professor in 2002.[1][6]

Career

Mochizuki proved Grothendieck conjecture on anabelian geometry in 1996. He was an invited speaker at the International Congress of Mathematicians in 1998.[7] In 2000-2008 he discovered several new theories including the theory of frobenioids, mono-anabelian geometry and the etale theta theory for line bundles over tempered covers of the Tate curve.

On August 30, 2012 Shinichi Mochizuki released four preprints, whose total size was about 500 pages, that develop inter-universal Teichmüller theory and apply it to attempt to prove several very famous problems in Diophatine geometry, part of number theory.[8] These include the strong Szpiro conjecture, the hyperbolic Vojta conjecture and the abc conjecture over every number field. While there were no experts on IUT in 2012, their number increased to a two-digital one in 2017.[2] The papers are expected to be published in 2018 by Publications of RIMS.[9]

Publications

  • Mochizuki, Shinichi (1997), "A Version of the Grothendieck Conjecture for p-adic Local Fields" (PDF), The International Journal of Mathematics, Singapore: World Scientific Pub. Co., 8 (3): 499–506, ISSN 0129-167X
  • Mochizuki, Shinichi (1998), "Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998)", Documenta Mathematica: 187–196, ISSN 1431-0635, MR 1648069
  • Mochizuki, Shinichi (1999), Foundations of p-adic Teichmüller theory, AMS/IP Studies in Advanced Mathematics, 11, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1190-0, MR 1700772

Inter-universal Teichmüller theory

  • Mochizuki, Shinichi (2011), "Inter-universal Teichmüller Theory: A Progress Report", Development of Galois–Teichmüller Theory and Anabelian Geometry (PDF), The 3rd Mathematical Society of Japan, Seasonal Institute .
  • Mochizuki, Shinichi (2012a), Inter-universal Teichmuller Theory I: Construction of Hodge Theaters (PDF) .
  • Mochizuki, Shinichi (2012b), Inter-universal Teichmuller Theory II: Hodge–Arakelov-theoretic Evaluation (PDF) .
  • Mochizuki, Shinichi (2012c), Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice (PDF) .
  • Mochizuki, Shinichi (2012d), Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations (PDF) .

References

  1. 1 2 3 4 5 Mochizuki, Shinichi. "Curriculum Vitae" (PDF). Retrieved 14 September 2012.
  2. 1 2 Crowell 2017.
  3. ↑ Leah P. (Edelman) Rauch Philly.com on Mar. 6, 2005
  4. ↑ MOCHIZUKI, Kiichi Dr. National Association of Japan-America Societies, Inc.
  5. 1 2 "Seniors address commencement crowd". Princeton Weekly Bulletin. 77. 20 June 1988. p. 4. Archived from the original on 3 April 2013.
  6. ↑ Castelvecchi 2015.
  7. ↑ "International Congress of Mathematicians 1998". Archived from the original on 2015-12-19.
  8. ↑ Inter-universal Teichmüller theory IV: log-volume computations and set-theoretic foundations, Shinichi Mochizuki, August 2012
  9. ↑ Ishikura 2017.

Bibliography

  • Castelvecchi, Davide (7 October 2015), "The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof", Nature, 526 (7572): 178–181, doi:10.1038/526178a
  • Crowell, Rachel (19 September 2017). "On a summary of Shinichi Mochizuki's proof for the abc conjecture". American Mathematical Society.
  • Fesenko, Ivan (2016), "Fukugen", Inference: International Review of Science, 2 (3)
  • Fesenko, Ivan (23 December 2017). "Facebook post". www.facebook.com. Retrieved 2017-12-31.
  • Ishikura, Tetsuya (16 December 2017). "Mathematician in Kyoto cracks formidable brainteaser". The Asahi Shimbun.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.