Updated on 2022/06/22

写真a

 
TANIMOTO Sho
 
Organization
Graduate School of Mathematics Division of Mathematics Fundamental Mathematics Associate professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Associate professor

Degree 2

  1. Ph. D. ( 2012.5   New York University ) 

  2. M. S. ( 2010.5   New York University ) 

Research Interests 8

  1. diophantine geometry

  2. algebraic geometry

  3. birational geometry

  4. arithmetic geometry

  5. rational curves

  6. moduli spaces

  7. the minimal model program

  8. rational points

Research Areas 1

  1. Natural Science / Algebra  / Algebraic geometry and Arithmetic Geometry

Research History 4

  1. Nagoya University   Graduate School of Mathematics   Associate professor

    2021.4

  2. Kumamoto University   Priority organization for Innovation and Excellence   Associate professor

    2018.1 - 2021.3

  3. University of Copenhagen   Department of Mathematical Sciences   PostDoc

    2015.7 - 2017.12

  4. Rice University   Department of Mathematics   G. C. Evans instructor

    2012.7 - 2015.6

Education 1

  1. New York University   Courant Institute of Mathematical Sciences   Department of Mathematics

    2007.9 - 2012.5

Professional Memberships 2

  1. American Mathematical Society

  2. THE MATHEMATICAL SOCIETY OF JAPAN

Committee Memberships 1

  1. Mathematical Society of Japan   Local delegate  

    2022.3 - 2023.2   

      More details

    Committee type:Academic society

Awards 3

  1. FOREST researcher

    2022.4   Japan Science and Technology Agency  

    Sho Tanimoto

  2. Excellent Young Researcher

    2017.11   MEXT Japan  

    Sho Tanimoto

  3. Wilhelm Magnus Memorial Prize

    2012.4   Courant Institute of Mathematical Sciences  

    Sho Tanimoto

 

Papers 24

  1. Geometric consistency of Manin's Conjecture Reviewed International coauthorship International journal

    Brian Lehmann, Akash Kumar Sengupta, Sho Tanimoto

    Compositio Mathematica     2022

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    Language:English   Publishing type:Research paper (scientific journal)  

    to appear

  2. Campana points of bounded height on vector group compactifications Reviewed International coauthorship

    M. Pieropan, A. Smeets, S. Tanimoto, A. Varilly-Alvarado

    Proceedings of the London Mathematical Society   Vol. 123 ( 1 ) page: 57 - 101   2021.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1112/plms.12391

  3. Rational curves on prime Fano threefolds of index 1 Reviewed International coauthorship International journal

    Brian Lehmann, Sho Tanimoto

    Journal of Algebraic Geometry   Vol. 30 ( 1 ) page: 151 - 188   2021.1

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/jag/751

  4. Classifying sections of del Pezzo fibrations, II Reviewed

    Brian Lehmann, Sho Tanimoto

    Geometry & Topology     2021

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    Authorship:Last author   Language:English   Publishing type:Research paper (scientific journal)  

    to appear

  5. Zero-loci of Brauer group elements on semi-simple algebraic groups Reviewed International coauthorship International journal

    Daniel Loughran, Ramin Takloo-Bighash, Sho Tanimoto

    Journal of the Institute of Mathematics of Jussieu   Vol. 19 ( 5 ) page: 1467 - 1507   2020.9

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1017/S1474748018000440

  6. On upper bounds of Manin type Reviewed

    Sho Tanimoto

    Algebra & Number Theory   Vol. 14 ( 3 ) page: 731 - 761   2020.5

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.2140/ant.2020.14.751

  7. Kodaira dimension of moduli of special cubic fourfolds Reviewed

    Tanimoto S, V\'arilly-Alvarado, A

    Journ. Reine und Angew. Math.   Vol. 2019 ( 752 ) page: 265 - 300   2019.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1515/crelle-2016-0053

  8. Geometric Manin's Conjecture and rational curves Reviewed

    Brian Lehmann, Sho Tanimoto

    Compositio Mathematica   Vol. 155 ( 5 ) page: 833 - 862   2019.5

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    Authorship:Last author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1112/S0010437X19007103

  9. Balanced line bundles on Fano varieties Reviewed International coauthorship International journal

    Lehmann, B. Tanimoto, S, Tschinkel, Y

    Journ. Reine und Angew. Math.   Vol. 2018 ( 743 ) page: 91 - 131   2018.10

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1515/crelle-2015-0084

  10. ON THE GEOMETRY OF THIN EXCEPTIONAL SETS IN MANIN'S CONJECTURE Reviewed

    Brian Lehmann, Sho Tanimoto

    DUKE MATHEMATICAL JOURNAL   Vol. 166 ( 15 ) page: 2815 - 2869   2017.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:DUKE UNIV PRESS  

    Manin's conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set. We study whether the exceptional set in Manin's conjecture is a thin set using the minimal model program and boundedness of log Fano varieties.

    DOI: 10.1215/00127094-2017-0011

    Web of Science

    Other Link: http://orcid.org/0000-0002-1884-7934

  11. The spaces of rational curves on del Pezzo threefolds of degree one Reviewed International journal

    Nobuki Shimizu, Sho Tanimoto

    European Journal of Mathematics   Vol. 8 ( 1 ) page: 291 - 308   2022.3

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    Authorship:Corresponding author   Language:Japanese   Publishing type:Research paper (scientific journal)  

    online publication

    DOI: 10.1007/s40879-021-00516-2

    Web of Science

    Scopus

  12. An introduction to Geometric Manin's conjecture Invited

    Sho Tanimoto

    Proceedings of Miyako-no-Seihoku Algebraic Geometry Symposium 2021, ``Positivity of tangent bundles and related topics''     page: 102 - 118   2021.12

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (conference, symposium, etc.)  

    to appear

  13. Campana points, Height zeta functions, and log Manin's conjecture

    Sho Tanimoto

    RIMS Kokyuroku   Vol. 2196   page: 26 - 36   2021.9

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    Authorship:Lead author, Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)  

    Problems and Prospects in Analytic Number Theory

  14. Unramified Brauer groups and rationality problems of invariant fields Invited

    Sho Tanimoto

    Proceedings of 27th Number Theory Summer School 2019 ``Constructive inverse Galois problem and rationality of invariant fields''     page: 255 - 266   2020.2

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    Authorship:Corresponding author   Language:Japanese   Publishing type:Research paper (conference, symposium, etc.)  

  15. Movable Bend and Break for sections of del Pezzo fibrations Invited

    Sho Tanimoto

    Proceedings of 64th Algebra Symposium 2019     page: 209 - 220   2020.2

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)  

    to appear

  16. On exceptional sets in Manin’s Conjecture Reviewed International coauthorship International journal

    Brian Lehmann, Sho Tanimoto

    Research in the Mathematical Sciences   Vol. 6   2019.3

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s40687-018-0174-9

  17. Geometric aspects of Manin's Conjecture Invited

    Sho Tanimoto

    Proceedings of Kinosaki Algebraic Geometry Symposium 2018     2019.1

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)  

  18. Abelian Calabi–Yau threefolds: Néron models and rational points Reviewed International coauthorship International journal

    Fedor Bogomolov, Lars Halvard Halle, Fabien Pazuki, Sho Tanimoto

    Mathematical Research Letters   Vol. 25 ( 2 ) page: 367 - 392   2018.7

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.4310/MRL.2018.v25.n2.a2

  19. Effective bounds for Brauer groups of Kummer surfaces over number fields Reviewed International coauthorship International journal

    Victoria Cantoral-Farfán, Yunqing Tang, Sho Tanimoto, Erik Visse

    Journal of the London Mathematical Society   Vol. 97 ( 3 ) page: 353 - 376   2018.6

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:John Wiley and Sons Ltd.  

    We study effective bounds for Brauer groups of Kummer surfaces associated to Jacobians of genus 2 curves defined over number fields.

    DOI: 10.1112/jlms.12118

    Scopus

    Other Link: http://orcid.org/0000-0002-1884-7934

  20. Brauer groups on K3 surfaces and arithmetic applications Reviewed

    McKinnie K, Sawon J, Tanimoto S, V\'arilly-Alvarado A

    Brauer groups and obstruction problems: moduli spaces and arithmetic     2017

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Birkh\"auser  

    DOI: 10.1007/978-3-319-46852-5_9

    Other Link: http://orcid.org/0000-0002-1884-7934

  21. Distribution of rational points of bounded height on equivariant compactifications of PGL_2 I Reviewed

    Takloo-Bighash R, Tanimoto S

    Research in Number Theory   Vol. 2   2016.3

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    Authorship:Last author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s40993-016-0037-7

    Other Link: http://orcid.org/0000-0002-1884-7934

  22. The distribution of S-integral points on SL2-orbit closures of binary forms Reviewed International coauthorship International journal

    S. Tanimoto, J. Tanis

    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES   Vol. 92 ( 3 ) page: 760 - 777   2015.12

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:OXFORD UNIV PRESS  

    We study the distribution of S-integral points on SL2-orbit closures of binary forms and prove an asymptotic formula for the number of S-integral points. This extends a result of Duke, Rudnick and Sarnak. The main ingredients of the proof are the method of mixing developed by Eskin-McMullen and Benoist-Oh, Chambert-Loir-Tschinkel's study of asymptotic volume of height balls and Hassett-Tschinkel's description of log resolutions of SL2-orbit closures of binary forms.

    DOI: 10.1112/jlms/jdv048

    Web of Science

    Other Link: http://orcid.org/0000-0002-1884-7934

  23. Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces Reviewed International coauthorship International journal

    Brendan Hassett, Sho Tanimoto, Yuri Tschinkel

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES   Vol. 2015 ( 15 ) page: 6375 - 6410   2015

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:OXFORD UNIV PRESS  

    Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety X in terms of global geometric invariants of X. The strongest form of the conjecture implies certain inequalities among geometric invariants of X and of its subvarieties. We provide a general geometric framework explaining these phenomena, via the notion of balanced line bundles, and prove the required inequalities for a large class of equivariant compactifications of homogeneous spaces.

    DOI: 10.1093/imrn/rnu129

    Web of Science

    Other Link: http://orcid.org/0000-0002-1884-7934

  24. Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups Reviewed

    Sho Tanimoto, Yuri Tschinkel

    ZETA FUNCTIONS IN ALGEBRA AND GEOMETRY   Vol. 566   page: 119 - 157   2012

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:AMER MATHEMATICAL SOC  

    We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct products.

    DOI: 10.1090/conm/566/11218

    Web of Science

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MISC 1

  1. Osamu Fujino: Foundations of the minimal model program Invited Reviewed

    Sho Tanimoto

    Sugaku   Vol. 73 ( 3 ) page: 323 - 327   2021.7

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    Authorship:Lead author, Corresponding author   Language:Japanese   Publishing type:Book review, literature introduction, etc.  

Presentations 31

  1. Rational curves on del Pezzo surfaces in characteristic p Invited

    Sho Tanimoto

    Miyako-no-Seihoku Algebraic Geometry Symposium 2021  2021.8.19  Waseda University

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    Event date: 2021.8

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:Waseda University (Zoom)   Country:Japan  

  2. Classifying rational curves on Fano threefolds Invited International conference

    Sho Tanimoto

    The 19th Affine Algebraic Geometry Meeting  2021.3.3  Saitama University

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    Event date: 2021.3

    Language:English  

    Venue:Saitama University (Zoom)  

  3. Some updates on thin exceptional sets in Manin’s conjecture Invited International conference

    Sho Tanimoto

    IML program “Number Theory: Rational points”  2021.4.21  Institut Mittag-Leffler

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    Event date: 2021.1 - 2021.4

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Institut Mittag-Leffler (Zoom)  

  4. Campana points, Height zeta functions, and log Manin's conjecture

    Sho Tanimoto

    Problems and Prospects in Analytic Number Theory  2020.11.24  Research Institute for Mathematical Sciences

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    Event date: 2020.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Zoom  

  5. Sections of del Pezzo fibrations over P^1 International conference

    Sho Tanimoto

    SQuaRE workshop: Geometric Manin's conjecture in characteristic p  2019.6.11  American Institute of Mathematics

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    Language:English  

  6. Sections of del Pezzo fibrations over P^1 Invited International conference

    Sho Tanimoto

    Rationality problems in algebraic geometry  2019.8.1  American Institute of Mathematics

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    Language:English  

  7. The space of rational curves and height zeta functions Invited International conference

    Sho Tanimoto

    Fourth International Workshop on Zeta Functions in Algebra and Geometry  2017.5  Bielefeld University

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    Language:English  

    Venue:Bielefeld Germany  

  8. The space of rational curves and Manin’s conjecture Invited International conference

    Sho Tanimoto

    Rational points and Zariski density  2017.11  University of Copenhagen

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    Language:English  

    Venue:University of Copenhagen  

  9. Thin exceptional sets in Manin’s conjecture Invited International conference

    Sho Tanimoto

    Positivity in Algebraic Geometry  2018.6  Yonsei University

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    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Yonsei University  

  10. Thin exceptional sets in Manin’s conjecture Invited

    Sho Tanimoto

    Younger generations in Algebraic and Complex geometry V  2018.8 

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    Language:English  

    Venue:Hakodate  

  11. Thin exceptional sets in Manin’s Conjecture Invited International conference

    Sho Tanimoto

    Connection for Algebraic Geometers  2018.11.21  Shanghai Center for Mathematical Science

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    Language:English  

  12. Towards a refinement of Manin’s conjecture International conference

    Sho Tanimoto

    AMS Summer Institute in Algebraic Geometry  2015.7  University of Utah

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    Language:English  

    Venue:University of Utah  

  13. Towards a refinement of Manin’s conjecture Invited International conference

    Sho Tanimoto

    Arithmetic Geometry Days  2015.11  University of Copenhagen

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    Language:English  

    Venue:University of Copenhagen  

  14. Towards a refinement of Manin’s conjecture Invited International conference

    Sho Tanimoto

    Belgian-Dutch Algebraic Geometry seminar  2016.4  University of Leuven

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    Language:English  

    Venue:University of Leuven  

  15. Zero-loci of Brauer elements on semisimple groups Invited International conference

    Sho Tanimoto

    Atkin workshop  2017.4  University of Illinois Chicago

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    Language:English  

    Venue:University of Illinois Chicago  

  16. Unramified Brauer groups and rationality problems of invariant fields Invited

    Sho Tanimoto

    27-th Number theory Summer School  2019.9.9  Sakata

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    Language:English  

  17. Sections of del Pezzo fibrations over P^1 Invited International conference

    Sho Tanimoto

    Rational points on Fano and similar varieties  2019.5.20  Institute Henri Poincare

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    Language:English   Presentation type:Oral presentation (general)  

  18. Arithmetic applications of Brauer groups on degree 2 K3 surfaces Invited International conference

    Sho Tanimoto

    FRG Workshop on Arithmetic and geometry of rational curves  2013.9  Rice University

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    Language:English  

    Venue:Rice University, USA  

  19. Balanced line bundles Invited International conference

    Sho Tanimoto

    CARP: Collaborations Around Rational Points  2014.1  Bellairs Research Institute

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    Language:English  

    Venue:Bellairs Research Institute  

  20. Distribution of S-integral points on SL2-orbit closures of binary forms

    Sho Tanimoto

    13th Hiroshima-Sendai Workshop on Number Theory at Sendai  2014.7  Tohoku University

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    Language:Japanese  

    Venue:Tohoku University  

  21. Exceptional sets in Manin’s conjecture Invited International conference

    Sho Tanimoto

    N-Cube Days V  2016.11  University of Gothenburg

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    Language:English  

    Venue:University of Gothenburg  

  22. Geometric consistency of Manin’s Conjecture Invited International conference

    Sho Tanimoto

    Rational Points on Schiermonnikoog,  2018.7 

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    Language:English  

    Venue:Schiermonnikoog, Netherlands  

  23. Geometric consistency of Manin’s Conjecture Invited

    Sho Tanimoto

    Kinosaki Algebraic Geometry Symposium 2018  2018.10.25 

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    Language:English   Presentation type:Oral presentation (general)  

  24. K3 surfaces and special cubic fourfolds International conference

    Sho Tanimoto

    miniPAGES Introductory school: Varieties of Calabi-Yau type  2016.4  Banach center in Warsaw

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    Language:English  

    Venue:Banach center in Warsaw  

  25. Log Manin’s conjecture for klt Campana points Invited International conference

    Sho Tanimoto

    Rational and Integral Points via Analytic and Geometric Methods  2018.5  Casa Matemática Oaxaca (CMO)

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    Language:English  

    Venue:Banff International Research Station, Oaxaca  

  26. Manin’s conjecture and balanced line bundles Invited International conference

    Sho Tanimoto

    AMS Special Session on Rational points on Varieties  2012.1  Joint Mathematics Meetings, Boston

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    Language:English  

    Venue:Joint Mathematics Meetings, Boston  

  27. Movable Bend and Break for sections of del Pezzo fibrations Invited International conference

    Sho Tanimoto

    Algebra Symposium  2019.9.5  Tohoku University

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    Language:English   Presentation type:Oral presentation (invited, special)  

  28. On exceptional sets in Manin’s conjecture Invited

    Sho Tanimoto

    Hiroshima-Okayama Algebra seminar in Kumamoto  2018.3  Kumamoto University

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    Language:Japanese  

    Venue:Kumamoto University  

  29. On the geometry of exceptional sets in Manin’s conjecture Invited International conference

    Sho Tanimoto

    Bogomolov 70 conference  2016.9  Higher School of Economics

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    Language:English  

    Venue:Higher School of Economics, Moscow  

  30. On the geometry of exceptional sets in Manin’s conjecture Invited International conference

    Sho Tanimoto

    Arithmetic and Algebraic Geometry  2016.12  University of Tokyo

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    Language:English  

    Venue:University of Tokyo  

  31. On the geometry of thin exceptional sets in Manin’s conjecture International conference

    Sho Tanimoto

    miniPAGES Varieties with trivial canonical bundles  2016.6  the Institute of Mathematics of the Polish Academy of Sciences

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    Language:English  

    Venue:the Institute of Mathematics of the Polish Academy of Sciences  

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KAKENHI (Grants-in-Aid for Scientific Research) 5

  1. New developments through the interaction between higher dimensional algebraic geometry and arithmetic geometry

    Grant number:JPMJFR212Z  2022.4 - 2029.3

    Japan Science and Technology Agency  Fusion Oriented REsearch for disruptive Science and Technology(FOREST) 

    Sho Tanimoto

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    Authorship:Principal investigator 

    Direct Cost: \57200000 )

  2. New developments and further evolution in higher dimensional algebraic geometry

    Grant number:JPJSBP120219935  2021.4 - 2023.3

    Japan Society for the Promotion and Science  Bilateral Joint Research Project 

    Sho Tanimoto, Brian Lehmann, Yoshinori Gongyo, Yusuke Nakamura

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\3800000

  3. Arithmetic Geometry via Higher Dimensional Algebraic Geometry

    Grant number:19K14512  2019.4 - 2022.3

    Japan Society for the Promotion of Science  KAKENHI Early-Career Scientists 

    Sho Tanimoto

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\3640000 ( Direct Cost: \2800000 、 Indirect Cost:\840000 )

  4. Research on rational and integral points via Higher Dimensional Algebraic Geometry

    2019.4 - 2021.3

    Inamori Foundation  Research Grants 

    Sho Tanimoto

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\1000000 ( Direct Cost: \1000000 )

  5. Higher Dimensional Arithmetic Geometry

    2017.11 - 2022.3

    MEXT Japan  Leading Initiative for Excellent Young Researchers (LEADER) 

    Sho Tanimoto

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\22000000 ( Direct Cost: \11000000 、 Indirect Cost:\11000000 )

 

Academic Activities 6

  1. SQuaRE workshop Geometric Manin’s conjecture in characteristic p III International contribution

    Role(s):Planning, management, etc.

    Brian Lehmann, Sho Tanimoto  ( American Institute of Mathematics ) 2022.4

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    Type:Academic society, research group, etc. 

  2. PRIMA 2021 Summer School: Rational curves and Moduli spaces in arithmetic geometry International contribution

    Role(s):Planning, management, etc.

    Katrina Honigs, Sho Tanimoto, and Bianca Viray  ( Pacific Insitiute for the Mathematical Sciences (Zoom) ) 2021.8

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    Type:Academic society, research group, etc. 

  3. Geometry via Arithmetic International contribution

    Role(s):Planning, management, etc.

    Brian Lehmann, Tim Browning, David McKinnon, Sho Tanimoto  ( Banff International Research Station (Zoom) ) 2021.7

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    Type:Academic society, research group, etc. 

  4. SQuaRE workshop Geometric Manin’s conjecture in characteristic p II International contribution

    Role(s):Planning, management, etc.

    Brian Lehmann and Sho Tanimoto  ( American Institute of Mathematics (Zoom) ) 2021.6

  5. Associate Editor: Nagoya Mathematical Journal

    Role(s):Review, evaluation

    2021.1

  6. Editor: Kumamoto Journal of Mathematics

    Role(s):Review, evaluation

    2020 - 2021.3

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