Organization
Graduate School of Mathematics Division of Mathematics Fundamental Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor
TANIMOTO Sho
Degree 2
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Ph. D. （ 2012.5 New York University ）
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M. S. （ 2010.5 New York University ）
Research Interests 8
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diophantine geometry
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algebraic geometry
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birational geometry
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arithmetic geometry
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rational curves
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moduli spaces
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the minimal model program
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rational points
Research Areas 1
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Natural Science / Algebra / Algebraic geometry and Arithmetic Geometry
Research History 5
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Nagoya University Graduate School of Mathematics Professor
2024.4
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Nagoya University Graduate School of Mathematics Associate professor
2021.4 - 2024.3
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Kumamoto University Priority organization for Innovation and Excellence Associate professor
2018.1 - 2021.3
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University of Copenhagen Department of Mathematical Sciences PostDoc
2015.7 - 2017.12
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Rice University Department of Mathematics G. C. Evans instructor
2012.7 - 2015.6
Education 1
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New York University Courant Institute of Mathematical Sciences Department of Mathematics
2007.9 - 2012.5
Professional Memberships 2
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American Mathematical Society
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THE MATHEMATICAL SOCIETY OF JAPAN
Committee Memberships 1
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Mathematical Society of Japan Local delegate
2022.3 - 2023.2
Committee type：Academic society
Awards 3
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FOREST researcher
2022.4 Japan Science and Technology Agency
Sho Tanimoto
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Excellent Young Researcher
2017.11 MEXT Japan
Sho Tanimoto
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Wilhelm Magnus Memorial Prize
2012.4 Courant Institute of Mathematical Sciences
Sho Tanimoto
Papers 30
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Classifying sections of del Pezzo fibrations, I Reviewed International coauthorship International journal
Brian Lehmann, Sho Tanimoto
Journal of the European Mathematical Society Vol. 26 ( 1 ) page： 289 - 354 2024
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Rational curves on del Pezzo surfaces in positive characteristic Reviewed International coauthorship International journal
Roya Beheshti, Brian Lehmann, Eric Riedl, Sho Tanimoto
Transactions of the American Mathematical Society, Series B Vol. 10 page： 407 - 451 2023.3
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Classifying sections of del Pezzo fibrations, II Reviewed International coauthorship International journal
Brian Lehmann, Sho Tanimoto
Geometry & Topology Vol. 26 ( 6 ) page： 2565 - 2647 2022.12
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Moduli spaces of rational curves on Fano threefolds Reviewed International coauthorship International journal
Roya Beheshti, Brian Lehmann, Eric Riedl, Sho Tanimoto
Advances in Mathematics Vol. 408 page： 108557 2022.10
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Geometric consistency of Manin's Conjecture Reviewed International coauthorship International journal
Brian Lehmann, Akash Kumar Sengupta, Sho Tanimoto
Compositio Mathematica Vol. 158 ( 6 ) page： 1375 - 1427 2022.8
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On Manin's conjecture Invited Reviewed
Sho Tanimoto
Sugaku 2022
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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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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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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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On upper bounds of Manin type Reviewed International journal
Sho Tanimoto
Algebra & Number Theory Vol. 14 ( 3 ) page： 731 - 761 2020.5
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Kodaira dimension of moduli of special cubic fourfolds Reviewed International coauthorship International journal
Tanimoto S, V\'arilly-Alvarado, A
Journ. Reine und Angew. Math. Vol. 2019 ( 752 ) page： 265 - 300 2019.7
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Geometric Manin's Conjecture and rational curves Reviewed International coauthorship International journal
Brian Lehmann, Sho Tanimoto
Compositio Mathematica Vol. 155 ( 5 ) page： 833 - 862 2019.5
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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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ON THE GEOMETRY OF THIN EXCEPTIONAL SETS IN MANIN'S CONJECTURE Reviewed International coauthorship International journal
Brian Lehmann, Sho Tanimoto
DUKE MATHEMATICAL JOURNAL Vol. 166 ( 15 ) page： 2815 - 2869 2017.10
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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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From exceptional sets to non-free sections Invited
Sho Tanimoto
RIMS Kokyuroku "Algebraic Number Theory and Related Topics 2023" 2024
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Non-free curves on Fano varieties Reviewed International coauthorship
Brian Lehmann, Eric Riedl, Sho Tanimoto
Osaka Journal of Mathematics 2023
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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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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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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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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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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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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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Geometric aspects of Manin's Conjecture Invited
Sho Tanimoto
Proceedings of Kinosaki Algebraic Geometry Symposium 2018 2019.1
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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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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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Brauer groups on K3 surfaces and arithmetic applications Reviewed International coauthorship International journal
McKinnie K, Sawon J, Tanimoto S, V\'arilly-Alvarado A
Brauer groups and obstruction problems: moduli spaces and arithmetic 2017
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Distribution of rational points of bounded height on equivariant compactifications of PGL_2 I Reviewed International coauthorship International journal
Takloo-Bighash R, Tanimoto S
Research in Number Theory Vol. 2 2016.3
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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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Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups Reviewed International coauthorship International journal
Sho Tanimoto, Yuri Tschinkel
ZETA FUNCTIONS IN ALGEBRA AND GEOMETRY Vol. 566 page： 119 - 157 2012
Books 1
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Proceedings of Kinosaki Algebraic Geometry Symposium 2023
Takeshi Abe, Isamu Iwanari, Sho Tanimoto（ Role： Joint editor）
2024.2
MISC 2
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From exceptional sets to non-free sections Invited International journal
Sho Tanimoto
Oberwolfach reports Vol. 20 ( 2 ) 2023
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Osamu Fujino: Foundations of the minimal model program Invited Reviewed
Sho Tanimoto
Sugaku Vol. 73 ( 3 ) page： 323 - 327 2021.7
Presentations 40
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Sections of Fano fibrations over curves Invited International conference
Sho Tanimoto
BIRS-CMI workshop: New Directions in Rational Points 2024.1.10 Chennai Mathematical Institute
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From exceptional sets to non-free sections Invited International conference
Sho Tanimoto
Algebraic Number Theory and Related Topics 2023 2023.12.12 RIMS, Kyoto University
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Sections of Fano fibrations over curves Invited
Sho Tanimoto
Niigata Algebra Symposium 2023.12.6 Niigata University
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Sections of Fano fibrations over curves Invited International conference
Sho Tanimoto
Junior Trimester Program on Algebraic Geometry: Derived categories, Hodge Theory and Chow Groups, Birational workshop 2023.11.21 Hausdorff Research Institute for Mathematics
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Non-free sections of Fano fibrations Invited International conference
Sho Tanimoto
Fano varieties, their Geometry and Moduli 2023.11.1 KIAS
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Exceptional sets in Manin’s conjecture and their applications to algebraic geometry Invited
Sho Tanimoto
Algebra section, MSJ Autumn Meeting 2023 2023.9.21 Mathematical Society of Japan
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From exceptional sets to non-free sections Invited International conference
Sho Tanimoto
Recent Trends in Algebraic Geometry 2023.6.22 Mathematisches Forschungsinstitut Oberwolfach
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Non-free sections of Fano fibrations Invited International conference
Sho Tanimoto
The 21st Affine Algebraic Geometry Meeting 2023.3.3 Saitama University
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From exceptional sets to non-free curves Invited International conference
Sho Tanimoto
Simons Symposium on Geometry of Arithmetic Statistics 2022.9.1 Simons Foundation
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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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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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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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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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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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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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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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On exceptional sets in Manin’s conjecture Invited
Sho Tanimoto
Hiroshima-Okayama Algebra seminar in Kumamoto 2018.3 Kumamoto University
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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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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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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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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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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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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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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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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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Thin exceptional sets in Manin’s conjecture Invited International conference
Sho Tanimoto
Positivity in Algebraic Geometry 2018.6 Yonsei University
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Thin exceptional sets in Manin’s conjecture Invited
Sho Tanimoto
Younger generations in Algebraic and Complex geometry V 2018.8
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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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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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Towards a refinement of Manin’s conjecture Invited International conference
Sho Tanimoto
Arithmetic Geometry Days 2015.11 University of Copenhagen
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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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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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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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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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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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Balanced line bundles Invited International conference
Sho Tanimoto
CARP: Collaborations Around Rational Points 2014.1 Bellairs Research Institute
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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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Exceptional sets in Manin’s conjecture Invited International conference
Sho Tanimoto
N-Cube Days V 2016.11 University of Gothenburg
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Geometric consistency of Manin’s Conjecture Invited International conference
Sho Tanimoto
Rational Points on Schiermonnikoog, 2018.7
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Geometric consistency of Manin’s Conjecture Invited International conference
Sho Tanimoto
Kinosaki Algebraic Geometry Symposium 2018 2018.10.25
KAKENHI (Grants-in-Aid for Scientific Research) 7
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Grant number：23K25764 2024.2 - 2028.3
科学研究費助成事業 基盤研究(B)
谷本 祥
Authorship：Principal investigator
Grant amount：\10400000 （ Direct Cost: \8000000 、 Indirect Cost：\2400000 ）
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Diversified study on Manin's conjecture for rational points/rational curves/motives
Grant number：23H01067 2023.4 - 2028.3
Japan Society for the Promotion and Science Grant-in-Aid for Scientific Research Grant-in-Aid (B) for Scientific Research
Sho Tanimoto
Authorship：Principal investigator Grant type：Competitive
Grant amount：\13260000 （ Direct Cost: \10200000 、 Indirect Cost：\3060000 ）
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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
Authorship：Principal investigator
（ Direct Cost: \57200000 ）
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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
Authorship：Principal investigator Grant type：Competitive
Grant amount：\3800000
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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 Grant-in-Aid for Early-Career Scientists
Sho Tanimoto
Authorship：Principal investigator Grant type：Competitive
Grant amount：\3640000 （ Direct Cost: \2800000 、 Indirect Cost：\840000 ）
Rational solutions to a system of polynomial equations have been studied since the age of Greece. Polynomial equations define an algebraic variety investigated by algebraic geometers, and rational solutions are called as rational points on the variety. When there are infinitely many rational points on an algebraic variety, one can consider the counting function of rational points on that variety. One of outstanding questions is an asymptotic formula of this counting function, and this asymptotic formula is predicted by Manin's conjecture. In our research, we resolved a long standing mystery of exceptional sets in Manin's conjecture. Moreover we formulated Manin's conjecture for Campana points which are intermediate objects between rational points and integral points. Finally using analogy between rational points and curves, we studied properties of moduli spaces of curves on an algebraic variety using the perspective of Manin's conjecture.
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Research on rational and integral points via Higher Dimensional Algebraic Geometry
2019.4 - 2021.3
Inamori Foundation Research Grants
Sho Tanimoto
Authorship：Principal investigator Grant type：Competitive
Grant amount：\1000000 （ Direct Cost: \1000000 ）
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Higher Dimensional Arithmetic Geometry
2017.11 - 2022.3
MEXT Japan Leading Initiative for Excellent Young Researchers (LEADER)
Sho Tanimoto
Authorship：Principal investigator Grant type：Competitive
Grant amount：\22000000 （ Direct Cost: \11000000 、 Indirect Cost：\11000000 ）
Media Coverage 3
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Seeking new potential through the interaction between algebraic geometry and arithmetic geometry Internet
Kawai Juku 2024.3
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Inamori Foundation 2024.2
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Visiting 3S Researchers #11 Dr. Sho Tanimoto Why do mathematicians study difficult problems? Internet
Inamori Foundation 2023.12
Academic Activities 16
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Kinosaki Algebraic Geometry Symposium 2023
Role(s)：Planning, management, etc.
Takeshi Abe, Isamu Iwanari, Sho Tanimoto （ Kinosaki ） 2023.10
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International workshop on Birational Geometry International contribution
Role(s)：Planning, management, etc.
Sho Tanimoto, Yoshinori Gongyo, Yusuke Nakamura 2023.10
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FOREST program Place for Fusion: Breakthroughs and Potentials of Deep Learning II
Role(s)：Planning, management, etc.
Kazuaki Tanaka （ Waseda University ） 2023.9
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SQuaRE workshop on Geometric Manin’s conjecture in positive characteristic IV International contribution
Role(s)：Planning, management, etc.
Brian Lehmann, Sho Tanimoto （ American Institute of Mathematics ） 2023.7
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CMND 2023 Thematic Program on Rationality and Hyperbolicity International contribution
Role(s)：Planning, management, etc.
Roya Beheshti, Izzet Coskun, Brian Lehmann, Eric Riedl, Sho Tanimoto （ University of Notre Dame ） 2023.6
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FOREST program Place for Fusion: Breakthroughs and potentials of Deep Learning
Role(s)：Planning, management, etc.
Kazuaki Tanaka, Sho Tanimoto （ Zoom ） 2023.5
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K3, Enriques Surfaces, and Related Topics
Role(s)：Planning, management, etc.
Akira Ishii, Shigo Taki, Sho Tanimoto （ Nagoya University ） 2023.3
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Special session in Arithmetic geometry: theory and computation in the Pacific Rim Mathematical Association Congress 2022 International contribution
Role(s)：Planning, management, etc.
Sho Tanimoto, Bianca Viray （ Pacific Institute for Mathematical Sciences ） 2022.12
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Rationality, Moduli Spaces, and Related Topics International contribution
Role(s)：Planning, management, etc.
Sho Tanimoto, Shigeyuki Kondo （ Nagoya University ） 2022.11
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Editor: Nagoya Mathematical Journal
Role(s)：Review, evaluation
2022.10
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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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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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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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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
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Associate Editor: Nagoya Mathematical Journal
Role(s)：Review, evaluation
2021.1 - 2022.10
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Editor: Kumamoto Journal of Mathematics
Role(s)：Review, evaluation
2020 - 2021.3