Basic Information

Faculty

• Faculty of Science

Email Address

• Email Address

  tanaka.hiromu.7zkyoto-u.ac.jp

Academic Degree

• 26 Mar. 2012

  京都大学修士（理学）
• 24 Sep. 2013

  京都大学博士（理学）

Academic Resume (Undergraduate School/Majors)

• 京都大学, 理学部理学科, 卒業

Research History

• From Apr. 2025, To Present

  京都大学大学院理学研究科
• From Nov. 2017, To Mar. 2025

  東京大学大学院数理科学研究科
• From Nov. 2014, To Oct. 2017

  Imperial College London
• From Nov. 2013, To Oct. 2014

  神戸大学大学院理学研究科

Profile

• Profile

  My research area is algebraic geometry in positive characteristic. In particular, I study the minimal model program, Fano varieties, and vanishing theorems.

ID,URL

• ORCID ID

  0000-0001-9307-0582

• J-Global ID

  202501014810849570

• Researcher number

  50724514

researchmap URL

• https://researchmap.jp/hiromu-research

Research

Research Interests

• positive characteristic, minimal model program, Fano varieties

Research Areas

• Natural sciences, Algebra

Papers

• Fano threefolds in positive characteristic I

  Hiromu Tanaka

  Kyoto Journal of Mathematics, 01 May 2026

  
• Kawamata-Viehweg vanishing for toric varieties

  Hiromu Tanaka

  Pure and Applied Mathematics Quarterly, 2026

  
• Quasi-F-splittings in birational geometry

  Tatsuro KAWAKAMI; Teppei TAKAMATSU; Hiromu TANAKA; Jakub WITASZEK; Fuetaro YOBUKO; Shou YOSHIKAWA

  Annales Scientifiques de l'École Normale Supérieure, 15 Sep. 2025

  
• Elliptic singularities and threefold flops in positive characteristic

  Hiromu Tanaka

  Proceedings of the Edinburgh Mathematical Society, 27 May 2025

  
• Weak quasi-F-splitting and del Pezzo varieties

  Tatsuro Kawakami; Hiromu Tanaka

  Journal of the London Mathematical Society, Feb. 2025

  
• Global F-regularity for weak del Pezzo surfaces

  Tatsuro Kawakami; Hiromu Tanaka

  Forum of Mathematics, Sigma, 2025

  
• Discriminant Divisors for Conic Bundles

  Hiromu Tanaka

  The Quarterly Journal of Mathematics, 26 Dec. 2024

  
• Boundedness of regular del Pezzo surfaces over imperfect fields

  Hiromu Tanaka

  manuscripta mathematica, May 2024

  
• Quasi‐F‐splittings in birational geometry II

  Tatsuro Kawakami; Teppei Takamatsu; Hiromu Tanaka; Jakub Witaszek; Fuetaro Yobuko; Shou Yoshikawa

  Proceedings of the London Mathematical Society, Apr. 2024

  
• Bertini theorems admitting base changes

  Hiromu Tanaka

  Journal of Algebra, Apr. 2024

  
• Vanishing theorems of Kodaira type for Witt canonical sheaves

  Hiromu Tanaka

  Selecta Mathematica, 01 Dec. 2021

  
• Invariants of algebraic varieties over imperfect fields

  Hiromu Tanaka

  Tohoku Mathematical Journal, 01 Dec. 2021

  
• On p‐power freeness in positive characteristic

  Hiromu Tanaka

  Mathematische Nachrichten, 13 Sep. 2021

  
• Pathologies on Mori fibre spaces in positive characteristic

  Hiromu Tanaka

  ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 11 Sep. 2020

  
• Relative semi‐ampleness in positive characteristic

  Paolo Cascini; Hiromu Tanaka

  Proceedings of the London Mathematical Society, 02 May 2020

  
• ON DEL PEZZO FIBRATIONS IN POSITIVE CHARACTERISTIC

  Fabio Bernasconi; Hiromu Tanaka

  Journal of the Institute of Mathematics of Jussieu, 30 Mar. 2020

  
• A Witt Nadel vanishing theorem for threefolds

  Yusuke Nakamura; Hiromu Tanaka

  Compositio Mathematica, 13 Jan. 2020

  
• Minimal model program for log canonical threefolds in positive characteristic

  Kenta Hashizume; Yusuke Nakamura; Hiromu Tanaka

  Mathematical Research Letters, 2020

  
• Infinitely generated symbolic Rees algebras over finite fields

  Akiyoshi Sannai; Hiromu Tanaka

  Algebra & Number Theory, 09 Oct. 2019

  
• Rational points on log Fano threefolds over a finite field

  Yoshinori Gongyo; Yusuke Nakamura; Hiromu Tanaka

  Journal of the European Mathematical Society, 13 Aug. 2019

  
• Abundance theorem for surfaces over imperfect fields

  Hiromu Tanaka

  Mathematische Zeitschrift, 24 Jun. 2019

  
• Purely Log Terminal Threefolds with Non-Normal Centres in Characteristic Two

  Paolo Cascini; Hiromu Tanaka

  American Journal of Mathematics, 2019

  
• Infinite dimensional excellent rings

  Hiromu Tanaka

  Communications in Algebra, 16 Oct. 2018

  
• Zariskian adic spaces

  Hiromu Tanaka

  Kodai Mathematical Journal, 01 Oct. 2018

  
• Minimal model program for excellent surfaces

  Hiromu Tanaka

  Annales de l'Institut Fourier, 17 Apr. 2018

  
• Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field

  Hiromu Tanaka

  International Journal of Mathematics, 21 Mar. 2017

  
• On log del Pezzo surfaces in large characteristic

  Paolo Cascini; Hiromu Tanaka; Jakub Witaszek

  Compositio Mathematica, 08 Mar. 2017

  
• Smooth rational surfaces violating Kawamata–Viehweg vanishing

  Paolo Cascini; Hiromu Tanaka

  European Journal of Mathematics, 25 Jan. 2017

  
• Klt del Pezzo surfaces which are not Globally F-split

  Paolo Cascini; Hiromu Tanaka; Jakub Witaszek

  International Mathematics Research Notices, 09 Jan. 2017

  
• ABUNDANCE THEOREM FOR SEMI LOG CANONICAL SURFACES IN POSITIVE CHARACTERISTIC

  Hiromu Tanaka

  Osaka Journal of Mathematics, Apr. 2016

  
• Behavior of canonical divisors under purely inseparable base changes

  Hiromu Tanaka

  Journal für die reine und angewandte Mathematik (Crelles Journal), 10 Mar. 2016

  
• A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf

  Akiyoshi Sannai; Hiromu Tanaka

  Mathematische Annalen, 09 Jan. 2016

  
• On rational connectedness of globally F-regular threefolds

  Yoshinori Gongyo; Zhiyuan Li; Zsolt Patakfalvi; Karl Schwede; Hiromu Tanaka; Runhong Zong

  Advances in Mathematics, Aug. 2015

  
• The trace map of Frobenius and extending sections for threefolds

  Hiromu Tanaka

  Michigan Mathematical Journal, 01 Jun. 2015

  
• On base point freeness in positive characteristic

  Paolo Cascini; Hiromu Tanaka; Chenyang Xu

  Annales scientifiques de l'École normale supérieure, 2015

  
• The X-method for klt surfaces in positive characteristic

  Hiromu Tanaka

  Journal of Algebraic Geometry, 29 Oct. 2014

  
• Minimal Models and Abundance for Positive Characteristic Log Surfaces

  Hiromu Tanaka

  Nagoya Mathematical Journal, 2014

  
• On log surfaces

  Osamu Fujino; Hiromu Tanaka

  Proceedings of the Japan Academy, Series A, Mathematical Sciences, 01 Aug. 2012

  

Presentations

• On smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  Fano varieties and Related topics, 17 Sep. 2026, Invited

  
• On smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  Recent Developments in Arithmetic and Algebraic Geometry in Positive Characteristic, 04 Sep. 2026, Invited

  
• On smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  Workshop on Algebraic Geometry in Kanazawa, 01 Dec. 2025, Invited

  
• Vanishing theorems for Fano threefolds in positive characteristic

  Hiromu Tanaka

  代数幾何学の諸問題に関する勉強会, 29 Sep. 2025, Invited

  
• On smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  P-adic and Characteristic p Methods in Algebraic Geometry, 11 Jun. 2025, Invited

  
• 正標数の3次元ファノ多様体について

  Hiromu Tanaka

  日本数学会、２０２５年度年会、特別講演, 20 Mar. 2025, Invited

  
• Liftability and vanishing theorems for Fano threefolds in positive characteristic

  Hiromu Tanaka

  東大代数幾何セミナー, 22 Jan. 2025, Invited

  
• Classification of smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  Birational Geometry and Number Theory, 30 Oct. 2024, Invited

  
• Classification of smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  Workshop on Algebraic Geometry over complex number field or in positive characteristic, 19 Sep. 2024, Invited

  
• Classification of smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  京大代数幾何セミナー, 10 Jul. 2024, Invited

  
• Classification of smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  Workshop on birational geometry, 04 Apr. 2024, Invited

  
• Classification of smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  One day workshop on Algebraic and Complex Geometry、, 12 Mar. 2024, Invited

  
• Classification of smooth Fano threefolds in positive characteristic

  Hiromu Tanaka

  Algebraic Geometry Seminar, 15 Sep. 2023, Invited

  
• On quasi-F-splitting

  Hiromu Tanaka

  Algebraic Geometry in East Asia, 28 Oct. 2022, Invited

  
• 極小モデル理論について

  Hiromu Tanaka

  日本数学会、２０２２年秋季総合分科会、企画特別講演, 16 Sep. 2022, Invited

  
• Pathological examples in minimal model program of positive characteristic

  Hiromu Tanaka

  National Taiwan University-The University of Tokyo, 2021, 09 Dec. 2021, Invited

  
• Pathological examples in minimal model program of positive characteristic

  Hiromu Tanaka

  Arithmetic algebraic geometry and mathematical physics, 30 Nov. 2021, Invited

  
• On Mori fibre spaces in positive characteristic

  Hiromu Tanaka

  Workshop on birational geometry, 22 Apr. 2021, Invited

  
• On Mori fibre spaces in positive characteristic

  Hiromu Tanaka

  Zoom in Algebraic Geometry, 14 Jan. 2021, Invited

  
• On Mori fibre spaces in positive characteristic

  Hiromu Tanaka

  Algebraic and Arithmetic Geometry Conference, 20 Dec. 2019, Invited

  
• Rational points and minimal model program in positive characteristic

  Hiromu Tanaka

  RIMS Symposia: Rational Points on Higher Dimensional Varieties, 06 Dec. 2019, Invited

  
• On Mori fibre spaces in positive characteristic

  Hiromu Tanaka

  Tokyo-Seoul Conference in Mathematics 2019 - Algebraic Geometry -, 30 Nov. 2019, Invited

  
• On Mori fibre spaces in positive characteristic

  Hiromu Tanaka

  ファノ多様体及び関連する代数幾何学, 14 Nov. 2019, Invited

  
• Del Pezzo fibrations in positive characteristic

  Hiromu Tanaka

  Del Pezzo surfaces and Fano varieties, 25 Jul. 2019, Invited

  
• On Witt analogues of the Kodaira vanishing theorem

  Hiromu Tanaka

  Algebraic Geometry in Positive Characteristic and Related Topics, 17 Dec. 2018, Invited

  
• On varieties of Fano type in positive characteristic

  Hiromu Tanaka

  2018 Fall Program of Moduli Spaces and Varieties, 16 Nov. 2018, Invited

  
• On varieties of Fano type in positive characteristic

  Hiromu Tanaka

  2018 Fall Program of Moduli Spaces and Varieties, 13 Nov. 2018, Invited

  
• On minimal model program in positive characteristic

  Hiromu Tanaka

  代数幾何学城崎シンポジウム, 23 Oct. 2018, Invited

  
• On varieties of Fano type in positive characteristic

  Hiromu Tanaka

  Modern Algebraic Geometry, 23 Jul. 2018, Invited

  
• Rational points for Fano varieties over finite fields and vanishing theorems for Witt vector cohomologies

  Hiromu Tanaka

  東北大代数幾何セミナー, 06 Jul. 2018, Invited

  
• On log Fano varieties in positive characteristic

  Hiromu Tanaka

  London-Tokyo Workshop in Birational Geometry, 01 Jun. 2018, Invited

  
• 正標数の３次元 klt 特異点の強 F-正則性について

  Hiromu Tanaka

  特異点論月曜セミナー, 14 May 2018, Invited

  
• Kodaira vanishing theorem for Witt canonical sheaves

  Hiromu Tanaka

  The 11th Conference on Arithmetic and Algebraic Geometry, Jan. 2018, Invited

  
• Kodaira vanishing theorem for Witt canonical sheaves

  Hiromu Tanaka

  東大代数幾何セミナー, Nov. 2017, Invited

  
• Relative semiampleness in positive characteristic

  Hiromu Tanaka

  第1回大阪高次元代数多様体論---正標数の世界---, Jun. 2017, Invited

  
• On varieties of Fano type in positive characteristic

  Hiromu Tanaka

  第1回大阪高次元代数多様体論---正標数の世界---, Jun. 2017, Invited

  
• Pathologies on Mori fibre spaces in positive characteristic

  Hiromu Tanaka

  NCTS Workshop in Higher Dimensional Algebraic Geometry, Jun. 2017, Invited

  
• Purely log terminal threefolds with non-normal centres

  Hiromu Tanaka

  Algebra and Number Theory Seminar, May 2017, Invited

  
• Minimal model programme in positive characteristic

  Hiromu Tanaka

  Birational geometry in positive characteristic, Apr. 2017, Invited

  
• Purely log terminal threefolds with non-normal centres

  Hiromu Tanaka

  Cambridge-Tokyo Algebraic Geometry workshop 2017, Mar. 2017, Invited

  
• Minimal model programme in positive characteristic

  Hiromu Tanaka

  Düsseldorf Research Seminar in Pure Mathematics, Feb. 2017, Invited

  
• On log del Pezzo surfaces in positive characteristic

  Hiromu Tanaka

  Edge days 2016 --workshop on birational geometry and reduction to positive characteristic--, Jun. 2016, Invited

  
• Behavior of canonical divisors under purely inseparable base change

  Hiromu Tanaka

  Higher dimensional algebraic geometry and around, Kobe-Kyoto, 2016, Feb. 2016, Invited

  
• Behavior of canonical divisors under purely inseparable base change

  Hiromu Tanaka

  Algebraic Geometry seminar, Jan. 2016, Invited

  
• On log del Pezzo surfaces in positive characteristic

  Hiromu Tanaka

  The 10th Anniversary Tokyo-Seoul Conference in Mathematics --Algebraic/Arithmetic/Complex Geometry, Dec. 2015, Invited

  
• Some applications of Witt vectors to 3-dimensional MMP of positive characteristic

  Hiromu Tanaka

  京大代数幾何セミナー, Nov. 2015, Invited

  
• Minimal model theory in positive characteristic

  Hiromu Tanaka

  Junior Geometry Seminar, May 2015, Invited

  
• Minimal model theory for surfaces over imperfect fields

  Hiromu Tanaka

  代数学シンポジウム, Sep. 2014, Invited

  
• Minimal model theory for surfaces over imperfect fields

  Hiromu Tanaka

  FRG Special Month in Ann Arbor, Jun. 2014, Invited

  
• Minimal model theory for surfaces over imperfect fields

  Hiromu Tanaka

  2014 Chengdu Workshop on Algebraic Geometry, May 2014, Invited

  
• Minimal model theory for surfaces over imperfect fields

  Hiromu Tanaka

  第三回若手代数複素幾何研究集会, Jan. 2014, Invited

  
• Minimal model theory for surfaces over non-closed fields

  Hiromu Tanaka

  京大代数幾何セミナー, Jan. 2014, Invited

  
• Cone theorem and MMP for threefolds in positive characteristic

  Hiromu Tanaka

  Algebraic Geometry seminar, Dec. 2013, Invited

  
• Cone theorem for threefolds in positive characteristic

  Hiromu Tanaka

  Mini workshop on birational geometry, Nov. 2013, Invited

  
• Cone theorem and MMP for threefolds in positive characteristic

  Hiromu Tanaka

  特異点論月曜セミナー, Nov. 2013, Invited

  
• The trace map of Frobenius and extending sections

  Hiromu Tanaka

  Birational Geometry and Singularities in Positive Characteristic, Nov. 2013, Invited

  
• 正標数の３次元代数多様体に対する錐定理と極小モデル

  Hiromu Tanaka

  日本数学会 2013年度秋季総合分科会, Sep. 2013

  
• Minimal model program in positive characteristic

  Hiromu Tanaka

  Algebraic Geometry seminar, Sep. 2013, Invited

  
• On base point freeness in positive characteristic

  Hiromu Tanaka

  代数幾何学サマースクール2013 -代数多様体の分類理論と正標数の手法II-, Aug. 2013, Invited

  
• Cone theorem and MMP for threefolds in positive characteristic

  Hiromu Tanaka

  東北大代数幾何セミナー, Jul. 2013, Invited

  
• Cone theorem and MMP for threefolds in positive characteristic

  Hiromu Tanaka

  都の西北代数幾何セミナー, Jul. 2013, Invited

  
• Cone theorem and MMP for threefolds in positive characteristic

  Hiromu Tanaka

  名大代数幾何学セミナー, Jun. 2013, Invited

  
• Cone theorem and MMP for threefolds in positive characteristic

  Hiromu Tanaka

  京大代数幾何セミナー, May 2013, Invited

  
• Strictly nef adjoint divisors in positive characteristic

  Hiromu Tanaka

  The minimal model program in characteristic p, May 2013, Invited

  
• The trace map of Frobenius and extending sections

  Hiromu Tanaka

  Characteristic p methods in Algebraic Geometry, Apr. 2013, Invited

  
• 正標数の曲面に対する消滅定理

  Hiromu Tanaka

  代数幾何学城崎シンポジウム, Oct. 2012, Invited

  
• 正標数のログ曲面に対する極小モデル理論

  Hiromu Tanaka

  第１０回アフィン代数幾何学研究集会, Sep. 2012, Invited

  
• 正標数の曲面に対する消滅定理

  Hiromu Tanaka

  京大代数幾何セミナー, Jun. 2012, Invited

  
• 正標数の曲面に対する極小モデル理論

  Hiromu Tanaka

  代数幾何学サマースクール2012 -代数多様体の分類理論と正標数の手法-, Jun. 2012, Invited

  
• 正標数の曲面に対する極小モデル理論

  Hiromu Tanaka

  日本数学会年会 2012, Mar. 2012

  
• 正標数のQ-分解的な曲面に対する極小モデルプログラム

  Hiromu Tanaka

  代数幾何ミニ研究集会, Mar. 2012, Invited

  
• 正標数の曲面に対する極小モデル理論

  Hiromu Tanaka

  京大代数幾何セミナー, Nov. 2011, Invited

  

Awards

• 25 Sep. 2013

  日本数学会賞建部賢弘賞奨励賞

Education

Teaching subject(s)

• From 01 Apr. 2026, To 31 Mar. 2027

  Advanced Linear Algebra

  N130, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2026, To 31 Mar. 2027

  Special study course (Mathematical Science)

  5140, Year-long, Faculty of Science, 12
• From 01 Apr. 2026, To 31 Mar. 2027

  Forefront of Mathematics and Mathematical Science I

  4138, Spring, Faculty of Science, 2
• From 01 Apr. 2026, To 31 Mar. 2027

  Algebra I

  3100, Spring, Faculty of Science, 4
• From 01 Apr. 2026, To 31 Mar. 2027

  Seminar on Algebraic Geometry C

  0530, Spring, Graduate School of Science, 3
• From 01 Apr. 2026, To 31 Mar. 2027

  Seminar on Algebraic Geometry B

  0529, Fall, Graduate School of Science, 3
• From 01 Apr. 2026, To 31 Mar. 2027

  Seminar on Algebraic Geometry A

  0528, Spring, Graduate School of Science, 3
• From 01 Apr. 2026, To 31 Mar. 2027

  Seminar on Algebraic Geometry D

  0531, Fall, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Exercises in Algebra I

  3180, Spring, Faculty of Science, 4
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Algebraic Geometry C

  0530, Spring, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Algebraic Geometry B

  0529, Fall, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Algebraic Geometry A

  0528, Spring, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Seminar on Algebraic Geometry D

  0531, Fall, Graduate School of Science, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Linear Algebra with Exercises B

  N152, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Linear Algebra with Exercises A

  N151, Spring, Institute for Liberal Arts and Sciences, 3