Yuuji Tanaka
Address: Beijing Institute of Mathematical Sciences and Applications (BIMSA), No. 544, Hefangkou Village, Huaibei Town, Huairou District, Beijing 101408, China
e-mail: ytanaka (at) bimsa.cn, yu2tanaka (at) gmail.com
Address: Beijing Institute of Mathematical Sciences and Applications (BIMSA), No. 544, Hefangkou Village, Huaibei Town, Huairou District, Beijing 101408, China
e-mail: ytanaka (at) bimsa.cn, yu2tanaka (at) gmail.com
Research interests: Gauge Theory, Algebraic Geometry, Geometric Analysis
More specifically, my current research interests are around the Vafa-Witten equations and the Kapustin-Witten ones on four-manifolds. They originated in an attractive theory called N=4 super Yang-Mills theory in (Theoretical) Particle Physics, or more broadly in Superstring Theory. I've reached these objects with huge surprise and excitement from mathematical studies in higher-dimensional gauge theories such as the Donaldson-Thomas invariants and Spin(7)-instantons. Now I'm working on these from both algebraic and analytic aspects. (article in case studies )
(MathSciNet, zbMATH, Google Scholar, arXiv)
N. Kuhn, O. Leigh, and Y. Tanaka, The blow-up formula for the instanton part of the Vafa-Witten invariants on projective surfaces, 22 pages, to appear in Algebraic Geometry. (arXiv)
D. Festi, D. Platt, R. Singhal, and Y. Tanaka, Examples of real stable bundles on K3 surfaces, Math. Z. 314 (2026), Paper No. 31. 23pp . (journal, arXiv)
M. Galdeano, D. Platt, Y. Tanaka, and L. Wang, Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds, J. Geom. Anal. 35 (2025), Paper No. 393, 57 pp. (journal, arXiv)
J. Gross, D. Joyce, and Y. Tanaka, Universal structures in ℂ-linear enumerative invariant theories, SIGMA 18 (2022), 068, 61pp, Special Issue on Enumerative and Gauge-Theoretic Invariants in honor of Lothar Göttsche on the occasion of his 60th birthday. (journal, arXiv)
C.-C. Liu, S. Rayan, and Y. Tanaka, The Kapustin-Witten equations and nonabelian Hodge theory, Eur. J. Math. 8 (2022), 23-41. (journal, arXiv)
Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces I: stable case, J. Algebraic Geom. 29 (2020), 603-668. (journal, arXiv) The 2024 JAG Best Paper Award
D. Joyce, Y. Tanaka, and M. Upmeier, On orientations for gauge-theoretic moduli spaces, Adv. Math. 362 (2020), 106957. (journal, arXiv)
Y. Tanaka, A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds, Glasg. Math. J. 61 (2019), 471-486. (journal, arXiv)
Y. Tanaka, On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kahler surfaces, Geom. Dedicata 199 (2019), 177-187. (journal, arXiv)
Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces II: semistable case, Pure Appl. Math. Q. 13 (2017), 517-562, Special Issue in Honor of Simon Donaldson. (journal, arXiv)
Y. Tanaka, Some boundedness properties of solutions to the Vafa-Witten equations on closed 4-manifolds, Q. J. Math. 68 (2017), 1203-1225. (journal, arXiv)
Y. Tanaka, On the moduli space of the Donaldson-Thomas instanton, Extracta Math. 31 (2016), 89-107. (journal, arXiv)
Y. Tanaka, Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces, Manuscripta Math. 146 (2015), 351-363. (journal, arXiv)
Y. Tanaka, A removal singularity theorem of the Donaldson-Thomas instantons on compact Kahler threefolds, J. Math. Anal. and Appl. 411 (2014), 422-428. (journal, arXiv)
Y. Tanaka, A weak compactness theorem of the Donaldson-Thomas instantons on compact Kahler threefolds, J. Math. Anal. and Appl. 408 (2013), 27-34. (journal, arXiv)
Y. Tanaka, A construction of Spin(7)-instantons, Ann. Global Anal. Geom. 42 (2012), 495-521. (journal, arXiv)
J. Kryczka, Y. Tanaka, S.-T. Yau, Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures, June 2026, 72 pages. (arXiv)
T. Ito, A. Kanemitsu, T. Takamatsu, and Y. Tanaka, Fano threefolds of genus 12 with large automorphism group in positive and mixed characteristic, January 2026, 57 pages. (arXiv)
T. Ito, A. Kanemitsu, T. Takamatsu, and Y. Tanaka, Quintic del Pezzo threefolds in positive and mixed characteristic, June 2025, 44 pages. (arXiv)
T. Ito, A. Kanemitsu, T. Takamatsu, and Y. Tanaka, Arithmetic finiteness of Mukai varieties of genus 7, October 2024, 42 pages. (arXiv)
N. Kuhn and Y. Tanaka, A blowup formula for virtual enumerative invariants on projective surfaces, July 2021, 117 pages. (arXiv)
Y. Tanaka, Seiberg-Witten type equations on compact symplectic 6-manifolds, September 2017, 26 pages. (arXiv)
J. Schmitt et. al., IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation, July 2026. (arXiv)
Number Theory Lunch Seminar, Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, March 2026.
Gauge Theory Learning seminar, Rutgers University, February 2026. (online)
Differential Geometry Seminar, Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, November 2025.
AMS Special Session on Gauge Theory and Low-Dimensional Topology, 2025 Fall Eastern Virtual Sectional Meeting, October 2025. (online) (slides)
Physical Mathematics of Quantum Field Theory, UMass Amherst, Amherst, 9-13 June 2025. (Lecture 1, Lecture 2, Lecture 3, Lecture 4)
British Isles Graduate Workshop III "Gauge theory with a view to higher dimensions", Jersey, 9-15 June 2019.
Masterclass, Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Aarhus, August 2018.
Introduction to Gauge Theory, Taught Course Centre, Oxford, Trinity 2019.
Online Workshop on Mirror Symmetry and Related Topics, Kyoto 2021, Kyoto, 13-15 December 2021. (online)
New Frontiers in Gauge Theory, Topology, and Physics, TSVP Thematic Program at Okinawa Institute of Science and Technology (OIST), co-organised with Izar Alonso, Sergei Gukov, and Hokuto Konno, September-October 2026.