Yuuji Tanaka
Addresses:
Department of Mathematics, Faculty of Science,
Kyoto University
Kitashirakawa Oiwakecho, Sakyoku,
Kyoto 6068502, Japan
email: ytanaka (at) math.kyotou.ac.jp
Research interests: Gauge Theory, Geometric Analysis, Algebraic Geometry
More specifically, my current research interests are around the VafaWitten equations and the KapustinWitten ones on fourmanifolds. They originated in an attractive theory called N=4 super (!) YangMills 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 higherdimensional gauge theories such as the DonaldsonThomas invariants and Spin(7)instantons. Now I'm working on these from both algebraic and analytic aspects.
(article in Case Studies)

Publications
(MathSciNet,
zbMATH,
arXiv)
Journal articles:

J. Gross, D. Joyce, and Y. Tanaka,
Universal structures in ℂlinear enumerative invariant theories, SIGMA 18 (2022), 068, 61pp, Special Issue on Enumerative
and GaugeTheoretic Invariants in honor of Lothar Göttsche on the occasion of his 60th birthday.
(journal, arXiv)

C.C. Liu, S. Rayan, and Y. Tanaka,
The KapustinWitten equations and nonabelian Hodge theory, Eur. J. Math. 8 (2022), 2341. (journal, arXiv)

Y. Tanaka and R. P. Thomas,
VafaWitten invariants for projective surfaces I: stable case, J. Algebraic Geom. 29 (2020), 603668.
(journal, arXiv)

D. Joyce, Y. Tanaka, and M. Upmeier,
On orientations for gaugetheoretic moduli spaces, Adv. Math. 362 (2020), 106957, 64pp.
(journal, arXiv)

Y. Tanaka,
A perturbation and generic smoothness of the VafaWitten moduli spaces on closed symplectic fourmanifolds, Glasg. Math. J. 61 (2019), 471486.
(journal, arXiv)

Y. Tanaka,
On the singular sets of solutions to the KapustinWitten equations and the VafaWitten ones on compact Kahler surfaces, Geom. Dedicata 199 (2019), 177187.
(journal, arXiv)

Y. Tanaka and R. P. Thomas,
VafaWitten invariants for projective surfaces II: semistable case, Pure Appl. Math. Q. 13 (2017), 517562, Special Issue in Honor of Simon Donaldson.
(journal, arXiv)

Y. Tanaka, Some boundedness properties of solutions to
the VafaWitten equations on closed 4manifolds, Q. J. Math. 68 (2017), 12031225.
(journal, arXiv)

Y. Tanaka,
On the moduli space of the DonaldsonThomas instanton, Extracta Math. 31 (2016), 89107.
(journal,
arXiv)

Y. Tanaka,
Stable sheaves with twisted sections and the VafaWitten equations on smooth projective surfaces, Manuscripta Math. 146 (2015), 351363.
(journal,
arXiv)

Y. Tanaka,
A removal singularity theorem of the DonaldsonThomas instantons on compact Kahler threefolds, J. Math. Anal. and Appl. 411 (2014), 422428.
(journal,
arXiv)

Y. Tanaka,
A weak compactness theorem of the DonaldsonThomas instantons on compact
Kahler threefolds, J. Math. Anal. and Appl. 408 (2013), 2734.
(journal,
arXiv)

Y. Tanaka, A construction of Spin(7)instantons,
Ann. Global Anal. Geom. 42 (2012), 495521.
(journal,
arXiv)
Preprints:

M. Galdeano, D. Platt, Y. Tanaka, and L. Wang,
Spin(7)instantons on Joyce's first examples of compact Spin(7)manifolds, October 2023, 70 pages.
(arXiv)

N. Kuhn, O. Leigh, and Y. Tanaka,
The blowup formula for the instanton part of the VafaWitten invariants on projective surfaces, May 2022, 20 pages.
(arXiv)

N. Kuhn and Y. Tanaka,
A blowup formula for virtual enumerative invariants on projective surfaces, July 2021, 117 pages.
(arXiv)

Y. Tanaka,
SeibergWitten type equations on compact symplectic 6manifolds, September 2017, 26 pages.
(arXiv)
Talks:
Workshop on Algebraic Geometry, Tsinghua Sanya International Mathematics Forum, Sanya, December 2023.
Geometry of moduli spaces of Higgs bundles,
Korea Institute for Advanced Study, Seoul, September 2023.
Physics and Special Holonomy, KITP, Santa Barbara, CA, March 2023.
Gauge Theory, Moduli Spaces and Representation Theory, Kashiwa 2023, In honor of the 60th birthday of Hiraku Nakajima, Kavli IPMU, University of Tokyo, Kashiwa, February, 2023.
(slides)
list (including the above)
Graduate workshop:
British Isles Graduate Workshop III
"Gauge theory with a view to higher dimensions", Jersey, 915
June 2019.
TCC course:
Introduction to Gauge Theory,
Taught
Course Centre, Trinity 2019.
As of 23 December 2023