I am a Postdoctoral Research Assistant in Geometry and Analysis working with Prof. Dominic Joyce in Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics.
+44 1865 273578
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
A PERTURBATION AND GENERIC SMOOTHNESS OF THE VAFA–WITTEN MODULI SPACES ON CLOSED SYMPLECTIC FOUR-MANIFOLDS
Glasgow Mathematical Journal page 1-16 (13 July 2018)
On the singular sets of solutions to the Kapustin–Witten equations and the Vafa–Witten ones on compact Kähler surfaces
Geometriae Dedicata page 1-11 (21 March 2018)
Some boundedness properties of solutions to the Vafa–Witten equations on closed 4-manifolds
The Quarterly Journal of Mathematics issue 4 volume 68 page 1203-1225 (1 December 2017)
Vafa-Witten invariants for projective surfaces II: semistable case
Pure and Applied Mathematics Quarterly
- Consultation sessions for B3.3 Algebraic Curves, Trinity term 2018.
- Intercollegiate class tutor for B3.3 Algebraic Curves, Hilary term 2018.
Major / Recent Publications:
- Y. Tanaka, A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds, to appear in Glasgow Mathematical Journal.
- Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces II: semistable case, to appear in Pure and Applied Mathematics Quarterly (2017), issue in honour of 60th birthday of Simon Donaldson.
- Y. Tanaka, On the singular sets of solutions to the Kapustin-Witten equations and the Vafa-Witten ones on compact Kahler surfaces, to appear in Geometriae Dedicata.
- Y. Tanaka, Some boundedness properties of solutions to the Vafa-Witten equations on closed 4-manifolds, Q. J. Math. 68 (2017), 1203-1225.
- Y. Tanaka, On the moduli space of the Donaldson-Thomas instanton, Extracta Math. 31 (2016), 89-107.
- Y. Tanaka, Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces, Manuscripta Math. 146 (2015), 351-363.
- Y. Tanaka, A removal singularity theorem of the Donaldson-Thomas instantons on compact Kahler threefolds, J. Math. Anal. and Appl. 411 (2014), 422-428.
- Y. Tanaka, A weak compactness theorem of the Donaldson-Thomas instantons on compact Kahler threefolds, J. Math. Anal. and Appl. 408 (2013), 27-34.
- Y. Tanaka, A construction of Spin(7)-instantons, Ann. Global Anal. Geom. 42 (2012), 495-521.