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
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)
- 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 and R. P. Thomas, Vafa-Witten invariants for projective surfaces II: semistable case, accepted for publication in Pure and Applied Mathematics Quarterly, issue in honor of Prof. Donaldson's 60th birthday.
- 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.