I am a Postdoctoral Research Assistant in Geometry and Analysis working with Prof. Dominic Joyce in Simons Collaboration in Special Holonomy in Geometry, Analysis, and Physics.
+44 1865 273578
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Some boundedness properties of solutions to the Vafa–Witten equations on closed 4-manifolds
The Quarterly Journal of Mathematics page 1-23 (12 April 2017)
gauge theory, geometric analysis, algebraic geometry
My current research interests are in the Vafa-Witten theory and Kapustin-Witten one, and their relations with gauge theories in higher dimensions such as Donaldson-Thomas theory, G_2 instantons and Spin(7)-instantons.
Intercollegiate class tutor for B3.3 Algebraic Curves, Hilary term 2018
Major / Recent Publications:
- 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.