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.
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
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.
Major / Recent Publications:
- Y. Tanaka, Some boundedness properties of solutions to the Vafa-Witten equations on closed 4-manifolds, 33 pages, to appear in The Quarterly Journal of Mathematics.
- 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.