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.

## Personal website:

+44 1865 273578

## Address

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

## Recent Publications:

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
issue 3
volume 13
page 517-562
(2017)
Full text available

Vafa-Witten invariants for projective surfaces I: stable case

Journal of Algebraic Geometry

## Research interests:

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.

## Teaching:

- Tutor in Linear Algebra I, Wycliffe Hall, Hilary term 2019.
- Tutor in Analysis II, St Edmund Hall, Hilary term 2019.
- Tutor in Topology, St Edmund Hall, Hilary term 2019.
- Tutor in Linear Algebra I, Wycliffe Hall, Michaelmas term 2018.
- Tutor in C3.7 Elliptic Curves, Michaelmas term 2018.
- Intercollegiate class tutor in B3.2 Geometry of Surfaces, Michaelmas term 2018.
- Consultation sessions in B3.3 Algebraic Curves, Trinity term 2018.
- Intercollegiate class tutor in B3.3 Algebraic Curves, Hilary term 2018.

## Major / recent publications:

- Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces I: stable case, to appear in Journal of Algebraic Geometry.
- 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, 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 and R. P. Thomas, Vafa-Witten invariants for projective surfaces II: semistable case, Pure Appl. Math. Q. 13 (2017), 517-562, Special Issue in Honor of Simon Donaldson.
- 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.